Geir Olve Storvik

• Hubin, Aliaksandr & Storvik, Geir Olve (2024). Sparse Bayesian Neural Networks: Bridging Model and Parameter Uncertainty through Scalable Variational Inference. Mathematics. ISSN 2227-7390. 12(6). doi: 10.3390/math12060788.
• Storvik, Geir Olve; Diz-Lois Palomares, Alfonso; Engebretsen, Solveig; Rø, Gunnar Øyvind Isaksson; Engø-Monsen, Kenth & Kristoffersen, Anja Bråthen [Show all 8 contributors for this article] (2023). A sequential Monte Carlo approach to estimate a time-varying reproduction number in infectious disease models: the Covid-19 case. Journal of the Royal Statistical Society: Series A (Statistics in Society). ISSN 0964-1998. 186(4), p. 616–632. doi: 10.1093/jrsssa/qnad043. Full text in Research Archive
• Lachmann, Jon; Storvik, Geir Olve; Frommlet, Florian & Hubin, Aliaksandr (2022). A subsampling approach for Bayesian model selection. International Journal of Approximate Reasoning. ISSN 0888-613X. 151, p. 33–63. doi: 10.1016/j.ijar.2022.08.018. Full text in Research Archive
• Hubin, Aliaksandr; Storvik, Geir & Frommlet, Florian (2021). Flexible Bayesian Nonlinear Model Configuration. The journal of artificial intelligence research. ISSN 1076-9757. 72, p. 901–942. doi: 10.1613/JAIR.1.13047. Full text in Research Archive Show summary

  Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between input variables and a response. Such relationships can be better described through flexible approaches such as neural networks, but this results in less interpretable models and potential overfitting. Alternatively, specific parametric nonlinear functions can be used, but the specification of such functions is in general complicated. In this paper, we introduce a flexible approach for the construction and selection of highly flexible nonlinear parametric regression models. Nonlinear features are generated hierarchically, similarly to deep learning, but have additional flexibility on the possible types of features to be considered. This flexibility, combined with variable selection, allows us to find a small set of important features and thereby more interpretable models. Within the space of possible functions, a Bayesian approach, introducing priors for functions based on their complexity, is considered. A genetically modified mode jumping Markov chain Monte Carlo algorithm is adopted to perform Bayesian inference and estimate posterior probabilities for model averaging. In various applications, we illustrate how our approach is used to obtain meaningful nonlinear models. Additionally, we compare its predictive performance with several machine learning algorithms.

• Hubin, Aliaksandr; Frommlet, Florian & Storvik, Geir Olve (2021). Reversible genetically modified mode jumping MCMC. In Makridis, Andreas; Milienos, Fotios; Papastamoulis, Panagiotis; Parpoula, Christina & Rakitzis, Athanasios (Ed.), 22nd European Young Statisticians Meeting – Proceedings. Department of Psychology & Department of Sociology, School of Social Science, Panteion University of Social and Political Sciences. ISSN 978-960-7943-23-1. p. 35–40. Show summary

  In this paper, we introduce a reversible version of a genetically modified mode jumping Markov chain Monte Carlo algorithm (GMJMCMC) for inference on posterior model probabilities in complex model spaces, where the number of explanatory variables is prohibitively large for classical Markov Chain Monte Carlo methods. Unlike the earlier proposed GMJMCMC algorithm, the introduced algorithm is a proper MCMC and its limiting distribution corresponds to the posterior marginal model probabilities in the explored model space under reasonable regularity conditions.

• Gramuglia, Emanuele; Storvik, Geir Olve & Stakkeland, Morten (2021). Clustering and automatic labelling within time series of categorical observations - with an application to marine log messages. The Journal of the Royal Statistical Society, Series C (Applied Statistics). ISSN 0035-9254. 70(3), p. 714–732. doi: 10.1111/rssc.12483. Full text in Research Archive Show summary

  System logs or log files containing textual messages with associated time stamps are generated by many technologies and systems. The clustering technique proposed in this paper provides a tool to discover and identify patterns or macrolevel events in this data. The motivating application is logs generated by frequency converters in the propulsion system on a ship, while the general setting is fault identification and classification in complex industrial systems. The paper introduces an offline approach for dividing a time series of log messages into a series of discrete segments of random lengths. These segments are clustered into a limited set of states. A state is assumed to correspond to a specific operation or condition of the system, and can be a fault mode or a normal operation. Each of the states can be associated with a specific, limited set of messages, where messages appear in a random or semi‐structured order within the segments. These structures are in general not defined a priori. We propose a Bayesian hierarchical model where the states are characterised both by the temporal frequency and the type of messages within each segment. An algorithm for inference based on reversible jump MCMC is proposed. The performance of the method is assessed by both simulations and operational data.

• Hubin, Aliaksandr; Storvik, Geir Olve; Grini, Paul Eivind & Butenko, Melinka Alonso (2020). A Bayesian binomial regression model with latent gaussian processes for modelling DNA methylation. Austrian Journal of Statistics. ISSN 1026-597X. 49(4), p. 46–56. doi: 10.17713/ajs.v49i4.1124. Full text in Research Archive Show summary

  Epigenetic observations are represented by the total number of reads from a given pool of cells and the number of methylated reads, making it reasonable to model this data by a binomial distribution. There are numerous factors that can influence the probability of success in a particular region. Moreover, there is a strong spatial (alongside the genome) dependence of these probabilities. We incorporate dependence on the covariates and the spatial dependence of the methylation probability for observations from a pool of cells by means of a binomial regression model with a latent Gaussian field and a logit link function. We apply a Bayesian approach including prior specifications on model configurations. We run a mode jumping Markov chain Monte Carlo algorithm (MJMCMC) across different choices of covariates in order to obtain the joint posterior distribution of parameters and models. This also allows finding the best set of covariates to model methylation probability within the genomic region of interest and individual marginal inclusion probabilities of the covariates.

