Statistical inference as a decision problem: the choice of sample size

Objective Priors for Discrete Parameter Spaces

This article considers the development of objective prior distributions for discrete parameter spaces. Formal approaches to such development—such as the reference prior approach—often result in a constant prior for a discrete parameter, which is questionable for problems that exhibit certain types of structure. To take advantage of structure, this article proposes embedding the original problem in a continuous problem that preserves the structure, and then using standard reference prior theory to determine the appropriate objective prior. Four different possibilities for this embedding are explored, and applied to a population-size model, the hypergeometric distribution, the multivariate hy…

Analisis bayesiano de un proceso binomial

En este trabajo se estudia el proceso de Bernouilli desde una perspectiva bayesiana. El analisis no se limita a la conocida obtencion de las distribuciones finales que corresponden a una determinada familia de distribuciones iniciales. Asi, se estudian con detalle los problemas de la especificacion de la distribucion inicial, y la determinacion del tamano muestral adecuado a las necesidades del investigador. Mediante el analisis de un conjunto de datos farmacologicos, se ejemplican los resultados y se ilustran una vez mas la flexibilidad y elegancia de los metodos bayesianos.

An overview of robust Bayesian analysis

Robust Bayesian analysis is the study of the sensitivity of Bayesian answers to uncertain inputs. This paper seeks to provide an overview of the subject, one that is accessible to statisticians outside the field. Recent developments in the area are also reviewed, though with very uneven emphasis. © 1994 SEIO.

Discussion of "Objective Priors: An Introduction for Frequentists" by M. Ghosh

Discussion of "Objective Priors: An Introduction for Frequentists" by M. Ghosh [arXiv:1108.2120]

Unacceptable implications of the left haar measure in a standard normal theory inference problem

For a very common statistical problem, inference about the mean of a normal random variable, some inadmissible consequences of the left Haar invariant prior measure, which is that recommended as a suitable prior by Jeffreys’ multivariate rule and by the methods of Villegas and Kashyap, are uncovered and investigated.

Bayesian hypothesis testing: A reference approach

Summary For any probability model M={p(x|θ, ω), θeΘ, ωeΩ} assumed to describe the probabilistic behaviour of data xeX, it is argued that testing whether or not the available data are compatible with the hypothesis H0={θ=θ0} is best considered as a formal decision problem on whether to use (a0), or not to use (a0), the simpler probability model (or null model) M0={p(x|θ0, ω), ωeΩ}, where the loss difference L(a0, θ, ω) –L(a0, θ, ω) is proportional to the amount of information δ(θ0, ω), which would be lost if the simplified model M0 were used as a proxy for the assumed model M. For any prior distribution π(θ, ω), the appropriate normative solution is obtained by rejecting the null model M0 wh…

A Bayesian analysis of classical hypothesis testing

The procedure of maximizing the missing information is applied to derive reference posterior probabilities for null hypotheses. The results shed further light on Lindley’s paradox and suggest that a Bayesian interpretation of classical hypothesis testing is possible by providing a one-to-one approximate relationship between significance levels and posterior probabilities.

Intrinsic credible regions: An objective Bayesian approach to interval estimation

This paper definesintrinsic credible regions, a method to produce objective Bayesian credible regions which only depends on the assumed model and the available data.Lowest posterior loss (LPL) regions are defined as Bayesian credible regions which contain values of minimum posterior expected loss: they depend both on the loss function and on the prior specification. An invariant, information-theory based loss function, theintrinsic discrepancy is argued to be appropriate for scientific communication. Intrinsic credible regions are the lowest posterior loss regions with respect to the intrinsic discrepancy loss and the appropriate reference prior. The proposed procedure is completely general…

Bayesian Methodology in Statistics

Bayesian methods provide a complete paradigm for statistical inference under uncertainty. These may be derived from an axiomatic system and provide a coherent methodology which makes it possible to incorporate relevant initial information, and which solves many of the difficulties that frequentist methods are known to face. If no prior information is to be assumed, the more frequent situation met in scientific reporting, a formal initial prior function, the reference prior, mathematically derived from the assumed model, is used; this leads to objective Bayesian methods, objective in the precise sense that their results, like frequentist results, only depend on the assumed model and the data…