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Reference analysis
 In Handbook of Statistics 25
, 2005
"... This chapter describes reference analysis, a method to produce Bayesian inferential statements which only depend on the assumed model and the available data. Statistical information theory is used to define the reference prior function as a mathematical description of that situation where data would ..."
Abstract

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This chapter describes reference analysis, a method to produce Bayesian inferential statements which only depend on the assumed model and the available data. Statistical information theory is used to define the reference prior function as a mathematical description of that situation where data would best dominate prior knowledge about the quantity of interest. Reference priors are not descriptions of personal beliefs; they are proposed as formal consensus prior functions to be used as standards for scientific communication. Reference posteriors are obtained by formal use of Bayes theorem with a reference prior. Reference prediction is achieved by integration with a reference posterior. Reference decisions are derived by minimizing a reference posterior expected loss. An information theory based loss function, the intrinsic discrepancy, may be used to derive reference procedures for conventional inference problems in scientific investigation, such as point estimation, region estimation and hypothesis testing.
Estimation of Binomial Parameters when Both n, p are Unknown
, 2004
"... We revisit the classic problem of estimation of the binomial parameters when both parameters n, p are unknown. We start with a series of results that illustrate the fundamental difficulties in the problem. Specifically, we establish lack of unbiased estimates for essentially any functions of just n ..."
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We revisit the classic problem of estimation of the binomial parameters when both parameters n, p are unknown. We start with a series of results that illustrate the fundamental difficulties in the problem. Specifically, we establish lack of unbiased estimates for essentially any functions of just n or just p. We also quantify just how badly biased the sample maximum is as an estimator of n. Then we motivate and present two new estimators of n. One is a new moment estimate and the other is a bias correction of the sample maximum. Both are easy to motivate, compute, and jackknife. The second estimate frequently beats most common estimates of n in the simulations, including the CarrollLombard estimate. This estimate is very promising. We end with a family of estimates for p; a specific one from the family is compared to the presently common estimate max{1 − s2,
Hierarchical Bayesian Analysis for the Number of Species
"... This paper is concerned with the estimation of the number of species in a population through a fully hierarchical Bayesian models using the Metropoliswithin Gibbs algorithm. The proposed Bayesian estimator is based on Poisson random variables with means that are distributed according to some prior ..."
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This paper is concerned with the estimation of the number of species in a population through a fully hierarchical Bayesian models using the Metropoliswithin Gibbs algorithm. The proposed Bayesian estimator is based on Poisson random variables with means that are distributed according to some prior distributions with unknown hyperparameters. An empirical Bayes approach is considered and compared with the fully Bayesian approach based on biological data. Keywords: EMPIRICAL BAYES; METROPOLISWITHINGIBBS SAMPLING; HIERARCHICAL MODEL; POISSONGAMMA MIXTURE. 1.
Normal linear models with genetically structured residual variance heterogeneity: A case study of litter size in pigs
"... Four normal mixed models with dierent levels of complexity in the residual variance are tted to litter size data in pigs. The model building process is partly guided using posterior predictive model checking based on residuals. Graphical summaries of posterior predictive checks contribute insight ab ..."
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Four normal mixed models with dierent levels of complexity in the residual variance are tted to litter size data in pigs. The model building process is partly guided using posterior predictive model checking based on residuals. Graphical summaries of posterior predictive checks contribute insight about speci c features of the data and suggests extensions of the model in a particular direction. Comparisons based on Bayes factors and related criteria favour models with a genetically structured residual variance heterogeneity. The Monte Carlo estimates of the posterior mean and of the 95% posterior interval of the correlation between additive genetic values affecting litter size and those aecting residual variance are 0:62 and ( 0:79; 0:43), respectively. The models are also compared according to the purposes for which they might be used, such as prediction of \future" data, inference about response to selection, and ranking candidates for selection. It is shown that a simple model may be adequate in a particular context, even though it fails to address features of the data accounted for by the more complex models. A brief overview is given of some implications for selection of the genetically structured residual variance model. 1
the Size of a Closed Population
, 1992
"... A Bayesian methodology for estimating the size of a closed population from multiple incomplete administrative lists is proposed. The approach allows for a variety of dependence structures between the lists, inclusion of covariates, and explicitly accounts for model uncertainty. Interval estimates fr ..."
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A Bayesian methodology for estimating the size of a closed population from multiple incomplete administrative lists is proposed. The approach allows for a variety of dependence structures between the lists, inclusion of covariates, and explicitly accounts for model uncertainty. Interval estimates from this approach are compared to frequentist and previously published Bayesian approaches, and found to be superior. Several examples are considered. KEYWORDS: Bayesian graphical model; Capturerecapture; Closed population estimation; Chordal graph; Contingency table; Decomposable loglinear model; Markov distribution. Contents