• Hubin, Aliaksandr; Storvik, Geir Olve; Grini, Paul Eivind & Butenko, Melinka Alonso (2019). Bayesian binomial regression model with a latent Gaussian field for analysis of epigenetic data. In Kharin, Y & Filzmoser, Peter (Ed.), Proceedings of Computer Data Analysis and Modeling: Stochastics and Data Science 2019. Belarusian State University Press. ISSN 978-985-566-811-5. p. 167–171.
• Mysterud, Atle; Bleka, Øyvind; Nielsen, Anders; Steinheim, Geir; Yoccoz, Nigel Gilles & Storvik, Geir Olve (2019). Climate and synchrony of lamb body mass. In Olaussen, Jon Olaf (Eds.), Contributions in natural resource economics. Festschrift to Anders Skonhoft. Fagbokforlaget. ISSN 9788245024715. p. 183–197.
• Grytten, Ivar; Rand, Knut Dagestad; Nederbragt, Alexander Johan; Storvik, Geir Olve; Glad, Ingrid Kristine & Sandve, Geir Kjetil (2019). Graph Peak Caller: Calling ChIP-seq peaks on graph-based reference genomes. PLoS Computational Biology. ISSN 1553-734X. 15(2), p. 1–13. doi: 10.1371/journal.pcbi.1006731. Full text in Research Archive
• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2018). A Novel Algorithmic Approach to Bayesian Logic Regression. Bayesian Analysis. ISSN 1936-0975. 15(1), p. 263–311. doi: 10.1214/18-BA1141. Full text in Research Archive Show summary

  Logic regression was developed more than a decade ago as a tool to construct predictors from Boolean combinations of binary covariates. It has been mainly used to model epistatic effects in genetic association studies, which is very appealing due to the intuitive interpretation of logic expressions to describe the interaction between genetic variations. Nevertheless logic regression has (partly due to computational challenges) remained less well known than other approaches to epistatic association mapping. Here we will adapt an advanced evolutionary algorithm called GMJMCMC (Genetically modified Mode Jumping Markov Chain Monte Carlo) to perform Bayesian model selection in the space of logic regression models. After describing the algorithmic details of GMJMCMC we perform a comprehensive simulation study that illustrates its performance given logic regression terms of various complexity. Specifically GMJMCMC is shown to be able to identify three-way and even four-way interactions with relatively large power, a level of complexity which has not been achieved by previous implementations of logic regression. We apply GMJMCMC to reanalyze QTL (quantitative trait locus) mapping data for Recombinant Inbred Lines in Arabidopsis thaliana and from a backcross population in Drosophila where we identify several interesting epistatic effects. The method is implemented in an R package which is available on github.

• Vanem, Erik & Storvik, Geir Olve (2018). Dynamical Linear Models for Condition Monitoring with Multivariate Sensor Data. International Journal of COMADEM. ISSN 1363-7681. 21(4), p. 7–18.
• Hubin, Aliaksandr & Storvik, Geir Olve (2018). Mode jumping MCMC for Bayesian variable selection in GLMM. Computational Statistics & Data Analysis. ISSN 0167-9473. 127, p. 281–297. doi: 10.1016/j.csda.2018.05.020. Full text in Research Archive
• Rand, Knut Dagestad; Grytten, Ivar; Nederbragt, Alexander Johan; Storvik, Geir Olve; Glad, Ingrid Kristine & Sandve, Geir Kjetil (2017). Coordinates and intervals in graph-based reference genomes. BMC Bioinformatics. ISSN 1471-2105. 18:263, p. 1–8. doi: 10.1186/s12859-017-1678-9. Full text in Research Archive
• Vanem, Erik & Storvik, Geir Olve (2017). Anomaly detection using dynamical linear models and sequential testing on a marine engine system, PHM 2017 Proceedings of the Annual Conference of the Prognostics and Health Management Society 2017. PHM Society. ISSN 978-1-936263-26-4. p. 185–200.
• Rogers, Lauren; Storvik, Geir Olve; Knutsen, Halvor; Olsen, Esben Moland & Stenseth, Nils Christian (2017). Fine-scale population dynamics in a marine fish species inferred from dynamic state-space models. Journal of Animal Ecology. ISSN 0021-8790. 86(4), p. 888–898. doi: 10.1111/1365-2656.12678. Full text in Research Archive
• Breivik, Olav Nikolai; Storvik, Geir Olve & Nedreaas, Kjell Harald (2017). Latent Gaussian models to predict historical bycatch in commercial fishery. Fisheries Research. ISSN 0165-7836. 185, p. 62–72. doi: 10.1016/j.fishres.2016.09.033. Full text in Research Archive Show summary

  Knowledge about how many fish that have been killed due to bycatch is an important aspect of ensuring a sustainable ecosystem and fishery. We introduce a Bayesian spatio-temporal prediction method for historical bycatch that incorporates two sources of available data sets, fishery data and survey data. The model used assumes that occurrence of bycatch can be described as a log-linear combination of covariates and random effects modeled as Gaussian fields. Integrated Nested Laplace Approximations (INLA) is used for fast calculations. The method introduced is general, and is applied on bycatch of juvenile cod (Gadus morhua) in the Barents Sea shrimp (Pandalus borealis) fishery. In this fishery we compare our prediction method with the well known ratio and effort methods, and make a strong case that the Bayesian spatio-temporal method produces more reliable historical bycatch predictions compared to existing methods.

