Jørund Inge Gåsemyr

• Scheel, Ida & Gåsemyr, Jørund Inge (2026). Graphical and Summary Diagnostics for Node Level Adequacy in Bayesian Hierarchical Models. Bayesian Analysis. ISSN 1936-0975. 21(2), p. 485–510. doi: 10.1214/24-BA1478. Full text in Research Archive Show summary

  For Bayesian hierarchical models represented by directed acyclic graphs, all neighbours of a node provide, potentially conflicting, information on the node. Hence identifying potential conflict between these different information sources can be important for assessing the adequacy of Bayesian hierarchical models. Building on this idea originating from O’Hagan (2003), Gåsemyr and Natvig (2009) constructed node based conflict measures that have been shown to be well calibrated. Sharing the idea of considering potential conflict between separate information sources for each node, Scheel et al. (2011) constructed the graphical diagnostic the local critique plot (lcp). This can be used both to identify conflict at each node, and provide insight into the nature of the conflict, hence being more informative than summary diagnostics. In the present paper we link these two ideas together by constructing a new diagnostic plot, the integrated information contributions local critique plot (iic-lcp), that is supplementary to lcp, but builds on the framework of Gåsemyr and Natvig (2009). It has the advantage over the lcp with the possibility to display curves corresponding to different parameters in the same plot, saving space and easing comparisons, particularly useful for sets of parameters representing exchangeable groups. Notably, we establish a relationship between the geometry of the iic-lcp plot and some of the conflict measures defined in Gåsemyr and Natvig (2009). This indicates how the conflict expressed visually in the graphical plots can be soundly assessed numerically.

• Gåsemyr, Jørund Inge & Hubin, Aliaksandr (2022). Prior distributions expressing ignorance about convex increasing failure rates. Scandinavian Journal of Statistics. ISSN 0303-6898. doi: 10.1111/sjos.12588. Full text in Research Archive Show summary

  This paper deals with the specification of probability distributions expressing ignorance concerning annual or otherwise discretized failure or mortality rates, when these rates can safely be assumed to be increasing and convex, but are completely unknown otherwise. Such distributions can be used as noninformative priors for Bayesian analysis of failure data. We demonstrate why a uniform distribution used in earlier work is unsatisfactory, especially from the point of view of insensitivity with respect to the time scale that is chosen for the problem at hand. We suggest alternative distributions based on Dirichlet distributed weights for the extreme points of relevant convex sets, and discuss which consequences a requirement for scale neutrality has for the choice of Dirichlet parameters.

• Binde, Caroline Ditlev; Tvete, Ingunn Fride; Gåsemyr, Jørund Inge; Natvig, Bent & Klemp, Marianne (2020). Comparative effectiveness of dopamine agonists and monoamine oxidase type-B inhibitors for Parkinson’s disease: a multiple treatment comparison meta-analysis. European Journal of Clinical Pharmacology. ISSN 0031-6970. 76(12), p. 1731–1743. doi: 10.1007/s00228-020-02961-6. Full text in Research Archive Show summary

  Purpose To investigate the comparative effectiveness of dopamine agonists and monoamine oxidase type-B (MAO-B) inhibitors available for treatment of Parkinson’s disease. Methods We performed a systematic literature search identifying randomized controlled trials investigating 4 dopamine agonists (cabergoline, pramipexole, ropinirole, rotigotine) and 3 MAO-B inhibitors (selegiline, rasagiline, safinamide) for Parkinson’s disease. We extracted and pooled data from included clinical trials in a joint model allowing both direct and indirect comparison of the seven drugs. We considered dopamine agonists and MAO-B inhibitors given as monotherapy or in combination with levodopa. Selected endpoints were change in the Unified Parkinson’s Disease Rating Scale (UPDRS) score, serious adverse events and withdrawals. We estimated the relative effectiveness of each dopamine agonist and MAO-B inhibitor versus comparator drug. Results Altogether, 79 publications were included in the analysis. We found all the investigated drugs to be effective compared with placebo when given as monotherapy except safinamide. When considering combination treatment, the estimated relative effects of selegiline, pramipexole, ropinirole, rotigotine, cabergoline, rasagiline and safinamide were 2.316 (1.819, 2.951), 2.091 (1.889, 2.317), 2.037 (1.804, 2.294), 1.912 (1.716, 2.129), 1.664 (1.113, 2.418), 1.584 (1.379, 1.820) and 1.179 (1.031, 1.352), respectively, compared with joint placebo and levodopa treatment. Conclusions Dopamine agonists were found to be effective as treatment for Parkinson’s disease, both when given as monotherapy and in combination with levodopa. Selegiline and rasagiline were also found to be effective for treating Parkinson’s disease, and selegiline was the best option in combination with levodopa among all the drugs investigated.

• Gåsemyr, Jørund Inge & Scheel, Ida (2019). Alternatives to post-processing posterior predictive p-values. Scandinavian Journal of Statistics. ISSN 0303-6898. 46(4), p. 1252–1273. doi: 10.1111/sjos.12393. Full text in Research Archive Show summary

  The posterior predictive p value (ppp) was invented as a Bayesian counterpart to classical p values. The methodology can be applied to discrepancy measures involving both data and parameters and can, hence, be targeted to check for various modeling assumptions. The interpretation can, however, be difficult since the distribution of the ppp value under modeling assumptions varies substantially between cases. A calibration procedure has been suggested, treating the ppp value as a test statistic in a prior predictive test. In this paper, we suggest that a prior predictive test may instead be based on the expected posterior discrepancy, which is somewhat simpler, both conceptually and computationally. Since both these methods require the simulation of a large posterior parameter sample for each of an equally large prior predictive data sample, we furthermore suggest to look for ways to match the given discrepancy by a computation‐saving conflict measure. This approach is also based on simulations but only requires sampling from two different distributions representing two contrasting information sources about a model parameter. The conflict measure methodology is also more flexible in that it handles non‐informative priors without difficulty. We compare the different approaches theoretically in some simple models and in a more complex applied example.

• Binde, Caroline Ditlev; Tvete, Ingunn Fride; Gåsemyr, Jørund Inge; Natvig, Bent & Klemp, Marianne (2018). A multiple treatment comparison meta-analysis of monoamine oxidase type B inhibitors for Parkinson's disease. British Journal of Clinical Pharmacology. ISSN 0306-5251. 84(9), p. 1917–1927. doi: 10.1111/bcp.13651. Full text in Research Archive Show summary

  Aims To the best of our knowledge, there are no systematic reviews or meta‐analyses that compare rasagiline, selegiline and safinamide. Therefore, we aimed to perform a drug class review comparing all available monoamine oxidase type B (MAO‐B) inhibitors in a multiple treatment comparison. Methods We performed a systematic literature search to identify randomized controlled trials assessing the efficacy of MAO‐B inhibitors in patients with Parkinson's disease. MAO‐B inhibitors were evaluated either as monotherapy or in combination with levodopa or dopamine agonists. Endpoints of interest were change in the Unified Parkinson's Disease Rating Scale (UPDRS) score and serious adverse events. We estimated the relative effect of each MAO‐B inhibitor versus the comparator drug by creating three networks of direct and indirect comparisons. For each of the networks, we considered a joint model. Results The systematic literature search and study selection process identified 27 publications eligible for our three network analyses. We found the relative effects of rasagiline, safinamide and selegiline treatment given alone and compared to placebo in a model without explanatory variables to be 1.560 (1.409, 1.734), 1.449 (0.873, 2.413) and 1.532 (1.337, 1.757) respectively. We also found all MAO‐B inhibitors to be efficient when given together with levodopa. When ranking the MAO‐B inhibitors given in combination with levodopa, selegiline was the most effective and rasagiline was the second best. Conclusions All of the included MAO‐B inhibitors were effective compared to placebo when given as monotherapy. Combination therapy with MAO‐B inhibitors and levodopa showed that all three MAO‐B inhibitors were effective compared to placebo, but selegiline was the most effective drug.

