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If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…

We explore the estimation of generalized additive models using basis expansion in conjunction with Bayesian model selection. Although Bayesian model selection is useful for regression splines, it has traditionally been applied mainly to…

The Gaussian mixture model is widely used in unsupervised learning, owing to its simplicity and interpretability. However, a fundamental limitation of the classical Gaussian mixture model is that it forces each observation to belong to…

Do expert-defined or diagnostically-labeled data groups align with clusters inferred through statistical modeling? If not, where do discrepancies between predefined labels and model-based groupings occur and why? In this work, we introduce…

Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…

Handling outliers is a fundamental challenge in multivariate data analysis because outliers may distort the structures of correlation or conditional independence. Although robust Bayesian inference has been extensively studied in univariate…

The association between a continuous and an ordinal variable is commonly modeled through the polyserial correlation model. However, this model, which is based on a partially-latent normality assumption, may be misspecified in practice, due…

We introduce a methodology for robust Bayesian estimation with robust divergence (e.g., density power divergence or {\gamma}-divergence), indexed by a single tuning parameter. It is well known that the posterior density induced by robust…

Robust Bayesian models are appealing alternatives to standard models, providing protection from data that contains outliers or other departures from the model assumptions. Historically, robust models were mostly developed on a case-by-case…

In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture…

Effective and accurate model selection is an important problem in modern data analysis. One of the major challenges is the computational burden required to handle large data sets that cannot be stored or processed on one machine. Another…

The efficient modeling for disorder in a phenomena depends on the chosen score and objective functions. The main parameters in modeling are location, scale and shape. The exponential power distribution known as generalized Gaussian is…

We describe and analyze a broad class of mixture models for real-valued multivariate data in which the probability density of observations within each component of the model is represented as an arbitrary combination of basis functions.…

Mixture models are a standard tool in statistical analyses, widely used for density modeling and model-based clustering. In this work, we propose a Bayesian mixture model with repulsion between mixture components. Such repulsion helps…

We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet…

Traditional power flow methods often adopt certain assumptions designed for passive balanced distribution systems, thus lacking practicality for unbalanced operation. Moreover, their computation accuracy and efficiency are heavily subject…

Many processes in chemistry and physics take place on timescales that cannot be explored using standard molecular dynamics simulations. This renders the use of enhanced sampling mandatory. Here we introduce an enhanced sampling method that…

Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…

Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…

Outlying observations can be challenging to handle and adversely affect subsequent analyses, especially in data with increasing dimensional complexity. Although outliers are not always undesired anomalies in the data and may possess…