• Hubin, Aliaksandr & Storvik, Geir Olve (2016). On Mode Jumping in MCMC for Bayesian Variable Selection within GLMM. In Aivazian, S; Filzmoser, Peter & Kharin, Y (Ed.), COMPUTER DATA ANALYSIS AND MODELING. Theoretical and Applied Stochastics. Proceedings of the XI International Conference.. Belarusian State University. ISSN 978-985-553-366-6. p. 275–278. doi: 10.1016/j.csda.2018.05.020. Show summary

  Generalized linear mixed models (GLMM) are addressed for inference and prediction in a wide range of different applications providing a powerful scientific tool for the researchers and analysts coming from different fields. At the same time more sources of data are becoming available introducing a variety of hypothetical explanatory variables for these models to be considered. Estimation of posterior model probabilities and selection of an optimal model is thus becoming crucial. We suggest a novel mode jumping MCMC procedure for Bayesian model averaging and model selection in GLMM.

• Eikeset, Anne Maria; Dunlop, Erin; Heino, Mikko Petteri; Storvik, Geir Olve; Stenseth, Nils Christian & Dieckmann, Ulf (2016). Roles of density-dependent growth and life history evolution in accounting for fisheries-induced trait changes. Proceedings of the National Academy of Sciences of the United States of America. ISSN 0027-8424. 113(52), p. 15030–15035. doi: 10.1073/pnas.1525749113.
• Bleka, Øyvind; Benschop, Corina C G; Storvik, Geir Olve & Gill, Peter (2016). A comparative study of qualitative and quantitative models used to interpret complex STR DNA profiles. Forensic Science International: Genetics. ISSN 1872-4973. 25, p. 85–96. doi: 10.1016/j.fsigen.2016.07.016. Full text in Research Archive
• Breivik, Olav Nikolai; Storvik, Geir Olve & Nedreaas, Kjell Harald (2016). Latent gaussian models to decide on spatial closures for bycatch management in the barents sea shrimp fishery. Canadian Journal of Fisheries and Aquatic Sciences. ISSN 0706-652X. 73(8), p. 1271–1280. doi: 10.1139/cjfas-2015-0322. Full text in Research Archive
• Bleka, Øyvind; Storvik, Geir Olve & Gill, Peter (2016). EuroForMix: An open source software based on a continuous model to evaluate STR DNA profiles from a mixture of contributors with artefacts. Forensic Science International: Genetics. ISSN 1872-4973. 21, p. 35–44. doi: 10.1016/j.fsigen.2015.11.008. Full text in Research Archive
• Heier, Lise; Viljugrein, Hildegunn & Storvik, Geir Olve (2015). Persistence of plague outbreaks among great gerbils in Kazakhstan: effects of host population dynamics. Population Ecology. ISSN 1438-3896. 57(3), p. 473–484. doi: 10.1007/s10144-015-0500-7.
• Gomes Marques, Reinaldo A. & Storvik, Geir Olve (2014). Reweighting Schemes Based on Particle Methods. In Lanzarone, Ettore & Ieva, Francesca (Ed.), The Contribution of Young Researchers to Bayesian Statistics. Springer. ISSN 978-3-319-02084-6. p. 73–76. doi: 10.1007/978-3-319-02084-6_14. Show summary

  Sequential Monte Carlo methods are widely used to deal with the intractability of complex models including state space models. Their aim is to approximate the distribution of interest by a set of properly weighted samples. To control the weight degeneracy, the resample step has been proposed as an inexpensive alternative to avoid the collapse of particle filter algorithms. When the sample becomes too poor with successive use of resample steps, MCMC moves have been added in particle filter algorithms in order to make the identical samples diverge. In this work we consider strategies where we first perform a moves step, and then we update the weights for reweighting the particles. The validity of this approach is based on the commonly used trick of working on an artificial extended distribution having the target distribution as marginal combined with the use of backwards kernels. By updating the weights via a diversification step, this approach can make their empirical distribution less skewed increasing the effective sample size.