• Ouassou, Mohammed; Natvig, Bent; Jensen, Anna B.O. & Gåsemyr, Jørund Inge (2018). Reliability Analysis of Network Real - Time Kinematic. Journal of Electrical and Computer Engineering. ISSN 2090-0147. 2018. doi: 10.1155/2018/8260479. Full text in Research Archive Show summary

  The multistate reliability theory was applied to the network real-time kinematic (NRTK) data processing chain, where the qualities of the network corrections, baseline residuals, and the associated variance-covariance matrices are considered as the system state vectors. The state vectors have direct influence on the rover receiver position accuracy. The penalized honored stochastic averaged standard deviation (PHSASD) is used to map the NRTK sensitive data, represented by the states vectors to different levels of performance. The study shows that the improvement is possible by identification of critical components in the NRTK system and implementation of some parallelism that makes the system more robust.

• Gåsemyr, Jørund Inge & Natvig, Bent (2017). Improved availability bounds for binary and multistate monotone systems with independent component processes. Journal of Applied Probability. ISSN 0021-9002. 54(3), p. 750–762. doi: 10.1017/jpr.2017.32. Full text in Research Archive Show summary

  Multistate monotone systems are used to describe technological or biological systems when the system itself and its components can perform at different operationally meaningful levels. This generalizes the binary monotone systems used in standard reliability theory. In this paper we consider the availabilities of the system in an interval, i.e. the probabilities that the system performs above the different levels throughout the whole interval. In complex systems it is often impossible to calculate these availabilities exactly, but if the component performance processes are independent, it is possible to construct lower bounds based on the component availabilities to the different levels over the interval. In this paper we show that by treating the component availabilities over the interval as if they were availabilities at a single time point, we obtain an improved lower bound. Unlike previously given bounds, the new bound does not require the identification of all minimal path or cut vectors.

• Gåsemyr, Jørund Inge & Natvig, Bent (2017). Node-Level Conflict Measures in Bayesian Hierarchical Models Based on Directed Acyclic Graphs. In Tejedor, Javier Prieto (Eds.), Bayesian Inference. IntechOpen. ISSN 9789535135777. p. 23–37. doi: 10.5772/intechopen.70058. Full text in Research Archive
• Gåsemyr, Jørund Inge (2016). Uniformity of node level conflict measures in Bayesian hierarchical models based on directed acyclic graphs. Scandinavian Journal of Statistics. ISSN 0303-6898. 43(1), p. 20–34. doi: 10.1111/sjos.12162. Full text in Research Archive
• Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils; Marianne, Røine & Klemp, Marianne (2015). Comparing Effects of Biologic Agents in Treating Patients with Rheumatoid Arthritis: A Multiple Treatment Comparison Regression Analysis. PLOS ONE. 10(9). doi: 10.1371/journal.pone.0137258. Full text in Research Archive Show summary

  Rheumatoid arthritis patients have been treated with disease modifying anti-rheumatic drugs (DMARDs) and the newer biologic drugs. We sought to compare and rank the biologics with respect to efficacy. We performed a literature search identifying 54 publications encompassing 9 biologics. We conducted a multiple treatment comparison regression analysis letting the number experiencing a 50% improvement on the ACR score be dependent upon dose level and disease duration for assessing the comparable relative effect between biologics and placebo or DMARD. The analysis embraced all treatment and comparator arms over all publications. Hence, all measured effects of any biologic agent contributed to the comparison of all biologic agents relative to each other either given alone or combined with DMARD. We found the drug effect to be dependent on dose level, but not on disease duration, and the impact of a high versus low dose level was the same for all drugs (higher doses indicated a higher frequency of ACR50 scores). The ranking of the drugs when given without DMARD was certolizumab (ranked highest), etanercept, tocilizumab/ abatacept and adalimumab. The ranking of the drugs when given with DMARD was certolizumab (ranked highest), tocilizumab, anakinra, rituximab, golimumab/ infliximab/ abatacept, adalimumab/ etanercept. Still, all drugs were effective. All biologic agents were effective compared to placebo, with certolizumab the most effective and adalimumab (without DMARD treatment) and adalimumab/ etanercept (combined with DMARD treatment) the least effective. The drugs were in general more effective, except for etanercept, when given together with DMARDs.

• Gåsemyr, Jørund Inge; Natvig, Bent & Tvete, Ingunn Fride (2014). Estimating Response Ratios from Continuous Outcome Data. Methodology and Computing in Applied Probability. ISSN 1387-5841. doi: 10.1007/s11009-014-9408-5. Full text in Research Archive Show summary

  Several methods for imputing the number of responders from summary continuous outcome data in randomized controlled trials exist. A method by Furukawa and others was used in the quite common case that only such summary continuous outcome measures, but not the actual numbers of responders, are reported in order to estimate response rates (probabilities) for different treatments and response ratios between treatments in such trials. The authors give some empirical justification, but encourage search for theoretical support and further empirical exploration. In particular, a problem that needs to be addressed is that randomness in baseline score is not taken into consideration. This will be done in the present paper. Assuming a binormal model for the data, we compare theoretically the true response rate for a single treatment arm to the theoretical response rate underlying two versions of the suggested imputation method. We also assess the performance of the method numerically for some choices of model parameters. We show that the method works satisfactorily in some cases, but can be seriously biased in others. Moreover, assessing the uncertainty of the estimates is problematic. We suggest an alternative Bayesian estimation procedure, based directly on the normal model, which avoids these problems and provides more precise estimates when applied to simulated data sets.

• Aursnes, Ivar; Tvete, Ingunn Fride; Gåsemyr, Jørund Inge; Natvig, Bent & Klemp, Marianne (2013). Are Both Antidepressant Drug Effects and Test Scores Unspecific? Journal of Pharmacological & Biomedical Analysis. ISSN 2327-4638. 1(1). doi: 10.4172/2327-4638.1000102. Full text in Research Archive
• Gåsemyr, Jørund Inge (2012). Bounds for the availabilities of multistate monotone systems based on decomposition into stochastically independent modules. Advances in Applied Probability. ISSN 0001-8678. 44(1), p. 292–308. doi: 10.1239/aap/1331216654. Full text in Research Archive
• Natvig, Bent; Gåsemyr, Jørund Inge & Reitan, Trond (2012). Bayesian Assessment of Availabilities and Unavailabilities of Multistate Monotone Systems. Methodology and Computing in Applied Probability. ISSN 1387-5841. 14(4), p. 1075–1095. doi: 10.1007/s11009-011-9221-3. Full text in Research Archive
• Klemp, Marianne; Tvete, Ingunn Fride; Gåsemyr, Jørund Inge; Natvig, Bent & Aursnes, Ivar (2011). Meta-Regression Analysis of Paroxetine Clinical Trial Data. Does Reporting Scale Matter? Journal of Clinical Psychopharmacology. ISSN 0271-0749. 31(2), p. 201–206. doi: 10.1097/JCP.0b013e318210bac1. Full text in Research Archive
• Klemp, Marianne; Tvete, Ingunn Fride; Skomedal, Tor; Gåsemyr, Jørund Inge; Natvig, Bent & Aursnes, Ivar (2011). A Review and Bayesian Meta-Analysis of Clinical Efficacy and Adverse Effects of 4 Atypical Neuroleptic Drugs Compared With Haloperidol and Placebo. Journal of Clinical Psychopharmacology. ISSN 0271-0749. 31(6), p. 698–704. doi: 10.1097/JCP.0b013e31823657d9. Full text in Research Archive
• Huseby, Arne; Natvig, Bent; Gåsemyr, Jørund Inge; Skutlaberg, Kristina & Isaksen, Stefan (2010). Advanced discrete event simulation methods with application to importance measure estimation in reliability. In Goti, Aitor (Eds.), Discrete Event Simulation. IntechOpen. ISSN 9789533071152. p. 205–222. Full text in Research Archive Show summary

  In the present chapter we use discrete event simulation in order to analyze a binary monotone system of repairable components. Asymptotic statistical properties of such a system, e.g., the asymptotic system availability and component criticality, can easily be estimated by running a single discrete event simulation on the system over a sufficiently long time horizon, or by working directly on the stationary component availabilities. Sometimes, however, one needs to estimate how the statistical properties of the system evolve over time. In such cases it is necessary to run many simulations to obtain a stable curve estimate. At the same time one needs to store much more information from each simulation. A crude approach to this problem is to sample the system state at fixed points of time, and then use the mean values of the states at these points as estimates of the curve. Using a sufficiently high sampling rate a satisfactory estimate of the curve can be obtained. Still, all information about the process between the sampling points is thrown away. To handle this issue, we propose an alternative sampling procedure where we utilize process data between the sampling points as well. This simulation method is particularly useful when estimating various kinds of component importance measures for repairable systems. Such measures can often be expressed as weighted integrals of the time-dependent Birnbaum measure of importance. By using the proposed simulation methods, stable estimates of the Birnbaum measure as a function of time are obtained. Combined with the appropriate weight function the importance measures of interest can be estimated.

