Posterior Model Probabilities Research Articles

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.

Fault identification and reliability evaluation using an SVM model based on 3-D seismic data volume

SUMMARY As an important method of 3-D seismic exploration, intelligent structural interpretation has been improved in recent years. Traditional human–computer interaction explanations typically assess fault risk on a hierarchical basis. However, the majority of intelligent fault interpretations utilize binary classification methods, which limits the utility and development of this technology to a certain extent. In order to break this limitation, a fault risk assessment scheme based on particle swarm optimization (PSO) and support vector machine (SVM) posterior probability model has been proposed. In this study, the fault exposure situations for 11 wells and 4 roadways of a coal mine in Yunnan Province, China, were identified. A total of 15 559 data points with known fault and non-fault information were obtained in the target coal seam. Based on these data, SVM fault recognition models were constructed. The key parameters of the SVM models were optimized by PSO, and the test accuracy of each model was above 87 per cent. Meanwhile, the SVM posterior probability model was introduced to evaluate the fault identification results in the study area. The SVM posterior probability model was used to convert the decision value of a standard SVM into a posterior probability value. Probability values in the range of [0, 0.5) are evaluated as non-fault points, [0.5, 0.7) as ‘unreliable’ fault points, [0.7, 0.9) as ‘less reliable’ fault points, and [0.9, 1] as ‘reliable’ fault points. By constructing data sets with different sample numbers and fault types, the influence of each factor on the evaluation of the SVM posterior probability model was analysed. The results show that the SVM posterior probability model can be used to hierarchically evaluate fault risk in the study area and provide decision makers with more accurate information for decision making.

Winners from Winners: A Tale of Risk Factors

Starting from twelve distinct factors from the recent literature, plus twelve principal components (PCs) of anomalies unexplained by the initial factors, a Bayesian comparison of approximately seventeen million models in terms of marginal likelihoods and posterior model probabilities shows that {Mkt, MOM, IA, ROE, MGMT, PERF, PEAD, FIN}, plus the nonconsecutive principal components, {[Formula: see text]} are the best supported risk factors. Pricing tests and annualized out-of-sample Sharpe ratios for tangency portfolios suggest that this asset pricing model should be used for computing expected returns, assessing investment strategies and building portfolios. This paper was accepted by Lukas Schmid, finance. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.4668 .

A Bayesian model averaging method for software reliability modeling and assessment

AbstractThe software reliability modeling is of great significance in improving software quality and managing the software development process. However, the existing methods are not able to accurately model software reliability improvement behavior because existing single model methods rely on restrictive assumptions and combination models cannot well deal with model uncertainties. In this article, we propose a Bayesian model averaging (BMA) method to model software reliability. First, the existing reliability modeling methods are selected as the candidate models, and the Bayesian theory is used to obtain the posterior probabilities of each reliability model. Then, the posterior probabilities are used as weights to average the candidate models. Both Markov Chain Monte Carlo (MCMC) algorithm and the Expectation–Maximization (EM) algorithm are used to evaluate a candidate model's posterior probability and for comparison purpose. The results show that the BMA method has superior performance in software reliability modeling, and the MCMC algorithm performs better than EM algorithm when they are used to estimate the parameters of BMA method.

Bayesian geoacoustic parameters inversion for multi-layer seabed in shallow sea using underwater acoustic field

Seabed geoacoustic parameters play an important role in underwater acoustic channel modeling. Traditional methods to determine these parameters, for example, drilling, are expensive and are being replaced by acoustic inverse technology. An inversion method based on Bayesian theory is presented to derive the structure and geoacoustic parameters of a layered seabed in a shallow sea. The seabed was considered a layered elastic medium. The objective of this research was to use the sound pressure detected by underwater acoustic sensors at different positions and to use nonlinear Bayesian inversion to estimate the geoacoustic parameters and their uncertainties in the multi-layer seabed. Specifically, the thickness, density, compression wave speed, shear wave speed, and the attenuation of these two wave speeds were determined. The maximum a posterior (MAP) model and posterior probability distribution of each parameter were estimated using the optimized simulated annealing (OSA) and Metropolis-Hastings sampling (MHS) methods. Model selection was carried out using the Bayesian information criterion (BIC) to determine the optimal model that thoroughly explained the experimental data for different parameterizations. The results showed that the OSA is much more capable of delivering high-accuracy results in multi-layer seabed models. The compression wave speed and shear wave speed were less uncertain than the other parameters, and the parameters in the upper layer had less uncertainty than those in the lower layer.