• Otero, Jaime; L'Abee-Lund, Jan Henning; Castro-Santos, Ted; Leonardsson, Kjell; Storvik, Geir Olve & Jonsson, Bror [Show all 46 contributors for this article] (2014). Basin-scale phenology and effects of climate variability on global timing of initial seaward migration of Atlantic salmon (Salmo salar). Global Change Biology. ISSN 1354-1013. 20(1), p. 61–75. doi: 10.1111/gcb.12363. Show summary

  Migrations between different habitats are key events in the lives of many organisms. Such movements involve annually recurring travel over long distances usually triggered by seasonal changes in the environment. Often, the migration is associated with travel to or from reproduction areas to regions of growth. Young anadromous Atlantic salmon (Salmo salar) emigrate from freshwater nursery areas during spring and early summer to feed and grow in the North Atlantic Ocean. The transition from the freshwater (‘parr’) stage to the migratory stage where they descend streams and enter salt water (‘smolt’) is characterized by morphological, physiological and behavioural changes where the timing of this parr-smolt transition is cued by photoperiod and water temperature. Environmental conditions in the freshwater habitat control the downstream migration and contribute to within- and among-river variation in migratory timing. Moreover, the timing of the freshwater emigration has likely evolved to meet environmental conditions in the ocean as these affect growth and survival of the post-smolts. Using generalized additive mixed-effects modelling, we analysed spatio-temporal variations in the dates of downstream smolt migration in 67 rivers throughout the North Atlantic during the last five decades and found that migrations were earlier in populations in the east than the west. After accounting for this spatial effect, the initiation of the downstream migration among rivers was positively associated with freshwater temperatures, up to about 10 ºC and levelling off at higher values, and with sea-surface temperatures. Earlier migration occurred when river discharge levels were low but increasing. On average, the initiation of the smolt seaward migration has occurred 2.5 days earlier per decade throughout the basin of the North Atlantic. This shift in phenology matches changes in air, river, and ocean temperatures, suggesting that Atlantic salmon emigration is responding to the current global climate changes. Atlantic salmon, smolt emigration, freshwater conditions, sea surface temperature, phenology, North Atlantic

• Marques, Reinaldo A. Gomes & Storvik, Geir Olve (2013). Particle move-reweighting strategies for online inference. Statistical research report (Universitetet i Oslo. Matematisk institut. ISSN 0806-3842. Full text in Research Archive
• Rivrud, Inger Maren; Sonkoly, Krisztina; Lehoczki, Róbert; Csányi, Sándor; Storvik, Geir Olve & Mysterud, Atle (2013). Hunter selection and long-term trend (1881-2008) of red deer trophy sizes in Hungary. Journal of Applied Ecology. ISSN 0021-8901. 50(1), p. 168–180. doi: 10.1111/1365-2664.12004.
• Storvik, Geir Olve (2012). Bayesian methods. In Veierød, Marit Bragelien; Lydersen, Stian & Laake, Petter (Ed.), Medical statistics in clinical and epidemiological research. Gyldendal Akademisk. ISSN 9788205399594. p. 559–584.
• Storvik, Geir Olve (2012). Bootstrapping. In Veierød, Marit Bragelien; Lydersen, Stian & Laake, Petter (Ed.), Medical statistics in clinical and epidemiological research. Gyldendal Akademisk. ISSN 9788205399594. p. 402–428.
• Hirst, David; Storvik, Geir Olve; Rognebakke, Hanne; Aldrin, Magne; Aanes, Sondre & Vølstad, Jon Helge (2012). A Bayesian modelling framework for the estimation of catch-at-age of commercially harvested fish species. Canadian journal of fisheries and aquatic sciences. Supplem ent = Journ al canadien des sciences halieutiques et aquati qu. ISSN 0714-7937. 69(12), p. 2064–2076. doi: 10.1139/CJFAS-2012-0075.
• Nielsen, Anders; Yoccoz, Nigel; Steinheim, Geir; Storvik, Geir Olve; Rekdal, Yngve & Angeloff, Michael [Show all 9 contributors for this article] (2012). Are responses of herbivores to environmental variability spatially consistent in alpine ecosystems? Global Change Biology. ISSN 1354-1013. 18(10), p. 3050–3062. doi: 10.1111/j.1365-2486.2012.02733.x.
• Villar, Jaime Otero; Jensen, Arne Johan; L'abee-Lund, Jan Henning; Stenseth, Nils Christian; Storvik, Geir Olve & Vøllestad, Leif Asbjørn (2012). Contemporary ocean warming and freshwater conditions are related to later sea age at maturity in Atlantic salmon spawning in Norwegian rivers. Ecology and Evolution. ISSN 2045-7758. 2(9), p. 2192–2203. doi: 10.1002/ece3.337. Full text in Research Archive
• Aldrin, Magne; Mortensen, Bjørnar Tumanjan; Storvik, Geir Olve; Nedreaas, Kjell; Aglen, Asgeir & Aanes, Sondre (2012). Improving management decisions by predicting fish bycatch in the Barents Sea shrimp fishery. ICES Journal of Marine Science. ISSN 1054-3139. 69(1), p. 64–74. doi: 10.1093/icesjms/fsr172. Show summary

  When the bycatch of juvenile fish within the Barents Sea shrimp fishery is too large, the area is closed to fishing for a certain period. Bycatch is estimated from sampled trawl hauls, for which the shrimp yield is recorded, along with the total number of various bycatch fish species. At present, bycatch estimation is based on a simple estimator, the sum of the number of fish caught within the area of interest within a small time window, divided by the corresponding shrimp yield (in weight). No historical data are used. A model-based estimation is proposed in which spatio-temporal models are constructed for the variation in both the yield of shrimp and the amount of bycatch in space and time. The main effects are described through generalized additive models, and local dependence structures are specified through correlated random effects. Model estimation includes historical and recent data. Experiments with both simulated and real data show that the model-based estimator outperforms the present simple estimator when a low or moderate number of samples (e. g. <20) is available, whereas the two estimators are equally good when the number of samples is high.