• Gåsemyr, Jørund Inge & Natvig, Bent (2009). Extensions of a Conflict Measure of Inconsistencies in Bayesian Hierarchical Models. Scandinavian Journal of Statistics. ISSN 0303-6898. 36(4), p. 822–838. doi: 10.1111/j.1467-9469.2009.00659.x. Full text in Research Archive
• Natvig, Bent; Eide, Kristina A.; Gåsemyr, Jørund Inge; Huseby, Arne & Isaksen, Stefan (2009). Simulation based analysis and an application to an offshore oil and gas production system of the Natvig measures of component importance in repairable systems. Reliability Engineering & System Safety. ISSN 0951-8320. 94(10), p. 1629–1638. doi: 10.1016/j.ress.2009.04.002. Full text in Research Archive
• Natvig, Bent & Gåsemyr, Jørund Inge (2009). New Results on the Barlow-Proschan and Natvig Measures of Component Importance in Nonrepairable and Repairable Systems. Methodology and Computing in Applied Probability. ISSN 1387-5841. 11(4), p. 603–620. doi: 10.1007/s11009-008-9079-1. Full text in Research Archive
• Natvig, Bent; Eide, Kristina A.; Gåsemyr, Jørund Inge; Huseby, Arne & Isaksen, Stefan (2009). The Natvig measures of component importance in repairable systems applied to an offshore oil and gas production system. In Martorell, Sebastián; Soares, C. Guedes & Barnett, Julie (Ed.), Safety, Reliability and Risk Analysis: Theory, Methods and Applications. CRC Press. ISSN 9780415485166. p. 2029–2035. Full text in Research Archive Show summary

  In the present paper the Natvig measures of component importance for repairable systems, and its extended version are applied to an offshore oil and gas production system. According to the extended version of the Natvig measure a component is important if both by failing it strongly reduces the expected system uptime and by being repaired it strongly reduces the expected system downtime. The results include a study of how different distributions affect the ranking of the components. All numerical results are computed using discrete event simulation. In a companion paper (Huseby, Eide, Isaksen, Natvig, and Gåsemyr 2008) the advanced simulation methods needed in these calculations are decribed

• Huseby, Arne; Eide, Kristina A.; Isaksen, Stefan; Natvig, Bent & Gåsemyr, Jørund Inge (2009). Advanced discrete event simulation methods with application to importance measure estimation. In Martorell, Sebastián; Soares, C. Guedes & Barnett, Julie (Ed.), Safety, Reliability and Risk Analysis: Theory, Methods and Applications. CRC Press. ISSN 9780415485166. p. 1747–1753. Full text in Research Archive Show summary

  In the present paper we use discrete event simulation in order to analyze a binary monotone system of repairable components. Asymptotic statistical properties of such a system, e.g., the asymptotic system availability and component criticality, can easily be estimated by running a single discrete event simulation on the system over a sufficiently long time horizon, or by working directly on the stationary availabilities. Sometimes, however, one needs to estimate how the statistical properties of the system evolve over time. In such cases it is necessary to run many simulations to obtain a stable curve estimate. At the same time one needs to store much more information from each simulation. A crude approach to this problem is to sample the system state at fixed points of time, and then use the mean values of the states at these points as estimates of the curve. Using a sufficiently high sampling rate a satisfactory estimate of the curve can be obtained. Still, all information about the process between the sampling points is thrown away. To handle this issue, we propose an alternative sampling procedure where we utilize process data between the sampling points as well. This simulation method is particularly useful when estimating various kinds of component importance measures for repairable systems. As explained in (Natvig and Gåsemyr 2008) such measures can often be expressed as weighted integrals of the time-dependent Birnbaum measure of importance. By using the proposed simulation methods, stable estimates of the Birnbaum measure as a function of time are obtained and combined with the appropriate weight function, and thus producing the importance measure of interest.

• Aursnes, Ivar Andreas; Osnes, Jan-Bjørn; Tvete, Ingunn; Gåsemyr, Jørund Inge & Natvig, Bent (2007). Does atenolol differ from other beta-adrenergic blockers? BMC Clinical Pharmacology. 7(4). doi: 10.1186/1472-6904-7-4. Full text in Research Archive
• Aursnes, Ivar Andreas; Osnes, Jan-Bjørn; Tvete, Ingunn Fride; Gåsemyr, Jørund Inge & Natvig, Bent (2007). Is atenolol different from other adrenergic blockers? BMC Clinical Pharmacology. 01.01.1904 07:04:00. Full text in Research Archive
• Natvig, Bent & Gåsemyr, Jørund Inge (2007). New results on component importance in nonrepairable and repairable systems. In Aven, Terje & Vinnem, Jan Erik (Ed.), Risk, Reliability and Societal Safety, volume 1: Specialisation Topics. Taylor & Francis. ISSN 9780415447836. p. 239–244. Full text in Research Archive
• Dahl, Fredrik Andreas; Gåsemyr, Jørund Inge & Natvig, Bent (2007). A robust conflict measure of inconsistencies in bayesian hierarchical models. Scandinavian Journal of Statistics. ISSN 0303-6898. 34, p. 816–828. doi: 10.1111/j.1467-9469.2007.00560.x. Full text in Research Archive Show summary

  O'Hagan (2003) introduces some tools for criticism of Bayesian hierarchical models that can be applied at each node of the model, with a view to diagnosing problems of model fit at any point in the model structure. His method relies on computing the posterior median of a conflict index, typically through MCMC simulations. We investigate a Gaussian model of two-way analysis of variance, and show that O'Hagan's approach gives unreliable false warning probabilities. We extend and refine the method, especially avoiding double use of data by a data splitting approach, accompanied by theoretical justifications from a non trivial special case. Through extensive numerical experiments we show that our method detects model misspecification about as well as O'Hagan's method does, while retaining the desired false warning probability for data generated from the assumed model. This also holds for a Student-t version of the model.

• Aursnes, Ivar Andreas; Tvete, Ingunn; Gåsemyr, Jørund Inge & Natvig, Bent (2006). Even more suicide attempts in clinical trials with paroxetine randomised against placebo. BMC Psychiatry. 6(55). doi: 10.1186/1471-244X-6-55. Full text in Research Archive Show summary

  Background Following our previous publication we have received critical comments to our conclusions as well as new data that are strengthening our findings. Results With the new data, 11 suicide attempts among patients on paroxetine against 1 among patients on placebo, we found with a Bayesian technique that the posterior probability that medication with paroxetine is associated with an increased intensity per year of a suicide attempt is from 0.98 to 0.99, depending on the prior. We found that the comment to our article by GSK representatives contained errors, misunderstanding and unwillingness to accept Bayesian principles in the analysis of clinical trials. Conclusion We were in our previous publication, with preliminary data and a Bayesian approach, able to raise a concern that suicide attempts might be connected with the use of paroxetine. This suspicion has now been confirmed.

