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Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty.…

Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…

Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as…

Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is…

Bayesian networks (BNs) are a widely used class of probabilistic graphical models employed in numerous application domains. However, inferring the network's graphical structure from data remains challenging. Bayesian structure learners…

In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior…

Quantitative studies in many fields involve the analysis of multivariate data of diverse types, including measurements that we may consider binary, ordinal and continuous. One approach to the analysis of such mixed data is to use a copula…

Inference in Bayesian statistics involves the evaluation of marginal likelihood integrals. We present algebraic algorithms for computing such integrals exactly for discrete data of small sample size. Our methods apply to both uniform priors…

Tensors are ubiquitous in science and engineering and tensor factorization approaches have become important tools for the characterization of higher order structure. Factorizations includes the outer-product rank Canonical Polyadic…

In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…

We investigate the sets of joint probability distributions that maximize the average multi-information over a collection of margins. These functionals serve as proxies for maximizing the multi-information of a set of variables or the mutual…

In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider…

It is common practice to use Laplace approximations to compute marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to…

This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…

In this note, we consider the problem of estimating multinomial cell probabilities under the entropy loss when side information in aggregated data is available. We use the Jeffreys prior to obtain Bayes estimators. It is shown that by…

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…

With several examples and in an analysis of the Pantheon+ supernova sample we discuss the properties of the marginal posterior distribution versus the profiled posterior distribution -- the profile likelihood in a Bayesian disguise. We…

Factor models are widely applied to the analysis of multivariate data across disparate fields of research. However, modern scientific data are often incomplete, and estimating a factor model from partially observed data can be very…

We develop an efficient Bayesian sequential inference framework for factor analysis models observed via various data types, such as continuous, binary and ordinal data. In the continuous data case, where it is possible to marginalise over…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…