• Villar, Jaime Otero; Jensen, Arne Johan; L'abee-Lund, Jan Henning; Stenseth, Nils Christian; Storvik, Geir Olve & Vøllestad, Leif Asbjørn (2011). Quantifying the Ocean, Freshwater and Human Effects on Year-to-Year Variability of One-Sea-Winter Atlantic Salmon Angled in Multiple Norwegian Rivers. PLOS ONE. ISSN 1932-6203. 6(8). doi: 10.1371/journal.pone.0024005. Full text in Research Archive
• Heier, Lise; Storvik, Geir Olve; Davis, Stephen; Viljugrein, Hildegunn; Ageyev, Vladimir & Klassovskaya, Evgeniya [Show all 7 contributors for this article] (2011). Emergence, spread, persistence and fade-out of sylvatic plague in Kazakhstan. Proceedings of the Royal Society of London. Biological Sciences. ISSN 0962-8452. 278(1720), p. 2915–2923. doi: 10.1098/rspb.2010.2614.
• Storvik, Geir Olve (2011). On the flexibility of Metropolis-Hastings acceptance probabilities in auxiliary variable proposal generation. Scandinavian Journal of Statistics. ISSN 0303-6898. 38(2), p. 342–358. doi: 10.1111/j.1467-9469.2010.00709.x.

View all works in Cristin

• Storvik, Geir Olve & Diz-Lois Palomares, Alfonso (2023). Sequential Monte Carlo for infectious disease models - the Covid-19 case.
• Hubin, Aliaksandr & Storvik, Geir Olve (2022). Variational Bayes for inference on model and parameter uncertainty in Bayesian neural networks. Show summary

  Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques [1]. There are several advantages of using a Bayesian approach: Parameter and prediction uncertainties become easily available, facilitating rigorous statistical analysis. Furthermore, prior knowledge can be incorporated. However, so far there have been no scalable techniques capable of combining both model (structural) and parameter uncertainty. In the presented piece of research [2] we introduce the concept of model uncertainty in BNNs and hence make inference in the joint space of models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Experimental results on a range of benchmark data sets show that we obtain comparable accuracy results with the competing models, but based on methods that are much more sparse than ordinary BNNs. This is particularly the case in model selection settings, but also within a Bayesian model averaging setting a considerable sparsification is achieved. As expected, model uncertainties give higher, but more reliable uncertainty measures. References: [1] Blundell, C., Cornebise, J., Kavukcuoglu, K., and Wierstra, D. (2015). Weight uncertainty in neural networks. International Conference on Machine Learning, 1613 - 1622. [2] Hubin, A., Storvik, G. (2019). Combining model and parameter uncertainty in Bayesian neural networks, arXiv preprint arXiv:1903.07594.

• Hubin, Aliaksandr & Storvik, Geir Olve (2022). Variational Inference for Bayesian Neural Networks under Model and Parameter Uncertainty.
• Lachmann, Jon; Storvik, Geir Olve; Frommlet, Florian & Hubin, Aliaksandr (2022). A subsampling approach for Bayesian model selection.
• Hubin, Aliaksandr; Frommlet, Florian & Storvik, Geir Olve (2021). Reversible Genetically Modified MCMCs. Show summary

  In this work, we introduce a reversible version of a genetically modified Markov chain Monte Carlo algorithm (GMJMCMC) for inference on posterior model probabilities in complex functional spaces, where the number of explanatory variables or functions of explanatory variables is prohibitively large for simple Markov Chain Monte Carlo methods. A genetically modified Markov chain Monte Carlo algorithm (GMJMCMC) was introduced in [5, 4, 2] for Bayesian model selection/averaging problems when the total number of function of covariates is prohibitively large. More specifically, these applications include GWAS studies with Bayesian generalized linear models [2] as well as Bayesian logic regressions [5] and Bayesian generalized nonlinear models [4]. If its regularity conditions are met, GMJMCMC algorithm can asymptotically explore all models in the defined model spaces. At the same time, GMJMCMC is not a proper MCMC in a sense that its limiting distribution does not correspond to marginal posterior model probabilities and thus only renormalized estimates of these probabilities [3, 1] can be obtained. Unlike the standard GMJMCMC algorithm, the introduced algorithm is a proper MCMC and its limiting distribution corresponds to posterior marginal model probabilities in the explored model spaces under reasonable regularity conditions.

• Hubin, Aliaksandr & Storvik, Geir Olve (2021). Variational Inference for Bayesian Neural Networks under Model and Parameter Uncertainty. Show summary

  Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a Bayesian approach: Parameter and prediction uncertainties become easily available, facilitating rigorous statistical analysis. Furthermore, prior knowledge can be incorporated. However so far there have been no scalable techniques capable of combining both model (structural) and parameter uncertainty. In this paper we introduce the concept of model uncertainty in BNNs and hence make inference in the joint space of models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Experimental results on a range of benchmark data sets show that we obtain comparable accuracy results with the competing models, but based on methods that are much more sparse than ordinary BNNs. This is particularly the case in model selection settings, but also within a Bayesian model averaging setting a considerable sparsification is achieved. As expected, model uncertainties give higher, but more reliable uncertainty measures.

