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Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex,…
An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through…
The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatoryor input variables X. We consider Bayesian models for this task. In…
One of the main goals of mathematical modeling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite…
This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…
In this work, we develop an objective Bayesian framework for the Dhillon probability distribution. We explicitly derive three objective priors: the Jeffreys prior, the overall reference prior, and the maximal data information prior. We show…
Linear mixed effects models are widely used in statistical modelling. We consider a mixed effects model with Bayesian variable selection in the random effects using spike-and-slab priors and developed a variational Bayes inference scheme…
Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…
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…
We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…
This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum $\gamma$-divergence estimator is well-known to work well estimation against heavy contamination. The robust Bayesian…
Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…
An objective Bayesian approach to estimate the number of degrees of freedom $(\nu)$ for the multivariate $t$ distribution and for the $t$-copula, when the parameter is considered discrete, is proposed. Inference on this parameter has been…
The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…
For many years it was routine to use equal model prior probabilities in Bayesian model uncertainty analysis. At least twenty years ago it became clear that this was problematic, leading to support of much too large models in the…
The original formulation of BEAMS - Bayesian Estimation Applied to Multiple Species - showed how to use a dataset contaminated by points of multiple underlying types to perform unbiased parameter estimation. An example is cosmological…