• Gåsemyr, Jørund Inge (2006). The spectrum of the independent Metropolis-Hastings Algorithm. Journal of theoretical probability. ISSN 0894-9840. 19(1), p. 152–165. doi: 10.1007/s10959-006-0009-2. Full text in Research Archive
• Aursnes, Ivar Andreas; Tvete, Ingunn; Gåsemyr, Jørund Inge & Natvig, Bent (2005). Suicide attempts in clinical trials with paroxetine randomised against placebo. BMC Medicine. 3(14). doi: 10.1186/1741-7015-3-14. Full text in Research Archive Show summary

  Inclusion of unpublished data on the effects of antidepressants on children has suggested unfavourable risk-benefit profiles for some of the drugs. Recent meta-analyses of studies on adults have indicated similar effects. We obtained unpublished data for paroxetine that have so far not been included in these analyses. Methods The documentation for drug registration contained 16 studies in which paroxetine had been randomised against placebo. We registered the number of suicides, suicide attempts and ideation. We corrected for duration of medication and placebo treatment and used a standard Bayesian statistical approach with varying priors. Results There were 7 suicide attempts in patients on the drug and 1 in a patient on placebo. We found that the probability of increased intensity of suicide attempts per year in adults taking paroxetine was 0.90 with a "pessimistic" prior, and somewhat less with two more neutral priors. Conclusion Our findings support the results of recent meta-analyses. Patients and doctors should be warned that the increased suicidal activity observed in children and adolescents taking certain antidepressant drugs may also be present in adults.

• Gåsemyr, Jørund Inge & Natvig, Bent (2005). Probabilistic modelling of monitoring and maintenance of multistate monotone systems with dependent components. Methodology and Computing in Applied Probability. ISSN 1387-5841. 7, p. 63–78. Full text in Research Archive Show summary

  In Gåsemyr and Natvig (2001) partial monitoring of components with applications to preventive system maintenance was considered for a binary monotone system of binary components. The purpose of the present paper is to extend this to a multistate monotone system of multistate components, where the states more realistically represent successive levels of performance ranging from the perfect functioning level down to the complete failure level. We start out close to the spirit of Arjas (1989) by using a marked point process with complete monitoring of all components, and hence of the system, as the basic reference framework. We then consider a marked point process linked to partial monitoring of some components, for instance in certain time intervals. Incorporation of information from the observed system history process is then treated. Mainly, we assume that the inspection strategy is determined by the observed component history process only, with a possible exception of a full or partial autopsy after an observed change of state of the system. Furthermore, we consider how to arrive at the posterior distribution for the relevant parameter vector by a standard simulation procedure, the data augmentation method. The idea is to extend the observed data to the complete component history process. The theory is applied to an electrical power generation system for two nearby oilrigs with some standby components, as considered in Natvig et al. (1986).

• Aursnes, Ivar Andreas; Tvete, Ingunn; Gåsemyr, Jørund Inge & Natvig, Bent (2003). Clinical efficacies of antihypertensive drugs. Scandinavian Cardiovascular Journal. ISSN 1401-7431. 37, p. 72–79. doi: 10.1080/14017430310001186. Full text in Research Archive Show summary

  According to published data, the ability to prevent various hypertension related events differs between the various anti-hypertensive drug groups. Although absolute drug effects differ among studies, relative drug effects could be considered constant. We therefore explored the possibility of drawing statistically valid conclusions about the differences in clinical efficacy between various drug groups by doing an overview of published data. We made a meta-analysis with a Bayesian fixed effect model in which we related the drug effects to the effects of placebo drugs. We selected 27 clinical trials from the literature according to specific criteria, including results both from studies reporting the effects of the newer drugs when tested against diuretics and beta-blockers, and from studies in which diuretics and beta-blockers had been tested against placebo. We calculated the posterior probability distributions of the relative effects of ACE-inhibitors versus calcium antagonists with three different endpoints: stroke, coronary disease and heart failure with point estimates of effects and with 95% credibility intervals. As an intermediate step in this procedure we obtained similar information about the effects of the three groups of active drugs, ACE-inhibitors, calcium antagonists and diuretics or beta-blockers, tested against placebo. For coronory disease we also tested calcium antagonists against diuretics or beta-blockers. ACE-inhibitors and calcium antagonists have an almost identical ability to prevent stroke in hypertensive individuals with a risk ratio (RR) of 1.04. On the other hand, calcium antagonists reduce coronary disease by only 8% relative to placebo. When ACE-inhibitors and calcium antagonists are compared by the Bayesian method, the outcome is a 14% difference in favour of the ACE-inhibitors to prevent coronary disease, with a credibility interval almost reaching identity. Nor do calcium antagonists do as well as diuretics or beta-blockers in this respect, RR = 1.12 with 95% credibility interval 1.01 to 1.24. All the tested drug groups have a profound preventive effect on the occurrence of heart failure when given to hypertensive patients, showing reductions of 42% to 54%. When ACE-inhibitors are compared with calcium antagonists the risk ratio is 0.79, with a credibility interval 0.65 to 0.95. There is statistically an indisputable difference between ACE-inhibitors and calcium antagonists in respect of effects on coronary disease and heart failure when treating hypertensive individuals, ACE-inhibitors being more efficacious. There are no differences in the effect on stroke. Moreover, beta-blockers or diuretics are also superior to calcium antagonists in preventing coronary events.

• Frigessi, Arnoldo; Gåsemyr, Jørund Inge & Rue, Håvard (2000). Antithetic Coupling of two Gibbs sampler Chains. Annals of Statistics. ISSN 0090-5364. 28(4), p. 1128–1149. doi: 10.1214/aos/1015956710. Full text in Research Archive Show summary

  Two coupled Gibbs sampler chains, both with invariant probability density $p$, are run in parallel so that the chains are negatively correlated.We define an asymptotically unbiased estimator of the $\pi$-expectation $E(f(\mathbf(X))$ which achieves significant variance reduction with respect to the usual Gibbs sampler at comparable computational cost. The variance of the estimator based on the new algorithm is always smaller than the variance of a single Gibbs sampler chain, if $\pi$ is attractive and $f$ is monotone nondecreasing in all components of $\mathbf{X}$. For nonattractive targets $\pi$, our results are not complete: The new antithetic algorithm outperforms the standard Gibbs sampler when $\pi$ is a multivariate normal density or the Ising model. More generally, nonrigorous arguments and numerical experiments support the usefulness of the antithetically coupled Gibbs samplers also for other nonattractive models. In our experiments the variance is reduced to at least a third and the efficiency also improves significantly.

• Aursnes, Ivar Andreas; Storvik, Geir Olve; Gåsemyr, Jørund Inge & Natvig, Bent (2000). A Bayesian Analysis of Bisphosphonate Effects and Cost-Effectiveness in Post-menopausal Osteoporosis. Pharmacoepidemiology and Drug Safety. ISSN 1053-8569. 9, p. 501–509. Full text in Research Archive Show summary

  OBJECTIVE - Effects of oral bisphosphonates on the rate of vertebral fractures in post-menopausal osteoporotic women have been found in clinical trials. We wanted to compare the effects of two bisphosphonates, alendronate and etidronate, and calculate the price difference that would give the same cost-effectiveness for the two drugs. We also intended to give by means of Bayesian statistics, probability distributions and point and interval estimates for key parameters. METHODS - We used published, double blind, randomized placebo controlled studies describing the results of occurrence of vertebral fractures at 3-year follow-up in postmenopausal women taking bisphosphonates. Four studies were identified, including altogether 3510 women. The women had either suffered a fracture at entry or had a bone density at least 2.5 SD below the mean value for young women. Two of the studies dealt with alendronate and two with etidronate. RESULTS - According to three of the studies, the number of women out of a 100 avoiding vertebral fractures during a 3-year observation period varied from two to seven. The fourth study did not contain the necessary data. The four studies showed that, for the incidence rate, the multiplicative treatment effects were respectively 0.45, 0.74, 0.40 and 0.36, where values less than 1 indicate positive treatment effects. Using data from all four studies, a comparison of the two drugs gave a point estimate of 0.247 with 95% credibility interval (CI): -0.051 to 0.496 for a difference in effect in favour of alendronate measured in terms of risk ratio of fracture and 0.302 (CI: 0.099 to 0.539) measured as incidence rate ratio. Based on two studies, showing about the same prevalence of fractures in the control groups, the difference in the risk difference between the two drugs was 0.028 (CI: -0.039 to 0.079). CONCLUSIONS - Bisphosphonates effectively reduce risk of new vertebral fractures, but alendronate is somewhat more effective than etidronate. To obtain equal cost-effectiveness alendronate should be priced 40-70% higher than etidronate.

