Related papers: Rejoinder: Gibbs Sampling, Exponential Families an…

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…

Solving a polynomial system, or computing an associated Gr\"obner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the…

We consider the sampling problem from a composite distribution whose potential (negative log density) is $\sum_{i=1}^n f_i(x_i)+\sum_{j=1}^m g_j(y_j)+\sum_{i=1}^n\sum_{j=1}^m\frac{\sigma_{ij}}{2\eta} \Vert x_i-y_j \Vert^2_2$ where each of…

We present a new notion of probabilistic duality for random variables involving mixture distributions. Using this notion, we show how to implement a highly-parallelizable Gibbs sampler for weakly coupled discrete pairwise graphical models…

In this paper, we propose generative probabilistic models for label aggregation. We use Gibbs sampling and a novel variational inference algorithm to perform the posterior inference. Empirical results show that our methods consistently…

The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…

In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…

This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…

We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…

Gaussian boson sampling is a model of photonic quantum computing that has attracted attention as a platform for building quantum devices capable of performing tasks that are out of reach for classical devices. There is therefore significant…

The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major…

This paper introduces a notion of 2-orthogonality for a sequence of polynomials to give extended versions of the Meixner and Feinsilver characterization results based on orthogonal polynomials. These new versions subsume the Letac-Mora…

We present a one-parameter family of bivariate absolutely continuous distributions based on location-scale family of variance Gaussian mixtures, with continuous densities with the same support (effective domain). The maximum likelihood…

The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each…

Statistical inference may follow a frequentist approach or it may follow a Bayesian approach or it may use the minimum description length principle (MDL). Our goal is to identify situations in which these different approaches to statistical…

Gibbs sampling is a Markov chain Monte Carlo method that is often used for learning and inference on graphical models. Minibatching, in which a small random subset of the graph is used at each iteration, can help make Gibbs sampling scale…

We construct new rational approximants of Euler's constant that improve those of Aptekarev et al. (2007) and Rivoal (2009). The approximants are given in terms of certain (mixed type) multiple orthogonal polynomials associated with the…

Gibbs states are familiar from statistical mechanics, yet their use is not limited to that domain. For instance, they also feature in the maximum entropy reconstruction of quantum states from incomplete measurement data. Outside the…

Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fundamental properties, such as relations between convergence characteristics of their various…