A platform trial approach to proof-of-concept (POC) studies in autism spectrum disorder: Autism spectrum POC initiative (ASPI)

BackgroundOver the past decade, autism spectrum disorder (ASD) research has blossomed, and multiple clinical trials have tested potential interventions, with varying results and no clear demonstration of efficacy. Lack of clarity concerning appropriate biological mechanisms to target and lack of sensitive, objective tools to identify subgroups and measure symptom changes have hampered the efforts to develop treatments. A platform trial for proof-of-concept studies in ASD could help address these issues. A major goal of a platform trial is to find the best treatment in the most expeditious manner, by simultaneously investigating multiple treatments, using specialized statistical tools for allocation and analysis. We describe the setup of a platform trial and perform simulations to evaluate the operating characteristics under several scenarios. We use the Autism Behavior Inventory (ABI), a psychometrically validated web-based rating scale to measure the change in ASD core and associated symptoms. MethodsDetailed description of the setup, conduct, and decision-making rules of a platform trial are explained. Simulations of a virtual platform trial for several scenarios are performed to compare operating characteristics. The success and futility criteria for treatments are based on a Bayesian posterior probability model. ResultsOverall, simulation results show the potential gain in terms of statistical properties especially for improved decision-making ability, while careful planning is needed due to the complexities of a platform trial. ConclusionsAutism research, shaped particularly by its heterogeneity, may benefit from the platform trial approach for POC clinical studies.

Bayesian design of multi-regional clinical trials with time-to-event endpoints.

Sponsors often rely on multi-regional clinical trials (MRCTs) to introduce new treatments more rapidly into the global market. Many commonly used statistical methods do not account for regional differences, and small regional sample sizes frequently result in lower estimation quality of region-specific treatment effects. The International Council for Harmonization E17 guidelines suggest consideration of methods that allow for information borrowing across regions to improve estimation. In response to these guidelines, we develop a novel methodology to estimate global and region-specific treatment effects from MRCTs with time-to-event endpoints using Bayesian model averaging (BMA). This approach accounts for the possibility of heterogeneous treatment effects between regions, and we discuss how to assess the consistency of these effects using posterior model probabilities. We obtain posterior samples of the treatment effects using a Laplace approximation, and we show through simulation studies that the proposed modeling approach estimates region-specific treatment effects with lower mean squared error than a Cox proportional hazards model while resulting in a similar rejection rate of the global treatment effect. We then apply the BMA approach to data from the LEADER trial, an MRCT designed to evaluate the cardiovascular safety of an anti-diabetictreatment.

Pronunciation Scoring With Goodness of Pronunciation and Dynamic Time Warping

The current pronunciation scoring based on Goodness of Pronunciation (GOP) uses posterior probabilities of the Acoustic Models. Such algorithms suffer from generalization since they are utilized to determine a score metric for each phoneme rather than on the completeness or comparison with the ideal utterance of the words. In this paper, a novel method is proposed for computing scores calculated using combined scores of prosodic, fluency, completeness, and accuracy. This is achieved using context-aware GOP in conjugation with dynamic time warping (DTW) matching of the pitch contours of a weighted average of the context tokens found in the audio file that is rich in mispronounced phonemes. The proposed work gives flexibility in tuning the results according to different speech aspects based on a single hyperparameter. The results achieved are encouraging and have been validated on the speechocean762 dataset, where Automatic Speech Recognition (ASR) model has been trained on the Librispeech dataset. The resultant mean error of the proposed approach is 3.38% and the value of the correlation coefficient achieved is 0.652.