• Gåsemyr, Jørund Inge & Aven, Terje (1999). Asymptotic distributions for downtimes of monotone systems. Journal of Applied Probability. ISSN 0021-9002. 36, p. 814–824. Full text in Research Archive Show summary

  Consider a monotone system with independent alternating renewal processes as component processes, and assume the component uptimes are exponentially distributed. In this paper we study the asymptotic properties of the distribution of the rth dovntime of the system, as the failure rates of the components converge to zero. We show that this distribution converges, and the limiting function has a simple form. Thus we have established an easy computable approximation formula for the downtime distribution of the system for highly available systems. We also show that the steady state downtime distribution, i.e. the downtime distribution of a system failure occurring after an infinite run-in period, converges to the same limiting function as the failure rates converge to zero.

• Natvig, Bent & Gåsemyr, Jørund Inge (1998). The posterior distribution of the parameters of component lifetimes based on autopsy data in a shock model. Scandinavian Journal of Statistics. ISSN 0303-6898. 25(2), p. 271–292. Full text in Research Archive Show summary

  In this paper we consider a binary, monotone system whose component states are dependent through the possible occurrence of independent common shocks, i.e. shocks that destroy several components at once. The individual failure of a component is also thought of as a shock. Such systems can be used to model common cause failures in reliability analysis. The system may be a technological one, or a human being. It is observed until it fails or dies. At this instant, the set of failed components and the failure time of the system are noted. The failure times of the components are not known. These are the so-called autopsy data of the system. For the case of independent components, i.e. no common shocks, Meilijson (1981), Nowik (1990), Antoine et al. (1993) and Gåsemyr (1998) discuss the corresponding identifiability problem, i.e. whether the component life distributions can be determined from the distribution of the observed data. Assuming a model where autopsy data is known to be enough for identifiability, Meilijson (1994) goes beyond the identifiability question and into maximum likelihood estimation of the parameters of the component lifetime distributions based on empirical autopsy data from a sample of several systems. He also considers life-monitoring of some components and conditional life-monitoring of some other. Here a corresponding Bayesian approach is presented for the shock model. Due to prior information one advantage of this approach is that the identifiability problem represents no obstacle. The motivation for introducing the shock model is that the autopsy model is of special importance when components can not be tested separately because it is difficult to reproduce the conditions prevailing in the functioning system. In Gåsemyr & Natvig (1999) we consider Bayesian inference based on partial monitoring of components with applications to preventive system maintenance.

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• Gåsemyr, Jørund Inge & Natvig, Bent (2017). Improved availability bounds for binary and multistate monotone systems with independent component processes. Full text in Research Archive
• Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils; Røine, Marianne & Klemp, Marianne (2016). En sammenligning av biologiske legemidler for behandlingen av leddgiktpasienter. Revmatologi BestPractice. Full text in Research Archive
• Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils; Røine, Marianne & Klemp, Marianne (2016). Comparing Effects of Biologic Agents in Treating Patients with Rheumatoid Arthritis. Full text in Research Archive
• Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils Christian; Røine, Marianne & Klemp, Marianne (2016). Correction: Comparing Effects of Biologic Agents in Treating Patients with Rheumatoid Arthritis: A Multiple Treatment Comparison Regression Analysis. PLOS ONE. doi: 10.1371/journal.pone.0146633. Full text in Research Archive
• Gåsemyr, Jørund Inge (2016). Some aspects of Bayesian methodology in reliability and hierarchical models. Full text in Research Archive
• Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils; Røine, Marianne & Skomedal, Tor [Show all 7 contributors for this article] (2014). Treating patients with Rheumatoid arthritis: a Mixed Treatment Comparison analysis of anti-TNF drug effects. Full text in Research Archive
• Tvete, Ingunn Fride; Gåsemyr, Jørund Inge; Natvig, Bent; Meland, Nils; Marianne, Roine & Skomedal, Tor [Show all 7 contributors for this article] (2014). A Mixed Treatment Comparison analysis of drugs for treating patients with Rheumatoid arthritis. Full text in Research Archive
• Tvete, Ingunn Fride; Klemp, Marianne; Natvig, Bent; Gåsemyr, Jørund Inge; Skomedal, Tor & Roine, Marianne [Show all 7 contributors for this article] (2013). Multiple treatment comparison analysis. Full text in Research Archive
• Natvig, Bent & Gåsemyr, Jørund Inge (2010). Evaluation of Bayesian hierarchical models. From Bayesian p-values to conflict measures. Full text in Research Archive
• Huseby, Arne; Eide, Kristina; Isaksen, Stefan; Natvig, Bent & Gåsemyr, Jørund Inge (2008). Advanced discrete event simulation methods with application to importance measure estimation. Full text in Research Archive Show summary

  In the present paper we use discrete event simulation in order to analyze a binary monotone system of repairable components. Asymptotic statistical properties of such a system, e.g., the asymptotic system availability and component criticality, can easily be estimated by running a single discrete event simulation on the system over a sufficiently long time horizon, or by working directly on the stationary availabilities. Sometimes, however, one needs to estimate how the statistical properties of the system evolve over time. In such cases it is necessary to run many simulations to obtain a stable curve estimate. At the same time one needs to store much more information from each simulation. A crude approach to this problem is to sample the system state at fixed points of time, and then use the mean values of the states at these points as estimates of the curve. Using a sufficiently high sampling rate a satisfactory estimate of the curve can be obtained. Still, all information about the process between the sampling points is thrown away. To handle this issue, we propose an alternative sampling procedure where we utilize process data between the sampling points as well. This simulation method is particularly useful when estimating various kinds of component importance measures for repairable systems. As explained in (Natvig and Gåsemyr 2008) such measures can often be expressed as weighted integrals of the time-dependent Birnbaum measure of importance. By using the proposed simulation methods, stable estimates of the Birnbaum measure as a function of time are obtained and combined with the appropriate weight function, and thus producing the importance measure of interest.

• Natvig, Bent; Eide, Kristina; Gåsemyr, Jørund Inge; Huseby, Arne & Isaksen, Stefan (2008). The Natvig measures of component importance in repairable systems applied to an offshore oil and gas production system. Full text in Research Archive Show summary

  In the present paper the Natvig measures of component importance for repairable systems, and its extended version are applied to an offshore oil and gas production system. According to the extended version of the Natvig measure a component is important if both by failing it strongly reduces the expected system uptime and by being repaired it strongly reduces the expected system downtime. The results include a study of how different distributions affect the ranking of the components. All numerical results are computed using discrete event simulation. In a companion paper (Huseby, Eide, Isaksen, Natvig, and Gåsemyr 2008) the advanced simulation methods needed in these calculations are decribed.

