相关论文: Conjugacy properties of time-evolving Dirichlet an…

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…

A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with Dirichlet weights, and put a prior on the number of components---that is, to use a mixture of finite mixtures…

In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent…

Density estimation represents one of the most successful applications of Bayesian nonparametrics. In particular, Dirichlet process mixtures of normals are the gold standard for density estimation and their asymptotic properties have been…

Gamma process has been extensively used to model monotone degradation data. Statistical inference for the gamma process is difficult due to the complex parameter structure involved in the likelihood function. In this paper, we derive a…

We propose autoregressive Bayesian semi-parametric models for waiting times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on…

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

It is becoming increasingly clear that complex interactions among genes and environmental factors play crucial roles in triggering complex diseases. Thus, understanding such interactions is vital, which is possible only through statistical…

This paper proposes a nonparametric Bayesian method for exploratory data analysis and feature construction in continuous time series. Our method focuses on understanding shared features in a set of time series that exhibit significant…

We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the…

In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…

We study fundamental properties of the gamma process and their relation to various topics such as Poisson-Dirichlet measures and stable processes. We prove the quasi-invariance of the gamma process with respect to a large group of linear…

Detecting associations between microbial compositions and sample characteristics is one of the most important tasks in microbiome studies. Most of the existing methods apply univariate models to single microbial species separately, with…

The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable…

Making inferences from data streams is a pervasive problem in many modern data analysis applications. But it requires to address the problem of continuous model updating and adapt to changes or drifts in the underlying data generating…

In this paper we provide general conditions to check on the model and the prior to derive posterior concentration rates for data-dependent priors (or empirical Bayes approaches). We aim at providing conditions that are close to the…

Many modern data analysis problems involve inferences from streaming data. However, streaming data is not easily amenable to the standard probabilistic modeling approaches, which assume that we condition on finite data. We develop…

In this paper, we present two classes of Bayesian approaches to the two-sample problem. Our first class of methods extends the Bayesian t-test to include all parametric models in the exponential family and their conjugate priors. Our second…

We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…

The Hierarchical Dirichlet Process (HDP) provides a flexible Bayesian nonparametric framework for modeling grouped data with a shared yet unbounded collection of mixture components. While existing applications of the HDP predominantly focus…