Posterior Model Probabilities Research Articles

A deep learning method for comparing Bayesian hierarchical models.

Bayesian model comparison (BMC) offers a principled approach to assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular class of hierarchical models due to their high-dimensional nested parameter structure. To address this intractability, we propose a deep learning method for performing BMC on any set of hierarchical models which can be instantiated as probabilistic programs. Since our method enables amortized inference, it allows efficient re-estimation of posterior model probabilities and fast performance validation prior to any real-data application. In a series of extensive validation studies, we benchmark the performance of our method against the state-of-the-art bridge sampling method and demonstrate excellent amortized inference across all BMC settings. We then showcase our method by comparing four hierarchical evidence accumulation models that have previously been deemed intractable for BMC due to partly implicit likelihoods. Additionally, we demonstrate how transfer learning can be leveraged to enhance training efficiency. We provide reproducible code for all analyses and an open-source implementation of our method. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Problematic meta-analyses: Bayesian and frequentist perspectives on combining randomized controlled trials and non-randomized studies

PurposeIn the literature, the propriety of the meta-analytic treatment-effect produced by combining randomized controlled trials (RCT) and non-randomized studies (NRS) is questioned, given the inherent confounding in NRS that may bias the meta-analysis. The current study compared an implicitly principled pooled Bayesian meta-analytic treatment-effect with that of frequentist pooling of RCT and NRS to determine how well each approach handled the NRS bias.Materials & methodsBinary outcome Critical-Care meta-analyses, reflecting the importance of such outcomes in Critical-Care practice, combining RCT and NRS were identified electronically. Bayesian pooled treatment-effect and 95% credible-intervals (BCrI), posterior model probabilities indicating model plausibility and Bayes-factors (BF) were estimated using an informative heavy-tailed heterogeneity prior (half-Cauchy). Preference for pooling of RCT and NRS was indicated for Bayes-factors > 3 or < 0.333 for the converse. All pooled frequentist treatment-effects and 95% confidence intervals (FCI) were re-estimated using the popular DerSimonian-Laird (DSL) random effects model.ResultsFifty meta-analyses were identified (2009–2021), reporting pooled estimates in 44; 29 were pharmaceutical-therapeutic and 21 were non-pharmaceutical therapeutic. Re-computed pooled DSL FCI excluded the null (OR or RR = 1) in 86% (43/50). In 18 meta-analyses there was an agreement between FCI and BCrI in excluding the null. In 23 meta-analyses where FCI excluded the null, BCrI embraced the null. BF supported a pooled model in 27 meta-analyses and separate models in 4. The highest density of the posterior model probabilities for 0.333 < Bayes factor < 1 was 0.8.ConclusionsIn the current meta-analytic cohort, an integrated and multifaceted Bayesian approach gave support to including NRS in a pooled-estimate model. Conversely, caution should attend the reporting of naïve frequentist pooled, RCT and NRS, meta-analytic treatment effects.

Linking Frequentist and Bayesian Change-Point Methods

We show that the two-stage minimum description length (MDL) criterion widely used to estimate linear change-point (CP) models corresponds to the marginal likelihood of a Bayesian model with a specific class of prior distributions. This allows results from the frequentist and Bayesian paradigms to be bridged together. Thanks to this link, one can rely on the consistency of the number and locations of the estimated CPs and the computational efficiency of frequentist methods, and obtain a probability of observing a CP at a given time, compute model posterior probabilities, and select or combine CP methods via Bayesian posteriors. Furthermore, we adapt several CP methods to take advantage of the MDL probabilistic representation. Based on simulated data, we show that the adapted CP methods can improve structural break detection compared to state-of-the-art approaches. Finally, we empirically illustrate the usefulness of combining CP detection methods when dealing with long time series and forecasting.

