'Bayesian inference challenges, perspectives, and prospects' theme issue includes this article.
Latent variable models are a frequently used category within the field of statistics. Deep latent variable models, augmented with neural networks, now exhibit significantly enhanced expressivity, resulting in their widespread adoption within machine learning. These models' inability to readily evaluate their likelihood function compels the use of approximations for inference tasks. A standard approach involves the maximization of an evidence lower bound (ELBO) generated from a variational approximation of the latent variables' posterior distribution. The standard ELBO, despite its theoretical validity, can offer a very loose approximation if the variational family is insufficiently rich. A common method to make these bounds more precise is to make use of an impartial, low-variance Monte Carlo estimate of the evidence's support. This section highlights recent advancements in importance sampling, Markov chain Monte Carlo, and sequential Monte Carlo techniques employed to reach this desired outcome. Included in the thematic issue 'Bayesian inference challenges, perspectives, and prospects' is this article.
Randomized clinical trials, while essential for clinical research, are often plagued by high expenses and the growing obstacle of patient recruitment. The utilization of real-world data (RWD) extracted from electronic health records, patient registries, claims data, and other sources is currently gaining momentum as a means of either substituting or complementing controlled clinical trials. Combining information from a multitude of sources, in this procedure, necessitates inference within the Bayesian paradigm's framework. We consider existing methods in conjunction with a new non-parametric Bayesian (BNP) approach. BNP priors are a natural approach to account for differences in patient populations, allowing for a comprehensive understanding and accommodation of population heterogeneities in various data sets. A key consideration in single-arm studies is the utilization of RWD for a synthetic control group, which we examine in detail. Within the proposed methodology, the model-driven adaptation ensures that patient populations are equivalent in the current study and the (modified) real-world data. This implementation process uses common atom mixture models. Inference is remarkably simplified by the sophisticated structure of these models. Using the weight ratios, one can determine the adjustment required to account for population disparities in the mixtures. As part of the theme issue dedicated to 'Bayesian inference challenges, perspectives, and prospects,' this article is presented.
Within the paper's scope, shrinkage priors are detailed, demonstrating increasing shrinkage across a series of parameters. A review of Legramanti et al.'s (2020, Biometrika 107, 745-752) cumulative shrinkage process, commonly referred to as CUSP, is presented here. read more The spike probability of the spike-and-slab shrinkage prior, as presented in (doi101093/biomet/asaa008), stochastically increases, built upon the stick-breaking representation of a Dirichlet process prior. The initial extension of this CUSP prior involves the inclusion of arbitrary stick-breaking representations, drawn from beta distributions. We further demonstrate, as our second contribution, that exchangeable spike-and-slab priors, prominent in sparse Bayesian factor analysis, can be expressed as a finite generalized CUSP prior, derived straightforwardly from the decreasing order of the slab probabilities. As a result, exchangeable spike-and-slab shrinkage priors demonstrate an augmenting shrinkage pattern as the position of the column in the loading matrix grows, while remaining independent of any prescribed ordering for the slab probabilities. This paper's results are validated through their successful implementation within the context of sparse Bayesian factor analysis. An innovative exchangeable spike-and-slab shrinkage prior, drawing inspiration from the triple gamma prior of Cadonna et al. (2020), is introduced in Econometrics 8, article 20. A simulation investigation reveals the usefulness of (doi103390/econometrics8020020) in determining the uncharacterized quantity of driving factors. This article is integral to the 'Bayesian inference challenges, perspectives, and prospects' theme issue.