• Natvig, Bent & Gåsemyr, Jørund Inge (2007). New results on component importance in nonrepairable and repairable systems. Full text in Research Archive
• Aursnes, Ivar Andreas; Osnes, Jan-Bjørn; Tvete, Ingunn; Gåsemyr, Jørund Inge & Natvig, Bent (2006). Er atenolol forskjellig fra andre beta-adrenerge blokkere? Bayesiansk analyse av publiserte data. Full text in Research Archive Show summary

  Er atenolol forskjellig fra andre -adrenerge blokkere? Bayesiansk analyse av publiserte data AURSNES I, OSNES JB, TVETE IF, GÅSEMYR J, NATVIG B Institutt for farmakoterapi, Farmakologisk Institutt og Matematisk Institutt, Univ. i Oslo Postboks 1065, 0316 Oslo i.a.aursnes@medisin.uio.no Problemstilling: Resultatene i en nylig publisert meta-analyse av Lindholm, Carlberg og Samuelsson1 kan tyde på at pasienter på en ikke-atenolol β-blokker kommer bedre ut enn pasienter på atenolol når det gjelder hjerteinfarkt: relativ risiko for ikke-atenolol β-blokker versus andre antihypertensive legemidler 0,86 (0,67 – 1,11), atenolol versus andre antihypertensive legemidler 1,05 (0,91 – 1,21); ikke-atenolol β-blokker versus placebo 0,89 (0,742 – 1,06); atenolol versus placebo 0,99 (0,83 -1,19). Forfatterne mener imidlertid at en slik forskjell ikke er reell.1 Vår hypotese er at atenolol skiller seg fra andre -blokkere. Metode: Vi kombinerte disse to sett av data fra: 1) 8 studier med andre antihypertensive legemidler, 2) 6 studier med placebo. Vi benyttet en tidligere publisert bayesiansk prosedyre2 og kombinerte først resultatene fra undersøkelser med like studiegrupper. Vi beregnet deretter den relative risikoen for ikke-atenolol blokkere mot atenolol ved å dividere samsvarende ratioer med hverandre. Vi kombinerte så de to resultatene, basert henholdsvis på 8 og 6 studier som begge anslo effekten av ikke-atenolol blokker versus atenolol, ved å oppdatere det ene resultatet ved hjelp av det andre resultatet ved hjelp av Bayes formel. Resultater: Frekvensen av hjerteinfarkt var 13 % lavere blant pasienter som fikk ikke-atenolol β-blokker versus pasienter som fikk atenolol. I henhold til tidligere publiserte resultater,3 ville vi vente dette resultatet og vi beregnet derfor 90 % kredibilitetsintervall. Det var 0,742 – 1,008; altså med en øvre grense som berører 1,0. Denne tilleggsanalysen av de foreliggende data ga et resultat for atenolol som er statistisk signifikant dårligere enn for andre betablokkere. Diskusjon: Atenolol er forskjellig fra de fleste andre β-blokkere ved at det er vannløselig og dermed i svært liten grad diffunderbart over blod-hjernebarrieren. Atenolol gir dermed ikke adrenerg blokade i CNS, noe som kan være en essensiell virkningskomponent for de lipidløselige β-blokkerne. Atenolol reduserer heller ikke perifer motstand og media til lumen ratio i små arterier ved langvarig bruk.4 Legemiddelet er ikke er blitt testet og vist å kunne forbedre langtidsprognosen hos postinfarktpasienter og hjertesviktpasienter, noe man har kunnet vise for flere andre β-blokkere. Konklusjon: Ved hypertensjonsbehandling gir atenolol dårligere effekt på hjerteinfarkt enn andre -blokkere. Observasjoner med atenolol er derfor ikke nødvendigvis overførbare til andre blokkere. Atenolol er ikke egnet som referanse--blokker i kliniske studier. 1. Lindholm LH, Carlberg B, Samuelsson O. Should β blockers remain first choice in the treatment of primary hypertension? A meta-analysis. Lancet 2005; 366: 1545-53. 2. Aursnes I, Tvete IF, Gåsemyr J. Natvig B. Clinical efficacies of antihypertensive drugs. Scand Cardiovasc J 2003; 37: 72-9. 3. The Steering Committee of the HAPPHY Trial. MAPHY and the two arms of HAPPHY. JAMA 1989; 262: 3273-4. 4. Christensen KL, Mulvany MJ. Vasodilatation, not hypotension, improves resistance vessel design during treatment of essential hypertension: a literature survey. Journal of Hypertension 2001; 19: 1001-6.

• Dahl, Fredrik A.; Gåsemyr, Jørund Inge; Natvig, Bent & Dahl, Fredrik A. (2005). An assessment of conflict measures in criticism of Bayesian hierarchical models. Full text in Research Archive
• Gåsemyr, Jørund; Natvig, Bent & Gåsemyr, Jørund Inge (2002). Bayesian inference based on partial monitoring of components with applications to preventive system maintenance. Full text in Research Archive
• Aursnes, Ivar Andreas; Natvig, Bent; Gåsemyr, Jørund Inge & Tvete, Ingunn Fride (2001). En Bayesiansk metaanalyse av effekten av to blodtrykkssenkende midler, ACE hemmere og Kalsium antagonister, på hjerneslag, hjerteinfarkt og hjertesvikt. Full text in Research Archive
• Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Klemp, Marianne & Binde, Caroline Ditlev (2019). Sammenligning av medikamenter for behandling av Parkinson pasienter. Norsk Regensentral. Full text in Research Archive
• Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Klemp, Marianne & Binde, Caroline Ditlev (2017). Behandling av Parkinson pasienter: sammenligning av monoamin oxidase type-B inhibitor medikamenter. Norsk Regnesentral. Full text in Research Archive
• Tvete, Ingunn Fride; Natvig, Bent; Gåsemyr, Jørund Inge; Meland, Nils; Røine, Marianne & Klemp, Marianne (2015). Rangering av biologiske legemidlers effekt i revmatoid artritt-behandling – ett tillegg til SAMBA-notat 22/2014. Norsk Regnesentral. Full text in Research Archive
• Gåsemyr, Jørund Inge (2014). Uniformity of node level conflict measures in Bayesian hierarchical models based on directed acyclic graphs. Universitetet i Oslo. Full text in Research Archive Show summary

  Hierarchical models defined by means of directed, acyclic graphs are a power- ful and widely used tool for Bayesian analysis of problems of varying degrees of complexity. A simulation based method for model criticism in such models has been suggested by O'Hagan in the form of a con ict measure based on contrasting separate local information sources about each node in the graph. This measure is however not well calibrated. In order to rectify this, alter- native mutually similar tail probability based measures have been proposed independently, and have been proved to be uniformly distributed under the assumed model in quite general normal models with known covariance matri- ces. In the present paper, exploiting the property of pivotality, we extend this result to a variety of models. An advantage of this is that computationally costly pre-calibration schemes needed for some other suggested methods can be avoided. Another advantage is that non-informative prior distributions can be used when performing model criticism.

• Natvig, Bent; Gåsemyr, Jørund Inge & Reitan, Trond (2010). Bayesian assessment of availabilities and unavailabilities of multistate monotone systems. Universitetet i Oslo. Full text in Research Archive Show summary

  In the present paper we consider a multistate monotone system of multistate components. Following a Bayesian approach, the ambition is to arrive at the posterior distributions of the system availabilities and unavailabilities to the various levels in a fixed time interval based on both prior information and data on both the components and the system. We argue that a realistic approach is to start out by describing our uncertainty on the component availabilities and unavailabilities to the various levels in a fixed time interval, based on both prior information and data on the components, by the moments up till order m of their marginal distributions. From these moments analytic bounds on the corresponding moments of the system availabilities and unavailabilities to the various levels in a fixed time interval are arrived at. Applying these bounds and prior system information we may then fit prior distributions of the system availabilities and unavailabilities to the various levels in a fixed time interval. These can in turn be updated by relevant data on the system. This generalizes results given in (Natvig and Eide 1987) considering a binary monotone system of binary components at a fixed point of time. Furthermore, considering a simple network system, we show that the analytic bounds can be slightly improved by straightforward simulation techniques.

• Gåsemyr, Jørund Inge (2010). Bounds for the availabilities for multistate monotone systems based on decomposition into stochastically independent modules. Universitetet i Oslo. Full text in Research Archive Show summary

  Multistate monotone systems are used to describe technological or biological systems when the system itself and its components can perform at different operationally meaningful levels. This generalizes the binary monotone systems used in standard reliability theory. In this paper we consider the availabilities and unavailabilities of the system in an interval, i.e. the probabilities that the system performs above or below the different levels throughout the whole interval. In complex systems it is often impossible to calculate these availabilities and unavailabilities exactly, but it is possible to construct lower and upper bounds based on the minimal path and cut vectors to the different levels. In this paper we consider systems which allow a modular decomposition. We analyse in depth the relationship between the minimal path an cut vectors for the system, the modules and the organizing structure. We analyse the extent to which the availability bounds are improved by taking advantage of the modular decomposition. This problem was treated also in Butler (1982) and Funnemark and Natvig (1985), but the treatment was based on an inadequate analysis of the relationship between the different minimal path and cut vectors involved, and as a result was somewhat inaccurate. We also extend to an interval bounds that have previously only been given for availabilities at a fixed point of time.

