Related papers: Asymptotics for power posterior mean estimation
We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…
The elicitation of power priors, based on the availability of historical data, is realized by raising the likelihood function of the historical data to a fractional power {\delta}, which quantifies the degree of discounting of the…
We propose a frequentist testing procedure that maintains a defined coverage and is optimal in the sense that it gives maximal power to detect deviations from a null hypothesis when the alternative to the null hypothesis is sampled from a…
The power prior and its variations have been proven to be a useful class of informative priors in Bayesian inference due to their flexibility in incorporating the historical information by raising the likelihood of the historical data to a…
The predictive Bayesian view involves eliciting a sequence of one-step-ahead predictive distributions in lieu of specifying a likelihood function and prior distribution. Recent methods have leveraged predictive distributions which are…
In this paper, we propose a novel Bayesian approach for nonparametric estimation in Wicksell's problem. This has important applications in astronomy for estimating the distribution of the positions of the stars in a galaxy given projected…
In this paper we leverage on probability over Riemannian manifolds to rethink the interpretation of priors and posteriors in Bayesian inference. The main mindshift is to move away from the idea that "a prior distribution establishes a…
A functional Bernstein - von Mises theorem is proved for posterior measures arising in a data assimilation problem with the two-dimensional Navier-Stokes equation where a Gaussian process prior is assigned to the initial condition of the…
The use of objective prior in Bayesian applications has become a common practice to analyze data without subjective information. Formal rules usually obtain these priors distributions, and the data provide the dominant information in the…
When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…
This paper studies the sparse normal mean models under the empirical Bayes framework. We focus on the mixture priors with an atom at zero and a density component centered at a data driven location determined by maximizing the marginal…
We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the…
We study nonparametric Bayesian statistical inference for the parameters governing a pure jump process of the form $$Y_t = \sum_{k=1}^{N(t)} Z_k,~~~ t \ge 0,$$ where $N(t)$ is a standard Poisson process of intensity $\lambda$, and $Z_k$ are…
Bernstein-von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete…
Normalized random measures with independent increments represent a large class of Bayesian nonaprametric priors and are widely used in the Bayesian nonparametric framework. In this paper, we provide the posterior consistency analysis for…
We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…
The Pitman-Yor process is a random probability distribution, that can be used as a prior distribution in a nonparametric Bayesian analysis. The process is of species sampling type and generates discrete distributions, which yield of the…
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the…
Power priors are used for incorporating historical data in Bayesian analyses by taking the likelihood of the historical data raised to the power $\alpha$ as the prior distribution for the model parameters. The power parameter $\alpha$ is…