Bayesian Estimation and Model Selection in Ordered Latent Class Models for Polytomous Items

The dynamic nature of the ocean environment presents numerous challenges to parameter estimation in ocean acoustics. We present a variational Bayesian method which selects an optimal model for parameter estimation in ocean acoustics using Gaussian process (GP) regression. GP model selection is based on Bayesian model selection, which treats the parameters and kernel selection of the model as hyperparameters and uses Bayesian inference to compute a model’s likelihood with respect to its hyperparameters. However, in Bayesian model selection, the integrals over parameter space are often intractable and require approximation or sampling methods such as Markov chain Monte Carlo. GP renders these integrals tractable by treating hyperparameters as multivariate Gaussian distributions, which greatly speeds up the optimization. Furthermore, model selection using GPs allows for straightforward evaluation of uncertainty in the selected model’s likelihood. In this study, we compare results of acoustic parameter estimation from Bayesian and GP model selection using an ocean acoustic propagation model.

Bayesian model selection for nonlinear aeroelastic systems using wind-tunnel data

The creep deformation process is constructed by complex interactions of multiple factors, and the measurement of creep deformation requires enormous economic costs and a long experimental time, so there is a small amount of measurement data. In such a situation, multiple models are often proposed to explain the same experimental data. The coexistence of multiple models based on different physical assumptions makes it difficult to understand the creep deformation process. The purpose of this study is to construct a framework to compare and evaluate coexistence models based on measurement data using the Bayesian model selection framework. Basically, in the creep deformation model, basis functions, usually the exponential function eat or power function tb, corresponding to the primary creep stage and the tertiary creep stage are set, and the time series of the whole creep deformation process is regressed as the linear sum of these bases. The parameters a and b of the basis functions are parameters that must also be optimized to regress the time series data. Izuno et al. proposed the Bayesian model selection method for the creep deformation process, and it was confirmed that the model with the linear term corresponding to the secondary creep stage, called the modified theta method, is a good model compared to the model without adding the linear term. To obtain the criterion of Bayesian model selection analytically, which can reduce the computational cost greatly, Izuno et al. treated only the regression coefficients as the probabilistic parameter of the creep model. In this method, parameters a and b of the basis functions are optimized by a grid search. Because the grid search requires significant computational costs if multiple basis functions are set for each creep stage, as in the model proposed by Kimura et al., it is difficult to apply the algorithm to models with multiple bases. In addition, if parameters a and b of the basis functions correlate with the regression coefficients, the method of Izuno et al. would offer a biased evaluation of the models. To improve such an existing method, we proposed a Bayesian model selection method that treats the parameters of the basis functions as probabilistic parameters. The large computational cost to treat the parameters of the basis functions as probabilistic parameters was reduced using the exchange Monte Carlo method, which is an efficient sampling method. By applying our proposed method to the evaluation of the creep deformation model, information was obtained to understand the creep deformation process deeply. For example, it was confirmed that there exists a model in which there is a correlation between the parameter of basis function and the regression coefficients.

Bayesian analysis of spatial dynamic panel data model with convex combinations of different spatial weight matrices: A reparameterized approach

Recently, Bayesian diagnostic classification modeling has been becoming popular in health psychology, education, and sociology. Typically information criteria are used for model selection when researchers want to choose the best model among alternative models. In Bayesian estimation, posterior predictive checking is a flexible Bayesian model evaluation tool, which allows researchers to detect Q‐matrix misspecification. However, model selection methods using posterior predictive checking (PPC) for Bayesian DCM are not well investigated. Thus, this research aims to propose a novel model selection approach using posterior predictive checking with limited‐information statistics for selecting the correct Q‐matrix. A simulation study was conducted to examine the performance of the proposed method. Furthermore, an empirical example was provided to illustrate how it can be used in real scenarios.

기존의 frequentist 추론에 비해 Bayesian 추론에서의 가설 검정 및 모형 선택 문제는 학자들 간에 일치된 견해를 보이지 못하고 있으며 아직도 논란이 되는 것들이 많다. Bayesian 추론에서 가설 검정 및 모형 선택의 기준으로 널리 쓰이는 Bayes factor는 이해하기 쉬우나 여러 경우에 구하기 어려운 단점이 존재한다. 그 외에 다른 기준으로 Spiegelhalter 등 (2002)가 제시한 DIC(Deviance Information Criterion)과 frequentist 추론에서의 P-value에 대비되는 Bayesian P-value가 있다. 본 논문에서는 Swiss banknote 자료를 Bayesian 로지스틱 회귀모형으로 분석하고 관련 기준들을 구하여 각 기준들이 일관성 있는 결론을 보이는지 확인하고자 한다. Model selection and hypothesis testing problems in Bayesian inference are still debated between scholars. Bayesian factors traditionally used as a criterion in Bayesian hypothesis testing and model selection, are easy to understand but sometimes hard to compute. In addition, there are other model selection criterions such as DIC(Deviance Information Criterion) by Spiegelhalter et al. (2002) and Bayesian P-values for testing. In this paper, we briefly introduce the Bayesian hypothesis testing and model selection procedure. In addition we have applied a Bayesian inference to Swiss banknote data by a fitting logistic regression model and computing several test statistics to see if they provide consistent results.

Acoustic emission analysis during fatigue crack propagation by Bayesian statistical modeling

Diseases of fruit and foliage caused by fungi and oomycetes are generally controlled by the application of fungicides. The use of decision support systems (DSSs) may assist to optimize fungicide programs to enhance application on the basis of risk associated with disease outbreak. Case-by-case evaluations demonstrated the performance of DSSs for disease control, but an overall assessment of the efficacy of DSSs is lacking. A literature review was conducted to synthesize the results of 67 experiments assessing DSSs. Disease incidence data were obtained from published peer-reviewed field trials comparing untreated controls, calendar-based and DSS-based fungicide programs. Two meta-analysis generic models, a “fixed-effects” vs. a “random-effects” model within the framework of generalized linear models were evaluated to assess the efficacy of DSSs in reducing incidence. All models were fit using both frequentist and Bayesian estimation procedures and the results compared. Model including random effects showed better performance in terms of AIC or DIC and goodness of fit. In general, the frequentist and Bayesian approaches produced similar results. Odds ratio and incidence ratio values showed that calendar-based and DSS-based fungicide programs considerably reduced disease incidence compared to the untreated control. Moreover, calendar-based and DSS-based programs provided similar reductions in disease incidence, further supporting the efficacy of DSSs.

Modeling the effects of telephone nursing on healthcare utilization

ABSTRACTTruncated regression models arise in many applications where it is not possible to observe values of the response variable that are above or below certain thresholds. We propose a Bayesian truncated beta nonlinear mixed-effects model by considering the truncated variable to follow a truncated beta distribution. The mean parameter of the distribution is modeled by a nonlinear function of unknown fixed parameters and covariates and by random effects. The proposed model is suitable for response variables, y, bounded to an interval without the need to consider a transformed variable to apply the well-known beta regression model and its extensions, which are primarily appropriate for responses in the interval . Bayesian estimates and credible intervals are computed based on draws from the posterior distribution of parameters generated using an MCMC procedure. Posterior predictive checks, Bayesian standardized residuals and a Bayesian influence measures are considered for model diagnostics. Model selection is performed using the sum of log-CPO metric and a Bayesian model selection criterion based on Bayesian mixture modeling. Simulated datasets are used for prior sensitivity analysis and to evaluate finite sample properties of Bayesian estimates. The model is applied to a real dataset on soil–water retention.

Ciprian M. Crainiceanu 'Likelihood ratio testing for zero variance components in linear mixed effects models.' - Daowen Zhang & Xihong Lin 'Variance component testing in generalized linear mixed models for longitudinal/clustered data and other related topics.' -Satkartar Kinney & David Dunson 'Bayesian model uncertainty in mixed effects models.' -Bo Cai & David Dunson 'Bayesian variable selection in generalized linear mixed models.' - Peter M. Bentler & Jiajuan Liang 'A unified approach to two-level structural equation models and linear mixed effects models.' - Sik-Yum Lee & Xin-Yuan Song 'Bayesian model comparison of structural equation models.' - Joyee Ghosh & David Dunson 'Bayesian model selection in factor analytic models.'

