Empirical Bayes methodology for estimating equipment failure rates with application to power generation plants

Many reliability databases pool event data for equipment across different plants. Pooling may occur both within and between organizations with the intention of sharing data across common items within similar operating environments to provide better estimates of reliability and availability. Frequentist estimation methods can be poor when few, or no, events occur even when equipment operate for long periods. An alternative approach based upon empirical Bayes estimation is proposed. The new method is applied to failure data analysis in power generation plants and found to provide credible insights. A statistical comparison between the proposed and frequentist methods shows that empirical Bayes is capable of generating more accurate estimates

Online but Accurate Inference for Latent Variable Models with Local Gibbs Sampling

We study parameter inference in large-scale latent variable models. We first propose an unified treatment of online inference for latent variable models from a non-canonical exponential family, and draw explicit links between several previously proposed frequentist or Bayesian methods. We then propose a novel inference method for the frequentist estimation of parameters, that adapts MCMC methods to online inference of latent variable models with the proper use of local Gibbs sampling. Then, for latent Dirich-let allocation,we provide an extensive set of experiments and comparisons with existing work, where our new approach outperforms all previously proposed methods. In particular, using Gibbs sampling for latent variable inference is superior to variational inference in terms of test log-likelihoods. Moreover, Bayesian inference through variational methods perform poorly, sometimes leading to worse fits with latent variables of higher dimensionality

Inference for VARs Identified with Sign Restrictions

There is a fast growing literature that set-identifies structural vector autoregressions (SVARs) by imposing sign restrictions on the responses of a subset of the endogenous variables to a particular structural shock (sign-restricted SVARs). Most methods that have been used to construct pointwise coverage bands for impulse responses of sign-restricted SVARs are justified only from a Bayesian perspective. This paper demonstrates how to formulate the inference problem for sign-restricted SVARs within a moment-inequality framework. In particular, it develops methods of constructing confidence bands for impulse response functions of sign-restricted SVARs that are valid from a frequentist perspective. The paper also provides a comparison of frequentist and Bayesian coverage bands in the context of an empirical application - the former can be substantially wider than the latter

An Essay on the Double Nature of the Probability

Classical statistics and Bayesian statistics refer to the frequentist and subjective theories of probability respectively. Von Mises and De Finetti, who authored those conceptualizations, provide interpretations of the probability that appear incompatible. This discrepancy raises ample debates and the foundations of the probability calculus emerge as a tricky, open issue so far. Instead of developing philosophical discussion, this research resorts to analytical and mathematical methods. We present two theorems that sustain the validity of both the frequentist and the subjective views on the probability. Secondly we show how the double facets of the probability turn out to be consistent within the present logical frame

An Agnostic Look at Bayesian Statistics and Econometrics

Bayesians and non-Bayesians, often called frequentists, seem to be perpetually at logger- heads on fundamental questions of statistical inference. This paper takes as agnostic a stand as is possible for a practising frequentist, and tries to elicit a Bayesian answer to questions of interest to frequentists. The argument is based on my presentation at a debate organised by the Rimini Centre for Economic Analysis, between me as the frequentist "advocate", and Christian Robert on the Bayesian side.Bayesian methods, bootstrap, Bahadur-Savage result

Discussion of "Impact of Frequentist and Bayesian Methods on Survey Sampling Practice: A Selective Appraisal" by J. N. K. Rao

Discussion of "Impact of Frequentist and Bayesian Methods on Survey Sampling Practice: A Selective Appraisal" by J. N. K. Rao [arXiv:1108.2356]Comment: Published in at http://dx.doi.org/10.1214/11-STS346C the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Enhancing the physical significance of Frequentist confidence intervals

It is shown that all the Frequentist methods are equivalent from a statistical point of view, but the physical significance of the confidence intervals depends on the method. The Bayesian Ordering method is presented and confronted with the Unified Approach in the case of a Poisson process with background. Some criticisms to both methods are answered. It is also argued that a general Frequentist method is not needed.Comment: 10 page

Inference for VARs identified with sign restrictions

There is a fast growing literature that partially identifies structural vector autoregressions (SVARs) by imposing sign restrictions on the responses of a subset of the endogenous variables to a particular structural shock (sign-restricted SVARs). To date, the methods that have been used are only justified from a Bayesian perspective. This paper develops methods of constructing error bands for impulse response functions of sign-restricted SVARs that are valid from a frequentist perspective. The authors also provide a comparison of frequentist and Bayesian error bands in the context of an empirical application — the former can be twice as wide as the latter.Vector autoregression ; Econometric models