Analyzing Parking Demand Characteristics Using a Bayesian Model Averaging

Parking duration analysis is an important aspect of evaluating parking demand. Identifying accurate distribution characteristics of parking duration can not only enhance parking efficiency and parking facility planning, but also provide essential support for parking delicacy management. Previous studies have proposed various statistical distributions to depict parking duration data. However, it is difficult to find a certain type of distribution to describe the characteristics of parking duration in diverse parking facilities, since model uncertainty is caused by stochastic parking behaviors and diverse parking environments. To address the model uncertainty, a Bayesian model averaging (BMA) was applied to integrate the advantages of different statistical distributions to depict parking duration characteristics. The parking dataset was collected from a commercial parking lot in Chengdu, China, and the dataset was categorized into two groups (i.e., temporary users and long-term users) to analyze. A set of statistical distributions was chosen as candidate models, and their corresponding unknown parameters were estimated. The posterior model probability for each candidate model was calculated according to the goodness-of-fit (GOF) metric. The findings of the study illustrate that there is no universally applicable distribution form (e.g., log-normal distribution) to depict the parking duration distribution for both user types, whereas the BMA approach assigns weights to candidate models and always provides an accurate description of the parking duration characteristics. The parking duration analysis is useful for improving parking management strategies and optimizing parking pricing policies.

Impact of heat stress on genetic evaluation of oocyte and embryo production in Gir dairy cattle.

Identifying and selecting genotypes tolerant to heat stress might improve reproductive traits in dairy cattle, including oocyte and embryo production. The temperature-humidity index (THI) was used, via random regression models, to investigate the impact of heat stress on genetic parameters and breeding values of oocyte and embryo production in Gir dairy cattle. We evaluated records of total oocytes (TO), viable oocytes (VO), cleaved embryos (CE), and viable embryos (VE) from dairy Gir donors. Twenty-four models were tested, considering age at ovum pick-up (AOPU) and THI means as a regressor in the genetic evaluation. We computed THI in eight periods, from 0 to 112days before ovum pick-up, which were adjusted by different orders of Legendre polynomials (second, third, and fourth). The best-fit model according to Akaike's information criterion (AIC) and Model Posterior Probabilities (MPP) considered Legendre polynomials of third order and THI means of 112days for TO, fourth order and 56days for VO, second order and 28days for CE, and second order and 42days for VE, respectively. The heritability (h2) estimates across AOPU and THI scales ranged from 0.34 to 0.62 for TO, 0.31 to 0.58 for VO, 0.26 to 0.39 for CE, and 0.15 to 0.26 for VE, respectively. The fraction of the phenotypic variance explained by the permanent environment in different AOPU and THI scales ranged from 0.03 to 0.25 for TO, 0.05 to 0.26 for VO, 0.09 to 0.36 for CE, and 0.15 to 0.27 for VE, respectively. Spearman's rank correlation between the estimated breeding values in different AOPU and THI scale from the top 5% sires and females ranged from 0.18 to 0.90 for TO, 0.31 to 0.95 for VO, 0.14 to 0.85 for CE, and 0.47 to 0.94 for VE, respectively. The h2estimates for all evaluated traits varied from moderate to high magnitude across AOPU and THI scales, indicating that genetic selection can result in rapid genetic progress for the evaluated traits. There was a reranking among the best animals in different AOPU and THI. It is possible to select dairy Gir cattle tolerant to heat stress to improve oocyte and embryo production.

Economic burden of Thalassemia treatment: An analysis from the Vietnam Social Security perspective.

Thalassemia is a genetic disorder that significantly impacts the health and well-being of individuals in Vietnam. This study aimed to assess the economic burden of Thalassemia treatment in Lam-Dong Province from the perspective of the Vietnam Social Security and to develop a model to forecast these costs. This study analyzed the medical records of all 288 health-insured Thalassemia patients who received treatment in Lam-Dong Province from 2019-2021. The annual economic burden was calculated as the total direct medical cost of treatment per patient over one year. Bayesian Model Averaging (BMA) was utilized to forecast economic burdens. The best fit model was selected based on evaluation criteria including the R2 value, the Bayesian information criterion (BIC), and posterior model probabilities. The study found that the average annual economic burden of Thalassemia treatment was VND 9,947,000 (±6,854,000), equivalent to approximately USD 426.7 (±294.0), with blood transfusions being the main contributor to costs (63%). Using BMA, the best fit model to forecast economic burdens included variables including patient age, sex, and length of hospitalization, with age being the key factor with the greatest impact on the increase in economic burden. These findings provided important information for policymakers in Vietnam, as they highlighted the significant economic burden of Thalassemia treatment in the country. By developing a model to forecast these costs, policymakers can make informed decisions on how to allocate resources and support individuals with Thalassemia and their families.