基于朴素贝叶斯算法评估页岩油藏产能

Shale oil, as an unconventional oil and gas resource with huge reserves, has become an important replacement resource and great significance to develop. Aiming at the problems of rapid decline oil production in the depletion development of shale oil reservoirs by "depleted horizontal well+volume fracturing", and the lower recovery factor predicted by the existing productivity evaluation methods in shale reservoir, we construct a productivity evaluation method for fractured horizontal wells based on naive Bayes algorithm. Taking the Jimsar shale reservoir in Xinjiang oilfield as the target reservoir, we establish the multi-classification Naive Bayes prior probability model and the conditional probability model containing five attributes of geological parameters and engineering parameters by taking the three-year cumulative production as the classification evaluation index. Then we obtain the posterior-probability model of the four types of production capacity based on Bayesian theory to achieve the capacity assessment of fractured horizontal wells in shale oil reservoirs. The results show that the proposed shale reservoir capacity classification method based on the Naive Bayes model is applicable. The accuracy of productivity prediction is 94% for Class Ⅰ wells, 71% for Class Ⅱ wells, 87% for Class Ⅲ wells, and 92% for Class Ⅳ wells, respectively. The productivity classification trend distribution map of fracturing horizontal wells in Jimsar shale reservoir is drawn, and the high-production potential area is mainly distributed in the southeast of the reservoir. The analysis of the constructed posterior probability model shows that the optimization of fracturing construction parameters can improve the probability of high well production rate. The study provides a guiding basis for the subsequent large-scale fracturing reconstruction of horizontal wells for shale oil development.

Bayesian Linear Seismic Inversion Integrating Uncertainty of Noise Level Estimation and Wavelet Extraction

Seismic impedance inversion is an important method to identify the spatial characteristics of underground rock physical properties. Seismic inversion results and uncertainty evaluation are the important scientific basis for risk decision-making in oil and gas development. Under the assumption that the impedance and the error of the observed seismic data meet the Gaussian distribution or log–Gaussian distribution, the Bayesian linear seismic inversion can analytically obtain the posterior probability distribution of impedance. However, errors from observation, calculation, model and other factors can lead to an inaccurate and incomplete uncertainty evaluation. In this paper, the noise variance is used to represent the noise level of seismic data and the uncertainties from seismic wavelet extraction and noise level estimation are considered in inversion. Assuming that the probability distribution of the noise variance meets the inverse gamma distribution and the seismic wavelet meets the Gaussian distribution, we could obtain the conditional distribution for one variable given another analytically using well-log data and seismic data. In order to integrate the uncertainty from noise level estimation and wavelet extraction into the seismic impedance inversion, the Gibbs sampler algorithm was applied to draw a set of realizations of noise variance and wavelet. For each realization, the corresponding posterior probability model of impedance was achieved by Bayesian linear inversion and the final posterior probability of the impedance model was obtained by integrating all the single posterior probabilities for each pair of wavelet and noise variance. Synthetic and real data experiments showed that the uncertainties of seismic wavelet extraction and noise level estimation have an important influence on inversion results and their uncertainties. The proposed method could effectively integrate the uncertainty of wavelet and noise estimation to obtain a more accurate and comprehensive uncertainty evaluation. Under the assumption that the model meets the linear relationship and the parameters meet some specified distribution, the proposed method has high calculation efficiency. However, it also loses some accuracy when the assumptions are not completely consistent with the actual situation.

Bayesian Model Averaging (BMA) Based on Logistic Regression for Gene Selection and Classification of Animal Tumor Disease on Microarray Data

Tumor is one of the deadly diseases which is frequently to be found in animals. However, identifying whether an animal has a tumor still becomes a big challenge. Classification of tumor disease can be done through gene expression, which consists of hundreds of genes, but only a small number of samples is taken. This data structure is called microarray data having the characteristic of high-dimensional data. The choice of a single model can be a problem for high-dimensional data because it ignores model uncertainty. This research proposed to use Bayesian Model Averaging (BMA) to model the uncertainty model by averaging the posterior distribution of all best models, weighted by their posterior model probabilities. Selecting relevant genes to diagnose animal tumors is very important; hence, variable selection needs to be carried out. The selection of predictor variables is carried out by using the iterative BMA algorithm. The BMA results showed that from 335 gene expressions, 12 genes were selected to be relevant genes for classifying whether the animals have a tumor or normal. Moreover, from 2335 possible models formed, 12 of the best models are selected. The accuracy of BMA results is assessed using the Brier Score, resulting from a value indicating that the BMA model is good enough to classify animals, whether they have a tumor or not. This research has proven that BMA with logistic performance has very good predictability; hence, the method can be applied to classify other diseases.