• Gåsemyr, Jørund Inge & Natvig, Bent (2008). Extensions of a Conflict Measure of Inconsistencies in Bayesian Hierarchical Models. Universitetet i Oslo. Full text in Research Archive Show summary

  In Dahl et al. (2007) we extended and refined some tools given in O'Hagan (2003) for criticism of Bayesian hierarchical models. Especially, avoiding double use of data by a data splitting approach was a main concern. Such tools can be applied at each node of the model, with a view to diagnosing problems of model fit at any point in the model structure. As in O'Hagan (2003) a Gaussian model of one-way analysis of variance was investigated. Through extensive MCMC simulations it was shown that our method detects model misspecification about as well as the one of O'Hagan, when this is properly calibrated, while retaining the desired false warning probability for data generated from the assumed model. In the present paper we suggest some new measures of conflict based on tail probabilities of the so-called integrated posterior distributions introduced in Dahl et al. (2007). These new measures are equivalent to the measure applied in the latter paper in simple Gaussian models, but seem more appropriately adjusted to deviations from normality and to conflicts not concerning location parameters. A general linear normal model with known covariance matrices is considered in detail.

• Natvig, Bent; Eide, Kristina A.; Gåsemyr, Jørund Inge; Huseby, Arne Bang & Isaksen, Stefan L. (2008). Simulation based analysis and an applicaiton to an offshore oil and gas production system of the Natvig measures of component importance in repairable systems. Universitetet i Oslo. Full text in Research Archive Show summary

  In the present paper the Natvig measures of component importance for repairable systems, and its extended version are analysed for two three component systems and a bridge system. The measures are also applied to an offshore oil and gas production system. According to the extended version of the Natvig measure a component is important if both by failing it strongly reduces the expected system uptime and by being repaired it strongly reduces the expected system downtime. The results include a study of how different distributions affect the ranking of the components. All numerical results are computed using discrete event simulation. In a companion paper (Huseby, Eide, Isaksen, Natvig and Gåsemyr 2008) the advanced simulation methods needed in these calculations are described.

• Huseby, Arne; Eide, Kristina; Isaksen, Stefan; Natvig, Bent & Gåsemyr, Jørund Inge (2008). Advanced discrete event simulation methods with application to importance measure estimation. Universitetet i Oslo. Full text in Research Archive Show summary

  In the present paper we use discrete event simulation in order to analyze a binary monotone system of repairable components. Asymptotic statistical properties of such a system, e.g., the asymptotic system availability and component criticality, can easily be estimated by running a single discrete event simulation on the system over a sufficiently long time horizon, or by working directly on the stationary component availabilities. Sometimes, however, one needs to estimate how the statistical properties of the system evolve over time. In such cases it is necessary to run many simulations to obtain a stable curve estimate. At the same time one needs to store much more information from each simulation. A crude approach to this problem is to sample the system state at fixed points of time, and then use the mean values of the states at these points as estimates of the curve. Using a sufficiently high sampling rate a satisfactory estimate of the curve can be obtained. Still, all information about the process between the sampling points is thrown away. To handle this issue, we propose an alternative sampling procedure where we utilize process data between the sampling points as well. This simulation method is particularly useful when estimating various kinds of component importance measures for repairable systems. As explained in Natvig and Gåsemyr (2009) such measures can often be expressed as weighted integrals of the time-dependent Birnbaum measure of importance. By using the proposed simulation methods, stable estimates of the Birnbaum measure as a function of time are obtained. Combined with the appropriate weight function the importance measures of interest can be estimated.

• Natvig, Bent & Gåsemyr, Jørund Inge (2006). New results on Barlow-Proschan type measures of component importance in nonrepairable and repairable systems. Universitetet i Oslo. Full text in Research Archive Show summary

  In this paper the Barlow and Proschan (1975) measure of the importance of a component in a binary coherent system is revisited. This measure is for the case of components not undergoing repair equal to the probability of the component causing system failure. It is a useful guide during the system development phase as to which components should receive more urgent attention in achieving system reliability growth. Here we suggest some possible extensions of this measure both for nonrepairable and repairable systems, and a series of new results are proved, also on the Natvig (1979) measure. For repairable systems we especially consider taking a dual term into account based on the probability of the component causing system repair.

• Dahl, Fredrik A.; Gåsemyr, Jørund Inge & Natvig, Bent (2005). A robust conflict measure of internal inconsistencies in Bayesian hierarchical models. Universitetet i Oslo. Full text in Research Archive Show summary

  O'Hagan (2003) introduces some tools for criticism of Bayesian hierarchical models that can be applied at each node of the model, with a view to diagnosing problems of model fit at any point in the model structure. His method relies on computing the posterior median of a conflict index, typically through MCMC simulations. We investigate a Gaussian model of two-way analysis of variance, and show that O'Hagan's approach gives unreliable false warning probabilities. We extend and refine the method, especially avoiding double use of data by a data splitting approach, accompanied by theoretical justifications from a non trivial special case. Through extensive numerical experiments we show that our method detects model misspecification about as well as O'Hagan's method does, while retaining the desired false warning probability for data generated from the assumed model. This also holds for a Student-t version of the model.

• Gåsemyr, Jørund Inge & Natvig, Bent (2003). Probabilistic Modelling of Monitoring and Maintenance of Multistate Monotone Systems with Dependent Components. Universitetet i Oslo. Full text in Research Archive Show summary

  In Gåsemyr and Natvig (2001) partial monitoring of components with applications to preventive system maintenance was considered for a binary monotone system of binary components. The purpose of the present paper is to extend this to a multistate monotone system of multistate components, where the states more realistically represent successive levels of performance ranging from the perfect functioning level down to the complete failure level. We start out close to the spirit of Arjas (1989) by using a marked point process with complete monitoring of all components, and hence of the system, as the basic reference framework. We then consider a marked point process linked to partial monitoring of some components, for instance in certain time intervals. Incorporation of information from the observed system history process is then treated. Mainly, we assume that the inspection strategy is determined by the observed component history process only, with a possible exception of a full or partial autopsy after an observed change of state of the system. Furthermore, we consider how to arrive at the posterior distribution for the relevant parameter vector by a standard simulation procedure, the data augmentation method. The idea is to extend the observed data to the complete component history process. The theory is applied to an electrical power generation system for two nearby oilrigs with some standby components, as considered in Natvig et al. (1986).

• Gåsemyr, Jørund Inge (2003). The spectrum of the independent Metropolis-Hastings algorithm. Universitetet i Oslo. Full text in Research Archive Show summary

  In this paper we perform a spectral analysis for the kernel operator associated with the transition kernel for the Metropolis-Hastings algorithm that uses a fixed, location independent proposal distribution. Our main result is to establish the spectrum of the kernel operator <I>T</I> in the continuous case. In the case of finite state spaces we give the eigenvalues and eigenvectors, thereby filling in a few missing details in the slightly incomplete analysis in Liu (1996). The spectrum of <I>T</I> is of interest for several reasons. Performance measures such as total variation distance after a finite number of iterations, rate of convergence in total variation norm, acceptance rate, autocovariances and efficiency can be expressed in terms of the spectrum of <I>T</I>.

