Related papers: Pochhammer Priors for Sparse Count Models
This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…
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…
Three different inferential problems related to a two dimensional categorical data from a Bayesian perspective have been discussed in this article. Conjugate prior distribution with symmetric and asymmetric hyper parameters are considered.…
Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…
Finite Gaussian mixture models are widely used for model-based clustering of continuous data. Nevertheless, since the number of model parameters scales quadratically with the number of variables, these models can be easily…
A Bayesian inference method for problems with small samples and sparse data is presented in this paper. A general type of prior ($\propto 1/\sigma^{q}$) is proposed to formulate the Bayesian posterior for inference problems under small…
Consider a situation of analyzing high-dimensional count data containing an excess of near-zero counts with a small number of moderate or large counts. Assuming that the observations are modeled by a Poisson distribution, we are interested…
We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…
Over the past 10 years Bayesian methods have rapidly grown more popular as several computationally intensive statistical algorithms have become feasible with increased computer power. In this paper, we begin with a general description of…
Let $X_1,\ldots,X_n$ be a random sample from an unknown probability distribution $P$ on the sample space ${\cal X}$, and let $\theta=\theta(P)$ be a parameter of interest. The present paper proposes a nonparametric `Bayesian bootstrap'…
Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on…
Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…
The paper proposes a novel model assessment paradigm aiming to address shortcoming of posterior predictive $p-$values, which provide the default metric of fit for Bayesian structural equation modelling (BSEM). The model framework of the…
In this paper we develop a novel approach for estimating large and sparse dynamic factor models using variational inference, also allowing for missing data. Inspired by Bayesian variable selection, we apply slab-and-spike priors onto the…
There is a rich literature proposing methods and establishing asymptotic properties of Bayesian variable selection methods for parametric models, with a particular focus on the normal linear regression model and an increasing emphasis on…
Count data is prevalent in various fields like ecology, medical research, and genomics. In high-dimensional settings, where the number of features exceeds the sample size, feature selection becomes essential. While frequentist methods like…
We introduce a sparse high-dimensional regression approach that can incorporate prior information on the regression parameters and can borrow information across a set of similar datasets. Prior information may for instance come from…
Precision matrix estimation in a multivariate Gaussian model is fundamental to network estimation. Although there exist both Bayesian and frequentist approaches to this, it is difficult to obtain good Bayesian and frequentist properties…
We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…
Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior…