Bayesian Look Research Articles

A Bayesian look at classical estimation: The shape of the pareto distribution and its functions

The Pareto Distribution has been found to be useful in describing socio-economic, physical, and biological phenomena. This paper explores different methods of estimating the shape parameter of the Pareto distribution and two of its functions (reliability and hazard functions), assuming the scale parameter is known. In particular, this paper shows that the Bayesian approach, using both the quadratic and entropy loss functions, can provide a general method for estimating the shape parameter and these two functions. These Bayesian estimators generalize the maximum likelihood estimator (MLE) and the uniformly most powerful unbiased estimator (UMVUE). Simulation results show that the general Bayesian method can perform better than the MLE and UMVUE, especially when the sample size is small.

A Bayesian look at American academic wages: From wage dispersion to wage compression

OECD countries have experienced a large increase in top wage inequality. Atkinson (2008) attributes this phenomena to the superstar theory leading to a Pareto tail in the wage distribution with a low Pareto coefficient. Do we observe a similar phenomena for academic wages? We examine wage formation in a public US university using for each academic rank a hybrid mixture formed by a lognormal distribution for regular wages and a Pareto distribution for top wages, using a Bayesian approach. The presence of superstars wages would imply a higher dispersion in the Pareto tail than in the lognormal body. We concluded that academic wages are formed in a different way than other top wages. There is an effort to propose competitive wages to some young Assistant Professors. But when climbing up the wage ladder, we found a phenomenon of wage compression which is just the contrary of a superstar phenomenon.

Three-Component Mixture of Rayleigh Model Under Doubly Censored Samples: A Bayesian Look

Feroze and Aslam (J Natl Sci Found Sri Lanka 42:325–334, 2014) and Sindhu et al. (J Mod Appl Stat Methods 13:259–286, 2014) have considered the Bayesian analysis of the two-component mixture of lifetime distributions under doubly censored samples. In this paper, the concept has been extended for the three-component mixture of lifetime (Rayleigh) distribution under doubly censored samples. The likelihood function for the mixture of lifetime models under doubly type-II censored samples has been introduced. Different priors and loss functions have been assumed for the derivation of Bayes estimators and posterior risks. The comparisons among various estimators have been made by analyzing the simulated and real data sets.

A Bayesian Look at the Baby Annie Case

The problem of how to help juries handle forensic statistics and other types of statistical evidence has long bedeviled the legal system. One longstanding proposal is to use Bayes Theorem, which pr...

Analysis of doubly censored Burr type II distribution: a Bayesian look

Burr model is especially suitable for the life-testing of the products that age with time. Trimmed samples are widely utilized in several areas of statistical practice, especially when some sample values at either or both extremes might have been adulterated. In this article, the problem of estimating the parameter of Burr distribution type II based on trimmed samples under informative and uninformative has been addressed. The problem discussed using Bayesian approach to estimate the shape parameter of Burr type II distribution. Elicitation of hyperparameter through prior predictive approach has also been discussed. Posterior predictive distributions along with posterior predictive intervals and credible intervals have also been derived under different priors. A comparison has been made using the Monte Carlo simulation. A real life data example has also been discussed.

A Bayesian Look at the Rao-Kupper Model for Paired Comparisons

The method of paired comparisons may be regarded as a special rank order technique. It is a method long used in psychological experimentation and is well adapted to sensory difference testing. This study deals with estimation and testing of the parameters of the Rao-Kupper (1967) model for paired comparisons which allows for tied observations in paired comparison experiments using informative prior. An elicitation of the hyper parameters is carried out. Predictive probabilities that one treatment would be preferred to other treatment in a future single comparison are determined. Graphs for the marginal posterior densities are presented. All calculations are based on numerical integration technique and Gibbs sampling procedure. Appropriateness of the model is checked which declares it a good fit.

A Bayesian Look at Nonidentifiability: A Simple Example

This article discusses the concept of identifiability in simple probability calculus. Emphasis is given to Bayesian solutions. In particular, we compare Bayes and maximum likelihood estimators. We advocate adoption of informative prior probabilities for the Bayesian operation in place of diffuse or reference priors. We also discuss the concept of identifying functions.

‘A modern Bayesian look at the multi‐armed bandit’ by Steven L. Scott: Discussion

Applied Stochastic Models in Business and IndustryVolume 26, Issue 6 p. 659-664 Discussion ‘A modern Bayesian look at the multi-armed bandit’ by Steven L. Scott: Discussion Deepak K. Agarwal, Deepak K. Agarwal dagarwal@yahoo-inc.com Yahoo! Research, Santa Clara, CA, U.S.A.Search for more papers by this author Deepak K. Agarwal, Deepak K. Agarwal dagarwal@yahoo-inc.com Yahoo! Research, Santa Clara, CA, U.S.A.Search for more papers by this author First published: 16 December 2010 https://doi.org/10.1002/asmb.872Citations: 1Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume26, Issue6November/December 2010Pages 659-664 RelatedInformation

A modern Bayesian look at the multi‐armed bandit

AbstractA multi‐armed bandit is an experiment with the goal of accumulating rewards from a payoff distribution with unknown parameters that are to be learned sequentially. This article describes a heuristic for managing multi‐armed bandits called randomized probability matching, which randomly allocates observations to arms according the Bayesian posterior probability that each arm is optimal. Advances in Bayesian computation have made randomized probability matching easy to apply to virtually any payoff distribution. This flexibility frees the experimenter to work with payoff distributions that correspond to certain classical experimental designs that have the potential to outperform methods that are ‘optimal’ in simpler contexts. I summarize the relationships between randomized probability matching and several related heuristics that have been used in the reinforcement learning literature. Copyright © 2010 John Wiley & Sons, Ltd.