Importance sampling and Bayesian model comparison in ecology and evolution

Abstract Bayesian approaches to the modelling of ecological systems are increasingly popular, but there are competing methods for formal model comparisons. Here, we focus on the task of performing multimodel inference through estimating posterior model weights, which encompasses uncertainties in the choice of competing model structure into the inference outputs. Model‐based approaches such as reversible‐jump Markov chain Monte Carlo (RJ‐MCMC) are flexible and allow multimodel inference, but can be complex to implement and optimise, and so we translate a model‐based approach for ecological applications using Importance Sampling to estimate the marginal likelihood of the data given a particular model. This approach allows for model comparison through the estimation of Bayes' Factors or interpretable posterior model probabilities, yielding model weights that facilitate multimodel inference through Bayesian model averaging. We demonstrate Importance Sampling with two case study investigations in animal demography: censused analysis of banded mongoose (Mungos mungo) survival where missing data are uncommon, and capture–mark–recapture analysis of European badger (Meles meles) survival where data are commonly missing. We compare outcomes of the model comparison using the Importance Sampling approach to those obtained through single‐model inference approaches using Deviance information criteria and the Watanabe–Akaike information criteria. The results of the Importance Sampling method aligns with RJ‐MCMC model comparisons while often being more straightforward to fit and optimise, particularly if the competing models are non‐nested.

Graphical posterior predictive classification: Bayesian model averaging with particle Gibbs

In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed features is represented by a set of decomposable Gaussian graphical models. Emphasis is then placed on the Bayesian model averaging which takes full account of the class-specific model uncertainty by averaging over the posterior graph model probabilities. An explicit evaluation of the model probabilities is well known to be infeasible. To address this issue, we consider the particle Gibbs strategy of J. Olsson, T. Pavlenko, and F. L. Rios [Electron. J. Statist. 13 (2019), no. 2, 2865–2897] for posterior sampling from decomposable graphical models which utilizes the so-called Christmas tree algorithm of J. Olsson, T. Pavlenko, and F. L. Rios [Stat. Comput. 32 (2022), no. 5, Paper No. 80, 18] as proposal kernel. We also derive a strong hyper Markov law which we call the hyper normal Wishart law that allows to perform the resultant Bayesian calculations locally. The proposed predictive graphical classifier reveals superior performance compared to the ordinary Bayesian predictive rule that does not account for the model uncertainty, as well as to a number of out-of-the-box classifiers.

Genetic parameters and genome-wide association studies for mozzarella and milk production traits, lactation length, and lactation persistency in Murrah buffaloes

Genetic and genomic analyses of longitudinal traits related to milk production efficiency are paramount for optimizing water buffaloes breeding schemes. Therefore, this study aimed to: 1) compare single-trait random regression models under a Single-step Genomic Best Linear Unbiased Prediction (ssGBLUP) setting based on alternative covariance functions (i.e., Wood - WD, Wilmink - WL, and Ali-and-Schaeffer - AS) to describe milk (MY), fat (FY), protein (PY), and mozzarella (MZY) yields, fat-to-protein ratio (FPR), somatic cell score (SCS), lactation length (LL), and lactation persistency (LP) in Murrah dairy buffaloes (Bubalus bubalis); 2) combine the best functions for each trait under a multiple-trait framework; 3) estimate time-dependent SNP effects for all the studied longitudinal traits; and, 5) identify the most likely candidate genes associated with the traits. A total of 323,140 test-day records from the first lactation of 4,588 Murrah buffaloes were made available for the study. The model included the average curve of the population nested within herd-year-season of calving, systematic effects of number of milkings per day, and age at first calving as linear and quadratic covariates, and additive genetic, permanent environment, and residual as random effects. The WD model had the best goodness of fit based on the deviance information criterion and posterior model probabilities for all traits. Moderate heritabilities were estimated over time for most traits (0.30 ± 0.02 for MY; 0.26 ± 0.03 for FY; 0.45 ± 0.04 for PY; 0.28 ± 0.05 for MZY; 0.13 ± 0.02 for FPR; and 0.15 ± 0.03 for SCS). The heritability estimates for LP ranged from 0.38 ± 0.02 to 0.65 ± 0.03 depending on the trait definition used. Similarly, heritabilities estimated for LL ranged from 0.10 ± 0.01 to 0.14 ± 0.03. The genetic correlation estimates across DIM for all traits ranged from -0.06 (186 to 215 DIM for MY-SCS) to 0.78 (66 to 95 DIM for PY-MZY). The SNP effects calculated for the random regression model coefficients were used to estimate the SNP effects throughout the lactation curve (from 5 to 305 d). Numerous relevant genomic regions and candidate genes were identified for all traits, confirming their polygenic nature. The candidate genes identified contribute to a better understanding of the genetic background of milk-related traits in Murrah buffaloes and reinforce the value of incorporating genomic information in their breeding programs.

