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The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be…

We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

Parton distribution functions (PDFs) form an essential part of particle physics calculations. Currently, the most precise predictions for these non-perturbative functions are generated through fits to global data. A problem that several PDF…

In many applications, the dataset under investigation exhibits heterogeneous regimes that are more appropriately modeled using piece-wise linear models for each of the data segments separated by change-points. Although there have been much…

We develop a new longitudinal count data regression model that accounts for zero-inflation and spatio-temporal correlation across responses. This project is motivated by an analysis of Iowa Fluoride Study (IFS) data, a longitudinal cohort…

Although variational autoencoders (VAE) are successfully used to obtain meaningful low-dimensional representations for high-dimensional data, the characterization of critical points of the loss function for general observation models is not…

Many data sets cannot be accurately described by standard probability distributions due to the excess number of zero values present. For example, zero-inflation is prevalent in microbiome data and single-cell RNA sequencing data, which…

Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…

In this paper, we explore advanced modifications to the Tweedie regression model in order to address its limitations in modeling aggregate claims for various types of insurance such as automobile, health, and liability. Traditional Tweedie…

This article introduces a k-Inflated Negative Binomial mixture distribution/regression model as a more flexible alternative to zero-inflated Poisson distribution/regression model. An EM algorithm has been employed to estimate the model's…

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…

In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…

We present a joint copula-based model for insurance claims and sizes. It uses bivariate copulae to accommodate for the dependence between these quantities. We derive the general distribution of the policy loss without the restrictive…

A novel sequential inferential method for Bayesian dynamic generalised linear models is presented, addressing both univariate and multivariate $k$-parametric exponential families. It efficiently handles diverse responses, including…

Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive…

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…

Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…

Over the last decades, the challenges in applied regression and in predictive modeling have been changing considerably: (1) More flexible model specifications are needed as big(ger) data become available, facilitated by more powerful…

Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…