• Gåsemyr, Jørund Inge (2002). Markov Chain Monte Carlo algorithms with independent proposal distribution and their relationship to importance sampling and rejection sampling. Universitetet i Oslo. Full text in Research Archive Show summary

  In this paper we define a class of MCMC algorithms, the generalized self regenerative chains (GSR), generalizing the SR chain of Sahu and Zhigljavski (2001), which contains rejection sampling as a special case. We show that this class contains members that are asymptotically more efficient and converge faster than the SR chains. We also consider generalizations of the Metropolis - Hastings independent chains or Metropolized independent sampling, and for some of these algorithms we are able to give the convergence rates and establish a lower bound for the asymptotic efficiency. All these MCMC algorithms use a proposal distribution that is independent of the current state. We discuss such algorithms generally. We are in particular interested in the number of times a given proposed value occurs consecutively as a state of the chain. We consider this number as a random integer weight that links these algorithms also to importance sampling. We show that for the generalizations of the SR and independent chains the expected values of these weights characterize the stationary distribution.

• Aursnes, Ivar Andreas; Tvete, Ingunn Fride; Gåsemyr, Jørund Inge & Natvig, Bent (2001). Differential effects of antihypertensive drugs in a Bayesian perspective. Norsk Regnesentral. Full text in Research Archive Show summary

  Background: According to published data, the ability to prevent various hypertension related events differs between the various anti-hypertensive drug groups. Although absolute drug effects with similar drugs also differ among the various studies, relative drug effects could be considered constant. We therefore explored the possibility of drawing statistically valid conclusions about the differences between various drug groups by doing an overview of published data. Methods: We performed a meta-analysis using a Bayesian fixed effect model in which we brought together 27 published studies. We chose to always relate the drug effects to the number of events observed with placebo drugs. We therefore obtained results both from studies reporting the effects of the newer drugs when tested against diuretics and beta-blockers, and from studies in which diuretics and beta-blockers had been tested against placebo. We constructed the posterior probability distributions of the relative effects of ACE-inhibitors versus calcium antagonists with three different endpoints: stroke, coronary disease and heart failure. We then calculated point estimates of effects with 95% credibility intervals. As an intermediate step in this procedure we obtained similar information about the effects of the three groups of active drugs, ACE-inhibitors, calcium antagonists and diuretics or beta-blockers, tested against placebo. Findings: ACE-inhibitors and calcium antagonists have an almost identical ability to prevent stroke in hypertensive individuals with a risk ratio (RR) of 1.04. On the other hand, calcium antagonists reduce coronary disease by only 9% relative to placebo. When ACE-inhibitors and calcium antagonists are compared by the Bayesian method, the outcome is a 14% difference in favour of the ACE-inhibitors to prevent coronary disease, with a credibility interval reaching identity. Nor do calcium antagonists do as well as diuretics or _-blockers in this respect, RR = 1.11 with 95% credibility interval 1.01 to 1.22. All the tested drug groups have a profound preventive effect on the occurrence of heart failure when given to hypertensive patients, showing reductions of 44% to 56%. When ACE-inhibitors are compared with calcium antagonists the risk ratio is 0.79, with a credibility interval 0.65 to 0.95. Interpretation: The conclusion of our analysis is a statistically significant difference between ACE-inhibitors and calcium antagonists in respect of effects on coronary disease and heart failure when treating hypertensive individuals, ACE-inhibitors being more efficacious. The difference is modest and both drug groups are acceptable as first line treatments together with diuretics and beta-blockers. There are no differences in the effect on stroke

• Gåsemyr, Jørund Inge (2000). On an adaptive version of the Metropolis-Hastings algorithm with independent proposal distribution. Universitetet i Oslo. Full text in Research Archive
• Gåsemyr, Jørund Inge; Natvig, Bent & Sørensen, Erik (1999). A Comparison of two Sequential Metropolis-Hastings Algorithms with Standard Simulation Techniques in Bayesian Inference in Reliability Models Involving the Generalized Gamma Distribution. Universitetet i Oslo. Full text in Research Archive Show summary

  In this paper we consider the generalized gamma distribution as introduced in Gåsemyr and Natvig (1998). This distribution enters naturally in Bayesian inference in exponential survival models with left censoring. In the paper mentioned above it is shown that the weighted sum of products of generalized gamma distributions is a conjugate prior for the parameters of component lifetimes, having autopsy data in a Marshall-Olkin shock model. A corresponding result is shown in Gåsemyr and Natvig (1999) for independent, exponentially distributed component lifetimes in a model with partial monitoring of components with applications to preventive system maintenance. A discussion in the present paper strongly indicates that expressing the posterior distribution in terms of the generalized gamma distribution is computationally efficient compared to using the ordinary gamma distribution in such models. Furthermore, we present two types of sequential Metropolis-Hastings algorithms that may be used in Bayesian inference in situations where exact methods are intractable. Finally these types of algorithms are compared with standard simulation techniques and analytical results in arriving at the posterior distribution of the parameters of component lifetimes in special cases of the mentioned models. It seems that one of these types of algorithms may be very favourable when prior assessments are updated by several data sets and when there are significant discrepancies between the prior assessments and the data.

• Gåsemyr, Jørund Inge & Natvig, Bent (1999). Bayesian Inference Based on Partial Monitoring of Components with Applications to Preventive System Maintenance. Universitetet i Oslo. Full text in Research Archive
• Gåsemyr, Jørund Inge & Natvig, Bent (1997). An application of the MTP2 property on bounds on system reliability. Universitetet i Oslo. Full text in Research Archive
• Gåsemyr, Jørund Inge & Natvig, Bent (1997). On lifemonitoring and Conditional Lifemonitoring of System Components with Application to Preventive System Maintenance. Universitetet i Oslo. Full text in Research Archive
• Storvik, Geir Olve; Natvig, Bent; Gåsemyr, Jørund Inge & Aursnes, Ivar Andreas (1997). Assessment of the scientific documentation of the drugs etidronat (Didronate) and alendronat (Fosamax) for the reduction of the number of fractures among women with osteoporosis. An analysis based on Bayesian statistics. Universitetet i Oslo. Full text in Research Archive
• Gåsemyr, Jørund Inge & Aven, Terje (1997). Asymptotic distributions for downtimes of monotone systems. Universitetet i Oslo. Full text in Research Archive
• Gåsemyr, Jørund Inge & Natvig, Bent (1996). On a generalization of the gamma distribution. Universitetet i Oslo. Full text in Research Archive
• Gåsemyr, Jørund Inge & Natvig, Bent (1995). The posterior distribution of the parameters of component lifetimes based on autopsy data in a shock model. Universitetet i Oslo. Full text in Research Archive
• Natvig, Bent & Gåsemyr, Jørund Inge (1995). On probabilistic risk analysis of technological systems. Universitetet i Oslo. Full text in Research Archive
• Gåsemyr, Jørund Inge (1995). On identifiability in the autopsy model of reliability systems of lifemonitored and conditionally lifemonitored components. Universitetet i Oslo. Full text in Research Archive
• Gåsemyr, Jørund Inge & Natvig, Bent (1994). Bayesian Estimation of Component Lifetimes Based on Autopsy Data. Universitetet i Oslo. Full text in Research Archive
• Huseby, Arne & Gåsemyr, Jørund Inge (1993). Optimal Project Acceleration Policies - A Bayesian Approach. Universitetet i Oslo. ISSN 9788255307983. Full text in Research Archive Show summary

  A project consists of a set of activities, A1,..., An with durations T1,..., Tn respectively. The duration of the entire project, T, may be expressed as T = f(T1,...,Tn), where f is a suitable increasing function. If T is large, e.g., exceeds a given time limit, tau, a penalty cost has to be paid. At certain milestones in the project a project manager is given the opportunity of accelerating some of the remaining activities. The price of accelerating an activity is typically smaller than the penalty cost. In this paper we consider the problem of finding an acceleration policy minimizing the expected total cost. The computational complexity of the problem grows very fast. Thus, exact solutions are obtainable only in very simple cases. The paper compares several approximate procedures under different sets of assumptions.

• Gåsemyr, Jørund Inge & Natvig, Bent (1991). Using expert opinions in bayesian estimation of component lifetimes in a shock model - a general predictive approach. Universitetet i Oslo. Full text in Research Archive

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