ClusterBMA: Bayesian model averaging for clustering.

Various methods have been developed to combine inference across multiple sets of results for unsupervised clustering, within the ensemble clustering literature. The approach of reporting results from one 'best' model out of several candidate clustering models generally ignores the uncertainty that arises from model selection, and results in inferences that are sensitive to the particular model and parameters chosen. Bayesian model averaging (BMA) is a popular approach for combining results across multiple models that offers some attractive benefits in this setting, including probabilistic interpretation of the combined cluster structure and quantification of model-based uncertainty. In this work we introduce clusterBMA, a method that enables weighted model averaging across results from multiple unsupervised clustering algorithms. We use clustering internal validation criteria to develop an approximation of the posterior model probability, used for weighting the results from each model. From a combined posterior similarity matrix representing a weighted average of the clustering solutions across models, we apply symmetric simplex matrix factorisation to calculate final probabilistic cluster allocations. In addition to outperforming other ensemble clustering methods on simulated data, clusterBMA offers unique features including probabilistic allocation to averaged clusters, combining allocation probabilities from 'hard' and 'soft' clustering algorithms, and measuring model-based uncertainty in averaged cluster allocation. This method is implemented in an accompanying R package of the same name. We use simulated datasets to explore the ability of the proposed technique to identify robust integrated clusters with varying levels of separation between subgroups, and with varying numbers of clusters between models. Benchmarking accuracy against four other ensemble methods previously demonstrated to be highly effective in the literature, clusterBMA matches or exceeds the performance of competing approaches under various conditions of dimensionality and cluster separation. clusterBMA substantially outperformed other ensemble methods for high dimensional simulated data with low cluster separation, with 1.16 to 7.12 times better performance as measured by the Adjusted Rand Index. We also explore the performance of this approach through a case study that aims to identify probabilistic clusters of individuals based on electroencephalography (EEG) data. In applied settings for clustering individuals based on health data, the features of probabilistic allocation and measurement of model-based uncertainty in averaged clusters are useful for clinical relevance and statistical communication.

Covariance structure estimation with Laplace approximation

The Gaussian covariance graph model is popular for revealing the underlying dependency structures among random variables. In this paper, we consider a spike and slab prior, which is a mixture of point-mass and normal distribution, on the off-diagonal entries. The spike and slab prior naturally introduces sparsity to the covariance structure so that the resulting posterior renders covariance structure learning. Under the spike and slab prior, we calculate the posterior model probabilities of covariance structures and natural Bayesian quantities for model selection using the Laplace approximation. We show that the error due to the Laplace approximation becomes asymptotically marginal at a rate that depends on the posterior convergence rate of the covariance matrix under the Frobenius norm. We propose a covariance structure estimation method based on the approximated posterior model probabilities. We also propose a block coordinate descent algorithm to determine the mode of the posterior density conditional on the structure of the covariance. The posterior mode is an estimate of the covariance matrix once the structure is chosen and the Laplace approximation is computed around it. Through a simulation study based on five numerical models, we demonstrate that the proposed method outperforms its competitors. The proposed method is applied to the breast cancer and Parkinson’s disease datasets, as well as the prediction of telephone call counts using telephone call center data, and compared with its competitors in terms of the linear discriminant analysis classification accuracy.