A subsampling approach for Bayesian model selection

It is common practice to use Laplace approximations to decrease the computational burden when computing the marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to compute the posterior marginal probabilities of models and individual covariates. This allows performing Bayesian model selection and model averaging. For large sample sizes, even the Laplace approximation becomes computationally challenging because the optimisation routine involved needs to evaluate the likelihood on the full dataset in multiple iterations. As a consequence, the algorithm is not scalable for large datasets. To address this problem, we suggest using stochastic optimisation approaches, which only use a subsample of the data for each iteration. We combine stochastic optimisation with Markov chain Monte Carlo (MCMC) based methods for Bayesian model selection and provide some theoretical results on the convergence of the estimates for the resulting time-inhomogeneous MCMC. Finally, we report results from experiments illustrating the performance of the proposed algorithm.

ZELLNER’S G-PRIORS IN BAYESIAN MODEL AVERAGING OF LARGE MODEL SPACE USING MARKOV CHAIN MONTE CARLO MODEL COMPOSITION APPLICABLE UNDER BAYESIAN MODEL SAMPLING

Applied researchers are frequently faced with the issue of model uncertainty in situations where many possible models exist. For large model space in regression analysis, the challenge has always been how to select a single model among competing large model space when making inferences. Bayesian Model Averaging (BMA) is a technique designed to help account for the uncertainty inherent in the model selection process. Informative prior distributions related to a natural conjugate prior specification are investigated under a limited choice of a single scalar hyper parameter called g-prior which corresponds to the degree of prior uncertainty on regression coefficients. This study focuses on situations with extremely large model space made up of large set of regressors generated by a small number of observations, when estimating model parameters. A set of g-prior structures in literature are considered with a view to identify an improved g-prior specification for regression coefficients in Bayesian Model Averaging. The study demonstrates the sensitivity of posterior results to the choice of g-prior on simulated dataand real-life data. Markov Chain Monte Carlo (MCMC) are used to generate a process which moves through large model space to adequately identify the high posterior probability models using the Markov Chain Monte Carlo Model Composition (MC3), a method applicable under Bayesian Model Sampling (BMS). To assess the sensitivity and predictive ability of the g-priors,predictive criteria like Log Predictive Score (LPS) and Log Marginal Likelihood (LML) are employed. The results reveal a g-prior structure that exhibited equally competitive and consistent predictive ability among considered g-prior structures in literature.

Approximate Bayesian Techniques for Statistical Model Selection and Quantifying Model Uncertainty-Application to a Gait Study.

Frequently, biomedical researchers need to choose between multiple candidate statistical models. Several techniques exist to facilitate statistical model selection including adjusted R2, hypothesis testing and p-values, and information criteria among others. One particularly useful approach that has been slow to permeate the biomedical literature is the notion of posterior model probabilities. A major advantage of posterior model probabilities is that they quantify uncertainty in model selection by providing a direct, probabilistic comparison among competing models as to which is the "true" model that generated the observed data. Additionally, posterior model probabilities can be used to compute posterior inclusion probabilities which quantify the probability that individual predictors in a model are associated with the outcome in the context of all models considered given the observed data. Posterior model probabilities are typically derived from Bayesian statistical approaches which require specialized training to implement, but in this paper we describe an easy-to-compute version of posterior model probabilities and inclusion probabilities that rely on the readily-available Bayesian information criterion. We illustrate the utility of posterior model probabilities and inclusion probabilities by re-analyzing data from a published gait study investigating factors that predict required coefficient of friction between the shoe sole and floor while walking.

Bayesian design of clinical trials using joint models for recurrent and terminating events.

Joint models for recurrent event and terminating event data are increasingly used for the analysis of clinical trials. However, few methods have been proposed for designing clinical trials using these models. In this article, we develop a Bayesian clinical trial design methodology focused on evaluating the effect of an investigational product (IP) on both recurrent event and terminating event processes considered as multiple primary endpoints, using a multifrailty joint model. Dependence between the recurrent and terminating event processes is accounted for using a shared frailty. Inferences for the multiple primary outcomes are based on posterior model probabilities corresponding to mutually exclusive hypotheses regarding the benefit of IP with respect to the recurrent and terminating event processes. We propose an approach for sample size determination to ensure the trial design has a high power and a well-controlled type I error rate, with both operating characteristics defined from a Bayesian perspective. We also consider a generalization of the proposed parametric model that uses a nonparametric mixture of Dirichlet processes to model the frailty distributions and compare its performance to the proposed approach. We demonstrate the methodology by designing a colorectal cancer clinical trial with a goal of demonstrating that the IP causes a favorable effect on at least one of the two outcomes but no harm on either.

