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The development of mechanistic models of biological systems is a central part of Systems Biology. One major task in developing these models is the inference of the correct model parameters. Due to the size of most realistic models and their…

We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed…

We present a nonparametric Bayesian joint model for multivariate continuous and categorical variables, with the intention of developing a flexible engine for multiple imputation of missing values. The model fuses Dirichlet process mixtures…

We consider the problem of drawing samples from posterior distributions formed under a Dirichlet prior and a truncated multinomial likelihood, by which we mean a Multinomial likelihood function where we condition on one or more counts being…

Ordinary differential equations are arguably the most popular and useful mathematical tool for describing physical and biological processes in the real world. Often, these physical and biological processes are observed with errors, in which…

A sparse Dirichlet prior is proposed for estimating the abundance vector of hyperspectral images with a nonlinear mixing model. This sparse prior is led to an unmixing procedure in a semi-supervised scenario in which exact materials are…

Inferring the causal direction between two variables from their observation data is one of the most fundamental and challenging topics in data science. A causal direction inference algorithm maps the observation data into a binary value…

For data assumed to come from a finite mixture with an unknown number of components, it has become common to use Dirichlet process mixtures (DPMs) not only for density estimation, but also for inferences about the number of components. The…

In this paper we propose a model with a Dirichlet process mixture of gamma densities in the bulk part below threshold and a generalized Pareto density in the tail for extreme value estimation. The proposed model is simple and flexible…

A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…

Each training step for a variational autoencoder (VAE) requires us to sample from the approximate posterior, so we usually choose simple (e.g. factorised) approximate posteriors in which sampling is an efficient computation that fully…

With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that…

Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…

This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we…

Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…

Pattern-mixture models provide a transparent approach for handling missing data, where the full-data distribution is factorized in a way that explicitly shows the parts that can be estimated from observed data alone, and the parts that…

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…

In nonclinical pharmaceutical development, tolerance intervals are critical in ensuring product and process quality. They are statistical intervals designed to contain a specified proportion of the population with a given confidence level.…

In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…

Dirichlet Process(DP) is a Bayesian non-parametric prior for infinite mixture modeling, where the number of mixture components grows with the number of data items. The Hierarchical Dirichlet Process (HDP), is an extension of DP for grouped…