Probabilistic Prediction of Satellite-Derived Water Quality for a Drinking Water Reservoir

A Bayesian network-based modelling framework was proposed to predict the probability of exceeding critical thresholds for chlorophyll-a and turbidity in an Australian subtropical drinking water reservoir, based on Sentinel-2 data and prior knowledge. The model was trained with quasi-synchronous historical in situ and satellite data for 2018–2023 and achieved satisfactory accuracy (Brier score &lt; 0.27 for all models) despite limited poor water quality events in the final dataset. The graphical output of the model (posterior probability maps of high turbidity or chlorophyll-a) provides an effective means for the user to evaluate both the prediction, and the uncertainty behind the predictions in a single map. This avoids loss of trust in the model and can trigger spatially targeted data collection in order to reduce uncertainty. Future work will focus on refining the modelling methodology and its automation, as well as including other data such as in situ high-frequency sensors.

Impaired salience network switching in psychopathy

Growing evidence suggests that psychopathy is related to altered connectivity within and between three large-scale brain networks that support core cognitive functions, including allocation of attention. In healthy individuals, default mode network (DMN) is involved in internally-focused attention and cognition such as self-reference. Frontoparietal network (FPN) is anticorrelated with DMN and is involved in externally-focused attention to cognitively demanding tasks. A third network, salience network (SN), is involved in detecting salient cues and, crucially, appears to play a role in switching between the two anticorrelated networks, DMN and FPN, to efficiently allocate attentional resources. Psychopathy has been related to reduced anticorrelation between DMN and FPN, suggesting SN’s role in switching between these two networks may be diminished in the disorder. To test this hypothesis, we used independent component analysis to derive DMN, FPN, and SN activity in resting-state fMRI data in a sample of incarcerated men (N = 148). We entered the activity of the three networks into dynamic causal modeling to test SN’s switching role. The previously established switching effect of SN among young, healthy adults was replicated in a group of low psychopathy participants (posterior model probability = 0.38). As predicted, SN’s switching role was significantly diminished in high psychopathy participants (t(145) = 26.39, p < .001). These findings corroborate a novel theory of brain function in psychopathy. Future studies may use this model to test whether disrupted SN switching is related to high psychopathy individuals’ abnormal allocation of attention.

Forecasting Pathogen Dynamics with Bayesian Model-Averaging: Application to Xylella fastidiosa.

Forecasting invasive-pathogen dynamics is paramount to anticipate eradication and containment strategies. Such predictions can be obtained using a model grounded on partial differential equations (PDE; often exploited to model invasions) and fitted to surveillance data. This framework allows the construction of phenomenological but concise models relying on mechanistic hypotheses and real observations. However, it may lead to models with overly rigid behavior and possible data-model mismatches. Hence, to avoid drawing a forecast grounded on a single PDE-based model that would be prone to errors, we propose to apply Bayesian model averaging (BMA), which allows us to account for both parameter and model uncertainties. Thus, we propose a set of different competing PDE-based models for representing the pathogen dynamics, we use an adaptive multiple importance sampling algorithm (AMIS) to estimate parameters of each competing model from surveillance data in a mechanistic-statistical framework, we evaluate the posterior probabilities of models by comparing different approaches proposed in the literature, and we apply BMA to draw posterior distributions of parameters and a posterior forecast of the pathogen dynamics. This approach is applied to predict the extent of Xylella fastidiosa in South Corsica, France, a phytopathogenic bacterium detected in situ in Europe less than 10 years ago (Italy 2013, France 2015). Separating data into training and validation sets, we show that the BMA forecast outperforms competing forecast approaches.