• Hubin, Aliaksandr & Storvik, Geir Olve (2021). Variational Bayes for inference on model and parameter uncertainty in Bayesian neural networks. Show summary

  Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques [1]. There are several advantages of using a Bayesian approach: Parameter and prediction uncertainties become easily available, facilitating rigorous statistical analysis. Furthermore, prior knowledge can be incorporated. However so far there have been no scalable techniques capable of combining both model (structural) and parameter uncertainty. In the presented piece of research [2] we introduce the concept of model uncertainty in BNNs and hence make inference in the joint space of models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Experimental results on a range of benchmark data sets show that we obtain comparable accuracy results with the competing models, but based on methods that are much more sparse than ordinary BNNs. This is particularly the case in model selection settings, but also within a Bayesian model averaging setting a considerable sparsification is achieved. As expected, model uncertainties give higher, but more reliable uncertainty measures.

• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2020). A novel algorithmic approach to Bayesian Logic Regression. Show summary

  Logic regression was developed more than a decade ago as a tool to construct predictors from Boolean combinations of binary covariates. It has been mainly used to model epistatic effects in genetic association studies, which is very appealing due to the intuitive interpretation of logic expressions to describe the interaction between genetic variations. Nevertheless logic regression has (partly due to computational challenges) remained less well known than other approaches to epistatic association mapping. Here we will adapt an advanced evolutionary algorithm called GMJMCMC (Genetically modified Mode Jumping Markov Chain Monte Carlo) to perform Bayesian model selection in the space of logic regression models. After describing the algorithmic details of GMJMCMC we perform a comprehensive simulation study that illustrates its performance given logic regression terms of various complexity. Specifically GMJMCMC is shown to be able to identify three-way and even four-way interactions with relatively large power, a level of complexity which has not been achieved by previous implementations of logic regression. We apply GMJMCMC to reanalyze QTL (quantitative trait locus) mapping data for Recombinant Inbred Lines in Arabidopsis thaliana and from a backcross population in Drosophila where we identify several interesting epistatic effects. The method is implemented in an R package which is available on github.

• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2020). Rejoinder for the discussion of the paper "A Novel Algorithmic Approach to Bayesian Logic Regression". Bayesian Analysis. ISSN 1936-0975. 15(1), p. 312–333. doi: 10.1214/18-ba1141. Full text in Research Archive Show summary

  Logic regression was developed more than a decade ago as a tool to construct predictors from Boolean combinations of binary covariates. It has been mainly used to model epistatic effects in genetic association studies, which is very appealing due to the intuitive interpretation of logic expressions to describe the interaction between genetic variations. Nevertheless logic regression has (partly due to computational challenges) remained less well known than other approaches to epistatic association mapping. Here we will adapt an advanced evolutionary algorithm called GMJMCMC (Genetically modified Mode Jumping Markov Chain Monte Carlo) to perform Bayesian model selection in the space of logic regression models. After describing the algorithmic details of GMJMCMC we perform a comprehensive simulation study that illustrates its performance given logic regression terms of various complexity. Specifically GMJMCMC is shown to be able to identify three-way and even four-way interactions with relatively large power, a level of complexity which has not been achieved by previous implementations of logic regression. We apply GMJMCMC to reanalyze QTL (quantitative trait locus) mapping data for Recombinant Inbred Lines in Arabidopsis thaliana and from a backcross population in Drosophila where we identify several interesting epistatic effects. The method is implemented in an R package which is available on github.

• Storvik, Geir Olve (2020). "Preliminaries for Deep Neural Networks: Recapture of Linear Algebra, Gradient Descents and Generalized Linear Models".
• Storvik, Geir Olve (2020). Neural networks vs generalized linear models.
• Hubin, Aliaksandr & Storvik, Geir Olve (2019). Combining Model and Parameter Uncertainty in Bayesian Neural Networks.
• Hubin, Aliaksandr & Storvik, Geir Olve (2019). Combining Model and Parameter Uncertainty in Bayesian Neural Networks. Show summary

  Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: Parameter and prediction uncertainty become easily available, facilitating rigid statistical analysis. Furthermore, prior knowledge can be incorporated. However so far there have been no scalable techniques capable of combining both model (structural) and parameter uncertainty. In this paper we introduce the concept of model uncertainty in BNNs and hence make inference in the joint space of models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Finally, we show that incorporating model uncertainty via Bayesian model averaging and Bayesian model selection allows to drastically sparsify the structure of BNNs without significant loss of predictive power.

• Hubin, Aliaksandr; Storvik, Geir Olve; Grini, Paul Eivind & Butenko, Melinka Alonso (2019). Bayesian binomial regression model with a latent Gaussian field for analysis of epigenetic data.
• Hubin, Aliaksandr & Storvik, Geir Olve (2019). Combining Model and Parameter Uncertainty in Bayesian Neural Networks.
• Hubin, Aliaksandr & Storvik, Geir Olve (2019). Combining Model and Parameter Uncertainty in Bayesian Neural Networks. Show summary

  Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using Bayesian approach: Parameter and prediction uncertainty become easily available, facilitating rigid statistical analysis. Furthermore, prior knowledge can be incorporated. However so far there have been no scalable techniques capable of combining both model (structural) and parameter uncertainty. In this paper we introduce the concept of model uncertainty in BNNs and hence make inference in the joint space of models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Finally, we show that incorporating model uncertainty via Bayesian model averaging and Bayesian model selection allows to drastically sparsify the structure of BNNs without significant loss of predictive power.

