Dennis Christensen

• (2024). Estimating sensitivity with the Bruceton method: Setting the record straight. Propellants, explosives, pyrotechnics. ISSN 0721-3115.
• (2024). Increased impact sensitivity in ageing high explosives; analysis of Amatol extracted from explosive remnants of war. Royal Society Open Science. ISSN 2054-5703. 11(3). doi: 10.1098/rsos.231344. Full text in Research Archive
• (2024). Inference for Bayesian Nonparametric Models with Binary Response Data via Permutation Counting. Bayesian Analysis. ISSN 1936-0975. 19(1), p. 293–318. doi: 10.1214/22-BA1353. Full text in Research Archive
• (2020). Models for predicting impact sensitivity of energetic materials based on the trigger linkage hypothesis and Arrhenius kinetics. Journal of Molecular Modeling. ISSN 1610-2940. 26(4). doi: 10.1007/s00894-019-4269-z. Show summary

  In order to predict the impact sensitivity of high explosives, we designed and evaluated several models based on the trigger linkage hypothesis and the Arrhenius equation. To this effect, we calculated the heat of detonation, temperature of detonation and bond dissociation energy for 70 energetic molecules. The bond dissociation energy divided by the temperature of detonation proved to be a good predictor of the impact sensitivity of nitroaromatics, with a coefficient of determination (R2) of 0.81. A separate Bayesian analysis gave similar results, taking model complexity into account. For nitramines, there was no relationship between the impact sensitivity and the bond dissociation energy. None of the models studied gave good predictions for the impact sensitivity of liquid nitrate esters. For solid nitrate esters, the bond dissociation energy divided by the temperature of detonation showed promising results (R2 = 0.85), but since this regression was based on only a few data points, it was discredited when model complexity was accounted for by our Bayesian analysis. Since the temperature of detonation correlated with the impact sensitivity for nitroaromatics, nitramines and nitrate esters, we consider it to be one of the leading predictive factors of impact sensitivity for energetic materials.

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• Christensen, Dennis & Moen, Per August Jarval (2023). Fast implementation of a general importance sampling algorithm for Bayesian nonparametric models with binary responses.
• Christensen, Dennis & Moen, Per August Jarval (2023). perms: Likelihood-free estimation of marginal likelihoods for binary response data in Python and R. arXiv.org. ISSN 2331-8422. doi: 10.48550/arXiv.2309.01536. Show summary

  In Bayesian statistics, the marginal likelihood (ML) is the key ingredient needed for model comparison and model averaging. Unfortunately, estimating MLs accurately is notoriously difficult, especially for models where posterior simulation is not possible. Recently, Christensen (2023) introduced the concept of permutation counting, which can accurately estimate MLs of models for exchangeable binary responses. Such data arise in a multitude of statistical problems, including binary classification, bioassay and sensitivity testing. Permutation counting is entirely likelihood-free and works for any model from which a random sample can be generated, including nonparametric models. Here we present perms, a package implementing permutation counting. As a result of extensive optimisation efforts, perms is computationally efficient and able to handle large data problems. It is available as both an R package and a Python library. A broad gallery of examples illustrating its usage is provided, which includes both standard parametric binary classification and novel applications of nonparametric models, such as changepoint analysis. We also cover the details of the implementation of perms and illustrate its computational speed via a simple simulation study.

• Christensen, Dennis; Unneberg, Erik; Høyheim, Eirik; Jensen, Tomas Lunde & Hjort, Nils Lid (2023). Improved measurements of impact sensitivities of energetic materials. Show summary

  Accurate estimation of impact sensitivity is crucial for safe production, handling, storage and transport of energetic materials. Indeed, molecular characteristics will affect sensitivity, and for solid materials, factors like particle size, lattice defects and morphology also play a role and make reproducibility difficult. As various synthesis and recrystallisation methods may lead to differences in crystal properties, it is important to determine the impact sensitivity whenever an energetic material is prepared. Of particular interest is the median ℎ50, namely the impact energy level at which there is a probability of 50% of an explosion occurring. This value has been shown to correlate with quantum chemical properties of the energetic material in question, providing insight into the underlying causes which govern sensitivity. However, in practical applications, it may be more important to estimate extreme values like the 99% quantile ℎ99. In addition to providing point estimates, we would like to derive confidence intervals to address their uncertainty. In this work, we cover the most common methods for constructing such confidence intervals (the delta method, Fieller’s theorem and the likelihood-ratio test) and compare their performance on sensitivity data via simulations. Our experiments indicate that Fieller’s theorem is the superior method, and we therefore use it to construct confidence intervals for ℎ50 and ℎ99 for cyclotetramethylene- tetranitramine (HMX), using new data. Based on our results, we formulate recommendations for researchers measuring sensitivities of synthesised molecules.

• (2022). Nonparametric Bayesian sensitivity testing with optimal design.

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