arXiv subjects

R. V. Ramamoorthi

Publications and source records attributed to R. V. Ramamoorthi.

6 recordsLinked to original sources

arXiv2026

Bayesian bivariate survival estimation

There is no easy extension of Kaplan-Meier and Nelson-Aalen estimators to the bivariate case, and estimating bivariate survival distributions nonparametrically is associated with various non-trivial problems. The Dabrowska estimator will for example associate negative mass to some subsets. Bayesian methods hold some promise as they will avoid the negative mass problem, butare also prone to difficulties. We simplify and extend an example by Pruitt to show that the posterior distribution from a Dirichlet process prior is inconsistent. We construct a different nonparametric prior via Beta processes and provide an updating scheme that utilizes only the most relevant parts of the likelihood, and show that this leads to a consistent estimator.

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arXiv2020

On posterior concentration rates for Bayesian quantile regression based on the misspecified asymmetric Laplace likelihood

The asymmetric Laplace density (ALD) is used as a working likelihood for Bayesian quantile regression. Sriram et al.(2013) derived posterior consistency for Bayesian linear quantile regression based on the misspecified ALD. While their paper also argued for $\sqrt{n}-$consistency, Sriram and Ramamoorthi (2017) highlighted that the argument was only valid for a rate less than $\sqrt{n}$. So, the question of $\sqrt{n}-$rate has remained unaddressed, but is necessary to carry out meaningful Bayesian inference based on the ALD. In this paper, we derive results to obtain posterior consistency rates for Bayesian quantile regression based on the misspecified ALD. We derive our results in a slightly general setting where the quantile function can possibly be non-linear. In particular, we give sufficient conditions for $\sqrt{n}-$consistency for the Bayesian linear quantile regression using ALD. We also provide examples of Bayesian non-linear quantile regression.

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arXiv2015

On Posterior Concentration in Misspecified Models

We investigate the asymptotic behavior of Bayesian posterior distributions under independent and identically distributed ($i.i.d.$) misspecified models. More specifically, we study the concentration of the posterior distribution on neighborhoods of $f^{\star}$, the density that is closest in the Kullback--Leibler sense to the true model $f_0$. We note, through examples, the need for assumptions beyond the usual Kullback--Leibler support assumption. We then investigate consistency with respect to a general metric under three assumptions, each based on a notion of divergence measure, and then apply these to a weighted $L_1$-metric in convex models and non-convex models. Although a few results on this topic are available, we believe that these are somewhat inaccessible due, in part, to the technicalities and the subtle differences compared to the more familiar well-specified model case. One of our goals is to make some of the available results, especially that of , more accessible. Unlike their paper, our approach does not require construction of test sequences. We also discuss a preliminary extension of the $i.i.d.$ results to the independent but not identically distributed ($i.n.i.d.$) case.

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arXiv2014

Posterior consistency in misspecified models for i.n.i.d response

We derive conditions for posterior consistency when the responses are independent but not identically distributed ($i.n.i.d$) and the model is "misspecified" to be a family of densities parametrized by a possibly infinite dimensional parameter. Our approach has connections to key ideas developed for $i.i.d$ models in Kleijn and van der Vaart(2006) and it's subsequent simplification in Ramamoorthi, et al.(2014) (unpublished manuscript). While key results in these two papers rely heavily on the convexity of the specified family of densities, parametric families are seldom convex. In this note, we take a direct approach to deriving posterior consistency with respect to natural topologies on the parameter space without having to impose conditions on the convex hull of the parametric family. We first derive our results for the case when the responses are $i.i.d$ and then extend it to the $i.n.i.d$ case. As an example, we demonstrate the applicability of the results to the Bayesian quantile estimation problem.

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arXiv2010

A Conversation with James Hannan

Jim Hannan is a professor who has lived an interesting life and one whose fundamental research in repeated games was not fully appreciated until late in his career. During his service as a meteorologist in the Army in World War II, Jim played poker and made weather forecasts. It is curious that his later research included strategies for repeated play that apply to selecting the best forecaster. James Hannan was born in Holyoke, Massachusetts on September 14, 1922. He attended St. Jerome's High School and in January 1943 received the Ph.B. from St. Michael's College in Colchester, Vermont. Jim enlisted in the US Army Air Force to train and serve as a meteorologist. This took him to army airbases in China by the close of the war. Following discharge from the army, Jim studied mathematics at Harvard and graduated with the M.S. in June 1947. To prepare for doctoral work in statistics at the University of North Carolina that fall, Jim went to the University of Michigan in the summer of 1947. The routine admissions' physical revealed a spot on the lung and the possibility of tuberculosis. This caused Jim to stay at Ann Arbor through the fall of 1947 and then at a Veterans Administration Hospital in Framingham, Massachusetts to have his condition followed more closely. He was discharged from the hospital in the spring and started his study at Chapel Hill in the fall of 1948. There he began research in compound decision theory under Herbert Robbins. Feeling the need for teaching experience, Jim left Chapel Hill after two years and short of thesis to take a three year appointment as an instructor at Catholic University in Washington, DC. When told that renewal was not coming, Jim felt pressure to finish his degree.

stat.OT↗

arXiv2008

Remarks on consistency of posterior distributions

In recent years, the literature in the area of Bayesian asymptotics has been rapidly growing. It is increasingly important to understand the concept of posterior consistency and validate specific Bayesian methods, in terms of consistency of posterior distributions. In this paper, we build up some conceptual issues in consistency of posterior distributions, and discuss panoramic views of them by comparing various approaches to posterior consistency that have been investigated in the literature. In addition, we provide interesting results on posterior consistency that deal with non-exponential consistency, improper priors and non i.i.d. (independent but not identically distributed) observations. We describe a few examples for illustrative purposes.

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