Bayesian model selection and parameter estimation is attracting a lot of interest in the astronomical community because of its power and logical consistency. Markov chain Monte Carlo provides the computational power for Bayesian parameter estimation problems in large parameter spaces but needs to be supported with other numerical techniques for efficient exploration of multi-modal probability distributions. Bayesian model selection is easy in concept but remains a difficult challenge for large parameter spaces. My comments here on the paper by Roberto Trotta are based on lessons learned from developing a controlled statistical fusion approach to some of these issues.KeywordsMarkov Chain Monte CarloMarginal LikelihoodProposal DistributionMarkov Chain Monte Carlo AlgorithmMarkov Chain Monte Carlo SampleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The key to the numerical implementation of Bayesian model selection and Bayesian model averaging is the computation of the model evidences. Defined as the probability of the observed data given a model, the model evidence can be shown to be equal to the normalising constant of the underlying posterior distribution. When posterior unimodality is a valid assumption, it can be adequately evaluated using methods such as the Laplace method and standard Markov chain Monte Carlo (MCMC) simulation techniques. However, in cases where posterior distributions are significantly multimodal, which typically arise in ill-conditioned problems, these methods tend to get trapped in local modes and consequently do not yield robust results. To facilitate movement around the multimodal parameter space, we introduce the reciprocal temperature parameter s and define an auxiliary distribution over both the parameters of interest and s. The Gibbs sampler is then employed to simulate this joint distribution and an importance reweight- ing procedure is incorporated for adaptively updating the ratios of the partition functions. The thermodynamic integration approach is adopted to evaluate the partition function at the highest temperature, at which point departure from unimodality is expected to be insignificant. The partition function at s = 1, which in the new formulation corresponds to the desired evidence value, can thus be obtained by multiplying the partition function evaluated at the highest temperature with the ratio of these two partition functions. The algorithm is illustrated by applying it to a simulated trimodal distribution.

In the context of Bayesian inversion for scientific and engineering modeling, Markov chain Monte Carlo (MCMC) sampling strategies have become the benchmark due to their flexibility and robustness in dealing with arbitrary posterior probability density functions (PDFs). However, these algorithms have been shown to be inefficient when sampling from high-dimensional posterior distributions or exhibit multimodality and/or strong parameter correlations. In such contexts, transitional MCMC (TMCMC) provides a more efficient alternative. Despite the recent applicability for Bayesian updating and model selection across a variety of disciplines, TMCMC may require a prohibitive number of tempering stages when the prior pdf is significantly different from the target posterior. Furthermore, the need to start with an initial set of samples from the prior distribution may present a challenge when dealing with implicit priors, e.g., based on feasible regions. Finally, TMCMC cannot be used for inverse problems with improper prior PDFs that represent a lack of prior knowledge on all or a subset of parameters. A generalization of TMCMC is proposed that alleviates such challenges and limitations toward providing a more robust and efficient tempering sampling strategy. We present convergence analysis, proving that the distance between the intermediate distributions and the target posterior distribution monotonically decreases as the algorithm proceeds. We also demonstrate the advantages of the proposed generalization through a series of test problems and an engineering application in the oil and gas industry.

While risk-adjusted outcomes are often used to compare the performance of hospitals and physicians, the most appropriate functional form for the risk adjustment process is not always obvious for continuous outcomes such as costs. Semi-log models are used most often to correct skewness in cost data, but there has been limited research to determine whether the log transformation is sufficient or whether another transformation is more appropriate. This study explores the most appropriate functional form for risk-adjusting the cost of coronary artery bypass graft (CABG) surgery. Data included patients undergoing CABG surgery at four hospitals in the midwest and were fit to a Box-Cox model with random coefficients (BCRC) using Markov chain Monte Carlo methods. Marginal likelihoods and Bayes factors were computed to perform model comparison of alternative model specifications. Rankings of hospital performance were created from the simulation output and the rankings produced by Bayesian estimates were compared to rankings produced by standard models fit using classical methods. Results suggest that, for these data, the most appropriate functional form is not logarithmic, but corresponds to a Box-Cox transformation of -1. Furthermore, Bayes factors overwhelmingly rejected the natural log transformation. However, the hospital ranking induced by the BCRC model was not different from the ranking produced by maximum likelihood estimates of either the linear or semi-log model.