Many applications reliant on counting demonstrate a significant proportion of zero entries (zero-heavy data). The sampling distribution for positive integers is a critical part of the hurdle model, which in turn explicitly models the probability of zero counts. Our analysis integrates data from a multitude of counting operations. An important area of study in this context is the identification of count patterns and the subsequent clustering of subjects. We describe a novel Bayesian approach to the task of clustering multiple, potentially correlated, zero-inflated processes. A joint model for zero-inflated counts is proposed, characterized by a hurdle model applied to each process, incorporating a shifted negative binomial sampling mechanism. The model parameters' influence on the processes' independence results in a substantial reduction of parameters compared to traditional multivariate approaches. Subject-specific probabilities of zero-inflation and the parameters of the sampling distribution are dynamically modeled using a flexible finite mixture with a variable number of components, enhanced with additional features. Subjects are grouped in two levels; the outer grouping is determined by zero/non-zero patterns, the inner by the sampling distribution. For posterior inference, Markov chain Monte Carlo techniques are specifically designed. Our proposed approach is highlighted in an application using the WhatsApp messaging service. This article forms part of the thematic issue 'Bayesian inference challenges, perspectives, and prospects'.
Bayesian approaches, now fundamental to the analytical toolkits of statisticians and data scientists, stem from three decades of progress in philosophy, theory, methodology, and computational techniques. Applied professionals, whether staunch Bayesians or opportunistic adopters, can now benefit from numerous aspects of the Bayesian paradigm. This paper investigates six contemporary trends and difficulties in applied Bayesian statistics, revolving around intelligent data collection, new information sources, federated analytical techniques, inference approaches for implicit models, model transfer methods, and the creation of beneficial software products. This article is an element of the special theme issue dedicated to 'Bayesian inference challenges, perspectives, and prospects'.
A decision-maker's uncertainty is represented by us, employing e-variables. Much like the Bayesian posterior, this e-posterior empowers predictive modeling using arbitrary loss functions, whose form may not be initially known. The Bayesian posterior is not the same as this method, which produces risk bounds that are frequentist-valid, no matter the appropriateness of the prior. Should the e-collection (functionally the same as the Bayesian prior) be chosen inadequately, the bounds loosen rather than become invalid, making e-posterior minimax strategies safer than Bayesian ones. The e-posterior representation of the Kiefer-Berger-Brown-Wolpert conditional frequentist tests, previously unified in a partial Bayes-frequentist approach, serves to illustrate the resulting quasi-conditional paradigm. This article forms part of a special edition dedicated to 'Bayesian inference challenges, perspectives, and prospects'.
The American criminal legal system finds significant utility in forensic science applications. In the historical context, many forensic disciplines, including firearms examination and latent print analysis, based on features, have not shown scientific validity. As a way to assess the validity of these feature-based disciplines, especially their accuracy, reproducibility, and repeatability, recent research has involved black-box studies. In forensic examinations, examiners often fail to address all test questions or opt for a 'don't know' response. In the statistical analyses of current black-box studies, these high levels of missing data are omitted. To the detriment of reproducibility, black-box study authors often do not provide the data needed to effectively recalculate estimates concerning the large proportion of missing responses. Extrapolating from prior work in small area estimation, our approach utilizes hierarchical Bayesian models that avoid the necessity of auxiliary data to account for non-response. These models allow for the first formal investigation of the role missingness plays in the reported error rate estimations of black-box studies. read more Our analysis suggests that error rates currently reported as low as 0.4% are likely to be much higher, perhaps as high as 84%, once non-response and inconclusive results are accounted for, and treated as correct. If inconclusive responses are considered missing data, this error rate climbs above 28%. The missingness problem within black-box studies is not satisfactorily answered by these proposed models. The provision of supplemental data provides a foundation for developing new methodologies that adapt to missing values within error rate estimation processes. read more Within the broader scope of 'Bayesian inference challenges, perspectives, and prospects,' this article sits.
Algorithmic cluster analyses are surpassed by Bayesian methods, which furnish not only the precise locations of clusters, but also the probabilistic uncertainties in the clustering patterns and the structures within each. Bayesian cluster analysis, both model-based and loss-based, is examined, highlighting the critical role of the kernel or loss function chosen and how prior distributions impact the results. The advantages of clustering cells and discovering latent cell types in single-cell RNA sequencing data are demonstrated in an application specifically designed for studying embryonic cellular development.