Influence of setting-dependent contacts and protective behaviours on asymptomatic SARS-CoV-2 infection amongst members of a UK university

We survey 62 users of a university asymptomatic SARS-CoV-2 testing service on details of their activities, protective behaviours and contacts in the 7 days prior to receiving a positive or negative SARS-CoV-2 PCR test result in the period October 2020–March 2021. The resulting data set is novel in capturing very detailed social contact history linked to asymptomatic disease status during a period of significant restriction on social activities. We use this data to explore 3 questions: (i) Did participation in university activities enhance infection risk? (ii) How do contact definitions rank in their ability to explain test outcome during periods of social restrictions? (iii) Do patterns in the protective behaviours help explain discrepancies between the explanatory performance of different contact measures? We classify activities into settings and use Bayesian logistic regression to model test outcome, computing posterior model probabilities to compare the performance of models adopting different contact definitions. Associations between protective behaviours, participant characteristics and setting are explored at the level of individual activities using multiple correspondence analysis (MCA). We find that participation in air travel or non-university work activities was associated with a positive asymptomatic SARS-CoV-2 PCR test, in contrast to participation in research and teaching settings. Intriguingly, logistic regression models with binary measures of contact in a setting performed better than more traditional contact numbers or person contact hours (PCH). The MCA indicates that patterns of protective behaviours vary between setting, in a manner which may help explain the preference for any participation as a contact measure. We conclude that linked PCR testing and social contact data can in principle be used to test the utility of contact definitions, and the investigation of contact definitions in larger linked studies is warranted to ensure contact data can capture environmental and social factors influencing transmission risk.

A new framework for the assessment of model probabilities of the different crystal plasticity models for lamellar grains in Titanium alloys

This paper presents a novel framework for assessing the relative accuracy of the different slip transfer criterion in modeling the constitutive response of the lamellar morphology grains in Titanium alloys. The main steps involved in the proposed framework include: (i) rigorous statistical evaluation of the salient morphological characteristics of the lamellar grains using image processing techniques, (ii) modeling the effects of dislocation slip transfer as additive penalties to the critical resolved shear strengths of the different slip systems in each phase, (iii) consideration of multiple geometric slip transfer criteria for the numerical evaluation of the different penalty terms, and (iv) the Bayesian calibration of the material parameters in the constitutive descriptions using spherical nanoindentation experimental data on a polycrystalline Ti-6Al-4V sample. Step (iv) described above involves the construction and refinement of a Gaussian process (GP) surrogate model for the indentation measurements, which is trained on crystal plasticity finite element simulations incorporating the constitutive descriptions selected in Steps (ii) and (iii). The GP surrogates are then combined with Markov Chain Monte Carlo sampling techniques to calibrate the parameters in the various constitutive models studied in this work. Additionally, we have computed the posterior model probabilities for all the constitutive models considered and identified the most plausible slip transfer criterion. This specific constitutive model is then utilized to present a homogenized crystal plasticity model for the lamellar morphology. The proposed framework presents a robust scale-bridging protocol for incorporating the uncertain information obtained from lower scales.

Inversion of TEM measurement data via a quantum particle swarm optimization algorithm with the elite opposition-based learning strategy

The fine interpretation and inversion of transient electromagnetic method measurement data have the problems of nonlinearity, multi-solution, and ill condition. However, the conventional particle swarm optimization (PSO) nonlinear inversion methods suffer from prematurity, slow convergence, and low calculation accuracy. To solve these problems, a quantum PSO (QPSO) algorithm based on the elite opposition-based learning (EOL) strategy is proposed. Firstly, three performances tests of the EOL-QPSO algorithm are carried out with Peaks, Schaffer and Rastrigin functions. The results show that the EOL-QPSO algorithm has excellent solution accuracy, efficient calculation speed and balanced exploitation and exploration capability. Secondly, the conventional PSO algorithm and the EOL-QPSO algorithm are used to compare the inversion of the theoretical model and the synthetic data with noise, and combined with Bayesian method, the posterior model probability statistics of the synthetic data are carried out. The research shows that the EOL-QPSO inversion algorithm is improved in terms of calculation accuracy, calculation efficiency, anti-noise performance and exploitation and exploration capability, and it can accurately obtain the posterior estimates of the real model. Finally, the inversion of field-measured data demonstrates that the EOL-PSO inversion method accurately reflects the position of the water-accumulated goaf.

