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Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform…
We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for `many'…
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…
We investigate the asymptotic behavior of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution…
As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the…
Penalized B-splines are routinely used in additive models to describe smooth changes in a response with quantitative covariates. It is typically done through the conditional mean in the exponential family using generalized additive models…
A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…
Penalized and robust regression, especially when approached from a Bayesian perspective, can involve the problem of simulating a random variable $\boldsymbol z$ from a posterior distribution that includes a term proportional to a sum of…
We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…
This work is motivated by the analysis of ecological interaction networks. Poisson stochastic blockmodels are widely used in this field to decipher the structure that underlies a weighted network, while accounting for covariate effects.…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
We study Bayesian inference in statistical linear inverse problems with Gaussian noise and priors in Hilbert space. We focus our interest on the posterior contraction rate in the small noise limit. Existing results suffer from a certain…
The random matrix model is popular in extended object tracking, due to its relative simplicity and versatility. In this model, the extended object state consists of a kinematic vector for the position and motion parameters (velocity, etc),…
While there have been a lot of recent developments in the context of Bayesian model selection and variable selection for high dimensional linear models, there is not much work in the presence of change point in literature, unlike the…
We study asymptotic frequentist coverage and approximately Gaussian properties of Bayes posterior credible sets in nonlinear inverse problems when a Gaussian prior is placed on the parameter of the PDE. The aim is to ensure valid…
There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…
Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…
We consider the Bayesian analysis of a few complex, high-dimensional models and show that intuitive priors, which are not tailored to the fine details of the model and the estimated parameters, produce estimators which perform poorly in…
We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…