• Hubin, Aliaksandr & Storvik, Geir Olve (2019). Combining Model and Parameter Uncertainty in Bayesian Neural Networks.
• Storvik, Geir Olve & Hubin, Aliaksandr (2019). Combining model and parameter uncertainty in Bayesian neural networks.
• Storvik, Geir Olve (2019). Flexible Bayesian Nonlinear Model Configuration.
• Storvik, Geir Olve (2019). Bayesian approaches to neural networks.
• Storvik, Geir Olve (2019). Bayesian approaches to neural networks.
• Storvik, Geir Olve (2019). On the use of Bayesian methods in machine learning.
• Storvik, Geir Olve (2019). Education in Statistics and Data Science at the University of Oslo .
• Storvik, Geir Olve (2019). Bayesian approaches to neural networks.
• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2018). Deep Bayesian regression models.
• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2018). Deep Bayesian regression models.
• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2018). Deep Bayesian regression models.
• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2018). Deep Bayesian regression models. Show summary

  Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as the number of potential explanatory variables is rapidly increasing. Variable selection and model averaging have become extremely important tools for improving inference and prediction. However, often linear models are not sufficient and the complex relationship between input variables and a response is better described by introducing non-linearities and complex functional interactions. Deep learning models have been extremely successful in terms of prediction although they are often difficult to specify and potentially suffer from overfitting. The aim of this paper is to bring the ideas of deep learning into a statistical framework which yields more parsimonious models and allows to quantify model uncertainty. To this end we introduce the class of deep Bayesian regression models (DBRM) consisting of a generalized linear model combined with a comprehensive non-linear feature space, where non-linear features are generated just like in deep learning but combined with variable selection in order to include only important features. DBRM can easily be extended to include latent Gaussian variables to model complex correlation structures between observations, which seems to be not easily possible with existing deep learning approaches. Two different algorithms based on MCMC are introduced to fit DBRM and to perform Bayesian inference. The predictive performance of these algorithms is compared with a large number of state of the art algorithms. Furthermore we illustrate how DBRM can be used for model inference in various applications.

• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2018). Deep Bayesian regression models. Show summary

  Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as the number of potential explanatory variables is rapidly increasing. Variable selection and model averaging have become extremely important tools for improving inference and prediction. However, often linear models are not sufficient and the complex relationship between input variables and a response is better described by introducing non-linearities and complex functional interactions. Deep learning models have been extremely successful in terms of prediction although they are often difficult to specify and potentially suffer from overfitting. The aim of this paper is to bring the ideas of deep learning into a statistical framework which yields more parsimonious models and allows to quantify model uncertainty. To this end we introduce the class of deep Bayesian regression models (DBRM) consisting of a generalized linear model combined with a comprehensive non-linear feature space, where non-linear features are generated just like in deep learning but combined with variable selection in order to include only important features. DBRM can easily be extended to include latent Gaussian variables to model complex correlation structures between observations, which seems to be not easily possible with existing deep learning approaches. Two different algorithms based on MCMC are introduced to fit DBRM and to perform Bayesian inference. The predictive performance of these algorithms is compared with a large number of state of the art algorithms. Furthermore we illustrate how DBRM can be used for model inference in various applications.

• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2018). Deep Bayesian regression models. Show summary

  Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as the number of potential explanatory variables is rapidly increasing. Variable selection and model averaging have become extremely important tools for improving inference and prediction. However, often linear models are not sufficient and the complex relationship between input variables and a response is better described by introducing non-linearities and complex functional interactions. Deep learning models have been extremely successful in terms of prediction although they are often difficult to specify and potentially suffer from overfitting. The aim of this paper is to bring the ideas of deep learning into a statistical framework which yields more parsimonious models and allows to quantify model uncertainty. To this end we introduce the class of deep Bayesian regression models (DBRM) consisting of a generalized linear model combined with a comprehensive non-linear feature space, where non-linear features are generated just like in deep learning but combined with variable selection in order to include only important features. DBRM can easily be extended to include latent Gaussian variables to model complex correlation structures between observations, which seems to be not easily possible with existing deep learning approaches. Two different algorithms based on MCMC are introduced to fit DBRM and to perform Bayesian inference. The predictive performance of these algorithms is compared with a large number of state of the art algorithms. Furthermore we illustrate how DBRM can be used for model inference in various applications.

• Storvik, Geir Olve (2018). Preliminaries for Deep Neural Networks: Recapture of Linear Algebra, Gradient Descents and Generalized Linear Models.
• Storvik, Geir Olve (2018). Statistical analysis for Time series.
• Storvik, Geir Olve; Vigeland, Magnus Dehli; Caliebe, Amke & Egeland, Thore (2018). Specification of mutation probabilities through Metropolis-Hastings steps.
• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2017). Deep non-linear regression models in a Bayesian framework.
• Hubin, Aliaksandr; Storvik, Geir Olve & Grini, Paul Eivind (2017). Variable selection in binomial regression with latent Gaussian field models for analysis of epigenetic data.
• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2017). A novel algorithmic approach to Bayesian Logic Regression.
• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2017). A novel GMJMCMC algorithm for Bayesian Logic Regression models.
• Hubin, Aliaksandr & Storvik, Geir Olve (2017). Efficient mode jumping MCMC for Bayesian variable selection and model averaging in GLMM.
• Hubin, Aliaksandr; Storvik, Geir Olve & Frommlet, Florian (2017). A novel algorithmic approach to Bayesian Logic Regression.
• Eikeset, Anne Maria; Dunlop, Erin; Heino, Mikko Petteri; Storvik, Geir Olve; Stenseth, Nils Christian & Dieckmann, Ulf (2017). Reply to Enberg and Jørgensen: Ecology and evolution both matter for explaining stock dynamics. Proceedings of the National Academy of Sciences of the United States of America. ISSN 0027-8424. 114(22), p. E4322–E4323. doi: 10.1073/pnas.1703865114.
• Hubin, Aliaksandr & Storvik, Geir Olve (2016). Efficient mode jumping MCMC for Bayesian variable selection in GLM with random effects models.
• Hubin, Aliaksandr & Storvik, Geir Olve (2016). On Mode Jumping in MCMC for Bayesian Variable Selection within GLMM.
• Hubin, Aliaksandr & Storvik, Geir Olve (2016). VARIABLE SELECTION IN BINOMIAL REGRESSION WITH LATENT GAUSSIAN FIELD MODELS FOR ANALYSIS OF EPIGENETIC DATA.
• Hubin, Aliaksandr & Storvik, Geir Olve (2016). Variable selection in logistic regression with a latent Gaussian field models with an application in epigenomics.
• Vanem, Erik; Glad, Ingrid Kristine & Storvik, Geir Olve (2016). Dynamical Linear Models for Condition Monitoring with Multivariate Sensor Data.
• Hubin, Aliaksandr & Storvik, Geir Olve (2015). On model selection in Hidden Markov Models with covariates.
• Hubin, Aliaksandr & Storvik, Geir Olve (2015). Variable selection in binomial regression with a latent Gaussian field models for analysis of epigenetic data.
• Hubin, Aliaksandr & Storvik, Geir Olve (2015). Variable selection in binomial regression with a latent Gaussian field models for analysis of epigenetic data.
• Storvik, Geir Olve; Aanes, Sondre & Maisha, Peter Nyangweso (2015). Estimation of fish abundance and demography in the Barents sea.
• Storvik, Geir Olve (2015). Estimation of fish abundance and demography in the Barents sea.
• Storvik, Geir Olve & Marques, Reinaldo (2014). Estimation of static parameters using particle filters and a block independence approximation.
• Storvik, Geir Olve (2013). Computational tools for analysis of models with latent structures.
• Storvik, Geir Olve (2012). Bayesian approaches to neural networks.
• Rognebakke, Hanne Therese Wist; Hirst, David; Aldrin, Magne & Storvik, Geir (2011). Modelling catch at age for multiple stock.
• Christensen, Arnfinn; Grunt, Hilde; Jødahl, Roar; Storvik, Geir Olve & Natvig, Bent (2011). Tilfeldig! Neppe? En statistiker klarte å knekke vinnerkoden i et stort kanadisk skrapelotteri. Hvor tilfeldig er vinnertallene? [Internet]. forskning.no.
• Storvik, Geir Olve (2011). Tilfeldig! Neppe? [Internet]. Forskning.no.
• Villar, Jaime Otero; Antonsson, Thorulfur; Armstrong, John; Arnason, Fridthjofur; Arnekleiv, Jo Vegar & Baglinière, Jean-Luc [Show all 26 contributors for this article] (2010). Environmental effects on ocean entry of Atlantic salmon (Salmo salar) smolt across its range of distribution.
• Storvik, Geir Olve & Marques, Reinaldo (2018). On Monte Carlo Contributions for Real-time Probabilistic Inference. Universitetet i Oslo.
• Storvik, Geir Olve & Hubin, A. (2018). Bayesian model configuration, selection and averaging in complex regression contexts. Universitetet i Oslo.
• Rognebakke, Hanne; Hirst, David; Aanes, Sondre & Storvik, Geir Olve (2016). Catch-at-age - Version 4.0: Technical Report. Norsk Regnesentral.
• Storvik, Geir Olve; Løland, Anders; Lykkja, Ola Martin & Gjevestad, Jon Glenn Omholt (2016). SAVE – tracking vehicle movements for toll object detection using particle filter. Norsk Regnesentral.
• Maisha, Peter Nyangweso; Storvik, Geir Olve & Aanes, Sondre (2015). A State-Space Model for Abundance Estimation from Bottom Trawl Data with Applications to Norwegian Winter Survey. Matematisk Institutt, UiO. Full text in Research Archive Show summary

  We study a hierarchical dynamic state-space model for abundance estimation. A generic data fusion approach for combining computer simulated posterior samples of catch output data with observed research survey indices using sequential importance sampling is presented. Posterior samples of catch generated from a computer software are used as a primary source of input data through which fisheries dependent information is mediated. Direct total stock abundance estimates are obtained without the need to estimate any intermediate parameters such as catchability and mortality. Numerical results of a simulation study show that our method provides a useful alternative to existing methods. We apply the method to data from the Barents Sea Winter survey for Northeast Arctic cod (Gadus morhua). The results based on our method are comparable to results based on current methods.

• Rognebakke, Hanne Therese Wist; Hirst, David & Storvik, Geir Olve (2011). Catch-at-age - Version 2.0: Technical Report. Norsk Regnesentral.
• Rognebakke, Hanne; Hirst, David; Storvik, Geir & Aldrin, Magne (2011). Catch-at-age for multiple stocks: Modelling Skrei and Coastal Cod simultaneously. Norsk Regnesentral.

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