Assessment of the Bering-Chukchi-Beaufort Seas stock of bowhead whales using Bayesian model averaging

Bayesian estimation methods are used to fit an age- and sex-structured population model to available data on abundance and stageproportions (i.e. calves/mature animals in the population) for the Bering-Chukchi-Beaufort Seas stock of bowhead whales (Balaena mysticetus). The analyses consider three alternative population modelling approaches: (1) modelling the entire population trajectory from 1848, using the ‘backwards’ method where the trajectory is back-calculated based on assigning a prior distribution to recent abundance; (2) modelling only the recent population trajectory, using the ‘forwards from recent abundance’ method, where the population is projected forwards from a recent year and the abundance in that year is not assumed to be at carrying capacity; and (3) a version of (2) that ignores density-dependence. The ‘backwards’ method leads to more precise estimates of depletion level. In contrast, the ‘forwards from recent abundance’ method provides an alternative way of calculating catch-related quantities without having to assume that the catch record is known exactly from 1848 to the present, or having to assume that carrying capacity has not changed since 1848. Not only are all three models able to fit the abundance data well, but each is also able to remain consistent with available estimates of adult survival and age of sexual maturity. Sensitivity to the stage-proportion data and the prior distributions for the life history parameters indicates that use of the 1985 stage-proportion data has the greatest effect on the results, and that those data are less consistent with data on trends in abundance and age of sexual maturity. The analyses indicate that the population has approximately doubled in size since 1978, and the ‘backwards’ analyses suggest that the population may be approaching carrying capacity, although there is no obvious sign in the data that the population growth rate has slowed. Bayes factors are calculated to compare model fits to the data. However, there is no evidence for selecting one model over another, and furthermore, the models considered in this study result in different posterior distributions for quantities of interest to management. Posterior model probabilities are therefore calculated and used as weights to construct Bayesian model-averaged posterior distributions for outputs shared among models to take this ambiguity into account. This study represents the first attempt to explicitly quantify model uncertainty when conducting a stock assessment of bowhead whales.

Bayesian history of science: The case of Watson and Crick and the structure of DNA

AbstractA naïve Bayes approach to theory confirmation is used to compute the posterior probabilities for a series of four models of DNA considered by James Watson and Francis Crick in the early 1950s using multiple forms of evidence considered relevant at the time. Conditional probabilities for the evidence given each model are estimated from historical sources and manually assigned using a scale of five probabilities ranging from strongly consistent to strongly inconsistent. Alternative or competing theories are defined for each model based on preceding models in the series. Prior probabilities are also set based on the posterior probabilities of these earlier models. A dramatic increase in posterior probability is seen for the final double helix model compared to earlier models in the series, which is interpreted as a form of “Bayesian surprise” leading to the sense that a “discovery” was made. Implications for theory choice in the history of science are discussed.

Reproducible Model Selection Using Bagged Posteriors.

Bayesian model selection is premised on the assumption that the data are generated from one of the postulated models. However, in many applications, all of these models are incorrect (that is, there is misspecification). When the models are misspecified, two or more models can provide a nearly equally good fit to the data, in which case Bayesian model selection can be highly unstable, potentially leading to self-contradictory findings. To remedy this instability, we propose to use bagging on the posterior distribution ("BayesBag") - that is, to average the posterior model probabilities over many bootstrapped datasets. We provide theoretical results characterizing the asymptotic behavior of the posterior and the bagged posterior in the (misspecified) model selection setting. We empirically assess the BayesBag approach on synthetic and real-world data in (i) feature selection for linear regression and (ii) phylogenetic tree reconstruction. Our theory and experiments show that, when all models are misspecified, BayesBag (a) provides greater reproducibility and (b) places posterior mass on optimal models more reliably, compared to the usual Bayesian posterior; on the other hand, under correct specification, BayesBag is slightly more conservative than the usual posterior, in the sense that BayesBag posterior probabilities tend to be slightly farther from the extremes of zero and one. Overall, our results demonstrate that BayesBag provides an easy-to-use and widely applicable approach that improves upon Bayesian model selection by making it more stable and reproducible.