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We derive the conjugate prior of the Dirichlet and beta distributions and explore it with numerical examples to gain an intuitive understanding of the distribution itself, its hyperparameters, and conditions concerning its convergence. Due…
Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool which allows one to describe the relationships among the variables of interest.…
Finite mixture models are flexible methods that are commonly used for model-based clustering. A recent focus in the model-based clustering literature is to highlight the difference between the number of components in a mixture model and the…
We consider joint inversion for two or more unknown parameters from observational data in the Bayesian framework. Standard approaches often either treat the parameters as independent or impose structural similarity through regularisation…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…
The design of an experiment can be always be considered at least implicitly Bayesian, with prior knowledge used informally to aid decisions such as the variables to be studied and the choice of a plausible relationship between the…
Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability…
Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions…
In Bayesian regression models with categorical predictors, constraints are needed to ensure identifiability when using all $K$ levels of a factor. The sum-to-zero constraint is particularly useful as it allows coefficients to represent…
Model Updating is frequently used in Structural Health Monitoring to determine structures' operating conditions and whether maintenance is required. Data collected by sensors are used to update the values of some initially unknown…
In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…
We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…
High-dimensional mediation analysis aims to identify mediating pathways and to estimate indirect effects linking an exposure to an outcome. In this paper, we propose a Bayesian framework to address key challenges in these analyses,…
Parameter estimates for associated genetic variants, report ed in the initial discovery samples, are often grossly inflated compared to the values observed in the follow-up replication samples. This type of bias is a consequence of the…
Several bivariate beta distributions have been proposed in the literature. In particular, Olkin and Liu (2003) proposed a 3 parameter bivariate beta model, which Arnold and Ng (2011) extend to 5 and 8 parameter models. The 3 parameter model…
Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…
Low-rank matrix estimation from incomplete measurements recently received increased attention due to the emergence of several challenging applications, such as recommender systems; see in particular the famous Netflix challenge. While the…
We consider a Bayesian method for simultaneous quantile regression on a real variable. By monotone transformation, we can make both the response variable and the predictor variable take values in the unit interval. A representation of…
Machine learning-aided clinical decision support has the potential to significantly improve patient care. However, existing efforts in this domain for principled quantification of uncertainty have largely been limited to applications of…
We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…