'Bayesian inference challenges, perspectives, and prospects' theme issue includes this article.

In the statistical realm, latent variable models are frequently employed. Deep latent variable models, augmented with neural networks, now exhibit significantly enhanced expressivity, resulting in their widespread adoption within machine learning. One impediment to these models is their intractable likelihood function, which compels the use of approximations for performing inference. A standard approach involves the maximization of an evidence lower bound (ELBO) generated from a variational approximation of the latent variables' posterior distribution. While the standard ELBO is a useful concept, its bound can be quite loose when the variational family lacks sufficient capacity. A general approach to narrowing these boundaries is the utilization of an impartial, low-variance Monte Carlo estimate of the evidentiary value. This section highlights recent advancements in importance sampling, Markov chain Monte Carlo, and sequential Monte Carlo techniques employed to reach this desired outcome. 'Bayesian inference challenges, perspectives, and prospects' is the focus of this included article.

Despite their crucial role in clinical research, randomized clinical trials are frequently hampered by exorbitant expenses and the increasing difficulty of patient enrollment. The trend toward utilizing real-world data (RWD) from electronic health records, patient registries, claims data, and other similar data sources is growing as a potential alternative to, or an adjunct to, controlled clinical trials. In this procedure, the act of combining information from various sources necessitates inference, guided by the Bayesian paradigm. In this analysis, we look at some current methods and a novel non-parametric Bayesian (BNP) technique. Adjusting for discrepancies in patient populations is inherently linked to the use of BNP priors, enabling an understanding of and adaptation to the heterogeneity across various data sources. We scrutinize the particular implementation of responsive web design (RWD) to produce a synthetic control group, a critical aspect of single-arm treatment studies. The model-calculated adjustment is at the heart of the proposed approach, aiming to create identical patient groups in the current study and the adjusted real-world data. Implementation of this involves common atom mixture models. The structure of such models facilitates a substantial simplification of inference. The disparity in populations can be quantified by examining the weight ratios within these mixtures. Within the thematic framework of 'Bayesian inference challenges, perspectives, and prospects,' this piece resides.

Using shrinkage priors, the paper explores how the degree of shrinkage augments in a sequence 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. 2-deoxyglucose 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. This CUSP prior is initially advanced by incorporating arbitrary stick-breaking representations, the genesis of which lies in beta distributions. We present, as our second contribution, a demonstration that exchangeable spike-and-slab priors, used extensively in sparse Bayesian factor analysis, can be shown to correspond to a finite generalized CUSP prior, easily derived from the decreasing order statistics of the slab probabilities. Consequently, exchangeable spike-and-slab shrinkage priors suggest that shrinkage intensifies as the column index within the loading matrix escalates, while avoiding explicit ordering restrictions on slab probabilities. This paper's results are validated through their successful implementation within the context of sparse Bayesian factor analysis. In Econometrics 8, article 20, Cadonna et al. (2020) detail a triple gamma prior, which underpins the development of a novel exchangeable spike-and-slab shrinkage prior. In a simulation study, (doi103390/econometrics8020020) proved useful in accurately estimating the number of underlying factors, which was previously unknown. This theme issue, 'Bayesian inference challenges, perspectives, and prospects,' includes this article.

Applications involving the enumeration of items frequently demonstrate a high concentration of zero counts (excess zeros data). The hurdle model, a prevalent data representation, explicitly calculates the probability of zero counts, simultaneously assuming a sampling distribution for positive integers. Multiple counting processes contribute data to our analysis. An important area of study in this context is the identification of count patterns and the subsequent clustering of subjects. We propose a novel Bayesian method for clustering multiple, possibly 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. Considering the model parameters, the different processes are assumed independent, which contributes to a significant reduction in parameters compared to conventional multivariate techniques. A flexible model, comprising an enriched finite mixture with a variable number of components, captures the subject-specific zero-inflation probabilities and the parameters of the sampling distribution. The subjects are clustered in two levels, one based on the presence or absence of zeros/non-zeros (outer clustering), and another based on the sampling distribution (inner clustering). For posterior inference, Markov chain Monte Carlo techniques are specifically designed. Our proposed approach is highlighted in an application using the WhatsApp messaging service. The theme issue 'Bayesian inference challenges, perspectives, and prospects' encompasses this article.

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. From dedicated Bayesian devotees to opportunistic users, the advantages of the Bayesian paradigm can now be enjoyed by applied professionals. This paper examines six contemporary opportunities and challenges within applied Bayesian statistics, encompassing intelligent data collection, novel data sources, federated analysis, inference involving implicit models, model transfer, and the development of purposeful software applications. The theme issue, 'Bayesian inference challenges, perspectives, and prospects,' contains this particular article.

E-variables inform our representation of a decision-maker's uncertainty. This e-posterior, comparable to the Bayesian posterior, permits predictions against any loss function not previously defined. Unlike Bayesian posterior estimates, this approach guarantees frequentist validity for risk bounds, regardless of prior assumptions. A flawed selection of the e-collection (similar to the Bayesian prior) results in weaker, but not incorrect, bounds, thereby making e-posterior minimax decision procedures more secure than Bayesian ones. A re-interpretation of the influential Kiefer-Berger-Brown-Wolpert conditional frequentist tests, previously unified via a partial Bayes-frequentist approach, demonstrates the resulting quasi-conditional paradigm in terms of e-posteriors. This article is one of several included in the thematic section devoted to 'Bayesian inference challenges, perspectives, and prospects'.

Forensic science's impact is undeniable in the United States' criminal legal framework. In the historical context, many forensic disciplines, including firearms examination and latent print analysis, based on features, have not shown scientific validity. Recently, black-box studies have been proposed as a means of evaluating the validity of these feature-based disciplines, specifically regarding their accuracy, reproducibility, and repeatability. The forensic examiner practice in these studies frequently sees either non-response to all test items or selection of answers equivalent to 'unfamiliar' or 'don't know'. Missing data, present in high quantities, are not factored into the statistical analyses used in current black-box studies. Unfortunately, the individuals responsible for black-box analyses typically fail to supply the data essential for appropriately adjusting estimates associated with the high rate of missing data points. Leveraging existing methodologies in small area estimation, we propose employing hierarchical Bayesian models to accommodate non-response without resorting to auxiliary data. By using these models, we initiate a formal investigation into the impact that missingness has on error rate estimations in black-box studies. 2-deoxyglucose While error rates are reported at a surprisingly low 0.4%, accounting for non-response and categorizing inconclusive decisions as correct predictions reveals potential error rates as high as 84%. Classifying inconclusive results as missing responses further elevates the true error rate to over 28%. In addressing black-box studies, these models do not fully tackle the missing data issue. With the disclosure of additional information, these variables form the bedrock of new methodological approaches to account for missing data in the assessment of error rates. 2-deoxyglucose Within the broader scope of 'Bayesian inference challenges, perspectives, and prospects,' this article sits.

Bayesian cluster analysis surpasses algorithmic approaches by not only pinpointing cluster centers, but also by quantifying the uncertainty inherent in the clustering structure and the discernible patterns within each cluster. Bayesian cluster analysis, encompassing model-based and loss-function-driven approaches, is presented, along with a detailed examination of kernel/loss function selection and prior parameterization's impact. An application for studying embryonic cellular development utilizes the advantages of clustering cells and identifying latent cell types from single-cell RNA sequencing data.