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A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…

The goal of causal inference is to understand the outcome of alternative courses of action. However, all causal inference requires assumptions. Such assumptions can be more influential than in typical tasks for probabilistic modeling, and…

Multiple imputation has become one of the standard methods in drawing inferences in many incomplete data applications. Applications of multiple imputation in relatively more complex settings, such as high-dimensional clustered data, require…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

In this manuscript, we discuss the substantial importance of Bayesian reasoning in Social Science research. Particularly, we focus on foundational elements to fit models under the Bayesian paradigm. We aim to offer a frame of reference for…

Survey data are often collected under multistage sampling designs where units are binned to clusters that are sampled in a first stage. The unit-indexed population variables of interest are typically dependent within cluster. We propose a…

Regression plays a key role in many research areas and its variable selection is a classic and major problem. This study emphasizes cost of predictors to be purchased for future use, when we select a subset of them. Its economic aspect is…

Probability forecasting is common in the geosciences, the finance sector, and elsewhere. It is sometimes the case that one has multiple probability-forecasts for the same target. How is the information in these multiple forecast systems…

The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…

In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by…

Bayesian models of legal arguments generally aim to produce a single integrated model, combining each of the legal arguments under consideration. This combined approach implicitly assumes that variables and their relationships can be…

Economic evaluations from individual-level data are an important component of the process of technology appraisal, with a view to informing resource allocation decisions. A critical problem in these analyses is that both effectiveness and…

When the data do not conform to the hypothesis of a known sampling-variance, the fitting of a constant to a set of measured values is a long debated problem. Given the data, fitting would require to find what measurand value is the most…

Bayesian inference is a powerful tool for combining information in complex settings, a task of increasing importance in modern applications. However, Bayesian inference with a flawed model can produce unreliable conclusions. This review…

A major challenge in sample-based inference (SBI) for Bayesian neural networks is the size and structure of the networks' parameter space. Our work shows that successful SBI is possible by embracing the characteristic relationship between…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…

Data clustering, including problems such as finding network communities, can be put into a systematic framework by means of a Bayesian approach. The application of Bayesian approaches to real problems can be, however, quite challenging. In…

Classically, Bayesian clustering interprets each component of a mixture model as a cluster. The inferred clustering posterior is highly sensitive to any inaccuracies in the kernel within each component. As this kernel is made more flexible,…

Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to…