‘A modern Bayesian look at the multi‐armed bandit’ by Steven L. Scott: Rejoinder

‘A modern Bayesian look at the multi‐armed bandit’ by Steven L. Scott: Rejoinder

A Bayesian Sequential Look at u-Control Charts

We extend the usual implementation of u-control charts (uCCs) in two ways. First, we overcome the restrictive (and often inadequate) assumptions of the Poisson model; next, we eliminate the need for the questionable base period by using a sequential procedure. We use empirical Bayes(EB) and Bayes methods and compare them with the traditional frequentist implementation. EB methods are somewhat easy to implement, and they deal nicely with extra-Poisson variability (and, at the same time, informally check the adequacy of the Poisson assumption). However, they still need the base period. The sequential, full Bayes approach, on the other hand, also avoids this drawback of traditional u-charts. The implementation requires numerical simulation, and also use of a prior distribution. Several possibilities for both objective and informative priors are explored. We argue that the sequential, full Bayesian uCC is a powerful and versatile tool for process monitoring.

A Bayesian Look at New Open Economy Macroeconomics]: Comment

A Bayesian Look at New Open Economy Macroeconomics]: Comment

A Bayesian Look at New Open Economy Macroeconomics]: Discussion

A Bayesian Look at New Open Economy Macroeconomics]: Discussion

A Bayesian Look at New Open Economy Macroeconomics

This paper develops a small-scale two-country model following the new open economy macroeconomics paradigm. Under autarky, the model specializes to the familiar three-equation New Keynesian dynamic stochastic general equilibrium (DSGE) model. We discuss two challenges to successful estimation of DSGE models: potential model misspecification and identification problems. We argue that prior distributions and Bayesian estimation techniques are useful to cope with these challenges. We apply these techniques to the two-country model and fit it to data from the United States and the Euro area. We compare parameter estimates from closed and open economy specifications, study the sensitivity of parameter estimates to the choice of prior distribution, examine the propagation of monetary policy shocks, and assess the model's ability to explain exchange-rate movements.

A Bayesian Look at New Open Economy Macroeconomics]: Comment

In this paper Thomas Lubik and Frank Schorfheide introduce and estimate a mid-size two-country model of monetary interdependence. The key building blocks of the model are rather well known, having been extensively investigated in the large (and growing) DSGE literature. The open-economy dimensions of the paper are perhaps less familiar, and it is precisely on those aspects that this comment is focused.

A Bayesian Look at Classical Estimation: The Exponential Distribution

Many undergraduate students are introduced to frequentist or classical methods of parameter estimation such as maximum likelihood estimation, uniformly minimum variance unbiased estimation, and minimum mean square error estimation in a reliability, probability, or mathematical statistics course. Rossman, Short, and Parks (1998) present some thought provoking insights on the relationship between Bayesian and classical estimation using the continuous uniform distribution. Our aim is to explore these relationships using the exponential distribution. We show how the classical estimators can be obtained from various choices made within a Bayesian framework.

Bayesian look ahead one-stage sampling allocations for selection of the best population

From k independent normal populations with unknown means and a common known variance, Bayesian selection procedures are considered for finding that population which has the largest mean. Suppose that a first stage has been completed already, where k samples have been observed, which may be of different sizes. Let there be m additional observations allowed to be taken at a future second stage. The problem of interest treated here is how to allocate these m observations in an optimum way among the k populations, given all of the information, prior and first stage observations, gathered so far. This allocation problem will be formulated and discussed in a more general framework, and specific results will be presented for the normal case with independent conjugate priors under linear loss.

Bayesian look ahead one stage sampling allocations for selecting the largest normal mean

From two independent normal populations with unknown means and a common known variance, samples of unequal sizes are observed at stage 1. The goal is to find that population with the larger mean. Using the Bayes approach, optimum allocations ofm additional observations, at stage 2, are derived under the linear and the 0–1 loss.

Cointegration tests in present value relationships: A Bayesian look at the bivariate properties of stock prices and dividends

A Bayesian methodology is used to examine the bivariate time series properties of stock prices and dividends. The hypothesis that stock prices and dividends are cointegrated is emphasized. Exact small sample results are calculated using a specific parameterization for the bivariate model. Some commonly encountered problems in conventional cointegration tests based on asymptotic theory are thereby eliminated. We consider three hypotheses whose nonlinear form entails the need for multidimensional Monte Carlo integration. In addition, three data sets are used, two of which are annual U.S. sets over long time periods and one a post-war Canadian set. The intention is to demonstrate that a more accurate understanding of the value and limitations of cointegration tests for investigating present value relationships is possible with a Bayesian methodology, employed over a variety of data configurations.

A Bayesian Look at Inverse Linear Regression

Abstract The model considered in this paper is simple linear regression , and the problem is to make statistical inferences about an unknown value of x corresponding to one or more additional observed values of y. The maximum likelihood estimator x of x and the classical (1 - α) 100% confidence set S for x have some undesirable properties. For example, has infinite mean square error and > 0. The purpose of this paper is to demonstrate that insight and understanding, as well as a useful class of solutions, can be obtained by looking at the problem from a Bayesian point of view. A result which follows from a general Bayes solution is that the inverse estimator [4] is Bayes with respect to a particular informative prior.