How does government attention matter in air pollution control? Evidence from government annual reports

Ambitious environmental action demands policymakers' attention. Since 2014, when China proclaimed a "war on pollution," government attention to environmental concerns has increased unprecedentedly. The purpose of this study is to determine empirically if, and to what extent, this government attention has had an effect on environmental quality, particularly local air pollution. We quantified local Chinese governments' attention to the environment from 2014 to 2019 using a dataset of the textual content of their Government Annual Reports (GARs) from 286 cities at or above prefectural level (APL). The Spatial Durbin Model (SDM) is selected as the most probable spatial econometric model using Bayesian posterior model probabilities. As demonstrated, environmental attention is related with perceptible increases in air quality. On average, a one-unit increase in environmental attention resulted with decreases of 4.2 %, 4.5 %, and 7.4 % in AQI index, PM10, and NO2 concentrations, respectively. As an auxiliary validation, we found evidence at provincial level that environmental agenda and investment in pollution control represent the primary outputs of increased environmental attention. A further analysis by subsample revealed that the effect of environmental attention on air pollution differed by region. In general, this study establishes a compelling rationale for municipal governments to prioritize environmental issues and devote additional attention and resources to pollution control.

Bayesian heterogeneity in a meta–analysis with two studies and binary data

The meta–analysis of two trials is valuable in many practical situations, such as studies of rare and/or orphan diseases focussed on a single intervention. In this context, additional concerns, like small sample size and/or heterogeneity in the results obtained, might make standard frequentist and Bayesian techniques inappropriate. In a meta–analysis, moreover, the presence of between–sample heterogeneity adds model uncertainty, which must be taken into consideration when drawing inferences. We suggest that the most appropriate way to measure this heterogeneity is by clustering the samples and then determining the posterior probability of the cluster models. The meta–inference is obtained as a mixture of all the meta–inferences for the cluster models, where the mixing distribution is the posterior model probability. We present a simple two–component form of Bayesian model averaging that is unaffected by characteristics such as small study size or zero–cell counts, and which is capable of incorporating uncertainties into the estimation process. Illustrative examples are given and analysed, using real sparse binomial data.

Reliability analysis of motorcycle crash severity outcomes: Consideration of model selection uncertainty

Objective While a large amount of work has been conducted on different types of crash injury severity models, model selection uncertainty remains a critical issue in traffic safety research. The objective of this study is to handle model selection uncertainty by combining multiple models. Methods Motorcycle crashes in Michigan from 2010 to 2014 are collected for the analysis. A model averaging approach is used to integrate useful information from three commonly used crash injury severity models: multinomial logit model, ordered logit model, and ordered probit model to deal with the situation where the model selection uncertainty exists in crash data analysis. The ratios of model posterior probabilities between models are used to quantify the model selection uncertainty. In addition, the effectiveness of the method is illustrated by comparing it with the single-best model. Results The ratios of model posterior probabilities among models approximate to 1. It means that three models have the same importance in statistical analysis of motorcycle injury severity, resulting in model selection uncertainty. The comparison between the results of model averaging approach and single-best model shows that the single-best model tends to overestimate the effects of risk factors on motorcycle injury severities because of ignoring the model selection uncertainty; parameter errors and confidence intervals of model averaging are greater and wider than those of the single-best model due to between-model uncertainty included in the model averaging; some risk factors are significant in the model averaging approach while not in the single-best model. Results from model averaging approach reveal that drunk or riding under influence, angle/sideswipe/head on crashes, speed limit of 35 mph or higher, and signal control play significant roles in the motorcycle crashes. Conclusions The study contributes to the existing crash injury-severity literature by developing a model averaging approach to explore the relationship between motorcyclist’s injury-severity and its contributing factors. The model averaging approach overcomes the limitations of the current crash injury-severity modeling approaches by (1) revealing the potential model selection uncertainty among injury-severity models with model posterior probabilities; (2) more reliably accounting for the effects of risk factors on motorcyclist’ injury severities through integrating all information from the candidate models; and (3) better presenting the underlying unreliability of the analysis results from each individual model.