Related papers: Bernstein - von Mises Theorem for growing paramete…

In this paper we consider a super-renormalizable theory of massless QED in $(2+1)$ dimensions and discuss their BRST symmetry transformation. By extending the BRST transformation we derive the Nielsen identities for the theory. Further, we…

We prove new, general versions of Bernstein-von Mises theorem for both well-specified and misspecified models when the log-likelihood is concave in the parameter and the prior distribution is log-concave. Unlike classical versions of…

This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed,…

Bernstein-von Mises results (BvM) establish that the Laplace approximation is asymptotically correct in the large-data limit. However, these results are inappropriate for computational purposes since they only hold over most, and not all,…

Bayesian networks are now being used in enormous fields, for example, diagnosis of a system, data mining, clustering and so on. In spite of their wide range of applications, the statistical properties have not yet been clarified, because…

The von Mises-Fisher family is a parametric family of distributions on the surface of the unit ball, summarised by a concentration parameter and a mean direction. As a quasi-Bayesian prior, the von Mises-Fisher distribution is a convenient…

Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the…

We consider the problem of inference for projection parameters in linear regression with increasing dimensions. This problem has been studied under a variety of assumptions in the literature. The classical asymptotic normality result for…

The Minkowski problem for a class of unbounded closed convex sets is considered. This is equivalent to a Monge-Amp\`ere equation on a bounded convex open domain with possibly non-integrable given data. A complete solution (necessary and…

In this paper we prove a conjecture of Bryant, Griffiths, and Yang concerning the characteristic variety for the determined isometric embedding system. In particular, we show that the characteristic variety is not smooth for any dimension…

In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…

Overparameterized models with millions of parameters have been hugely successful. In this work, we ask: can the need for large models be, at least in part, due to the \emph{computational} limitations of the learner? Additionally, we ask, is…

We announce a new four parameter partition theorem from which the (big) theorem of Gollnitz follows by setting any one of the parameters equal to 0. This settles a problem of Andrews who asked whether there exists a result that goes beyond…

Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter weighting information in the loss relative to the prior and providing a control of posterior uncertainty.…

Typical Bayesian inference requires parameter identification via likelihood parameterization, which has invited criticism for being less flexible than the Frequentist framework and subject to misspecification. Though misspecification may be…

In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…

Let $M_{l,n}$ be the number of blocks with frequency $l$ in the exchangeable random partition induced by a sample of size $n$ from the Ewens-Pitman sampling model. We show that, as $n$ tends to infinity, $n^{-1}M_{l,n}$ satisfies a large…

Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…

Many Bayesian inference problems involve high dimensional models for which only a subset of the model variables are of actual interest. All other variables are just nuisance parameters that one would ideally like to integrate out…

Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…