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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 ..."
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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.
Hierarchical spatiotemporal matrix models for characterizing invasions
 Biometrics
, 2007
"... Summary. The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular ..."
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Summary. The growth and dispersal of biotic organisms is an important subject in ecology. Ecologists are able to accurately describe survival and fecundity in plant and animal populations and have developed quantitative approaches to study the dynamics of dispersal and population size. Of particular interest are the dynamics of invasive species. Such nonindigenous animals and plants can levy significant impacts on native biotic communities. Effective models for relative abundance have been developed; however, a better understanding of the dynamics of actual population size (as opposed to relative abundance) in an invasion would be beneficial to all branches of ecology. In this article, we adopt a hierarchical Bayesian framework for modeling the invasion of such species while addressing the discrete nature of the data and uncertainty associated with the probability of detection. The nonlinear dynamics between discrete time points are intuitively modeled through an embedded deterministic population model with densitydependent growth and dispersal components. Additionally, we illustrate the importance of accommodating spatially varying dispersal rates. The method is applied to the specific case of the Eurasian CollaredDove, an invasive species at midinvasion in the United States at the time of this writing.
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,
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
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
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"... The development of objective prior distributions for discrete parameter spaces is considered. 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 st ..."
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The development of objective prior distributions for discrete parameter spaces is considered. 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 populationsize model, the hypergeometric distribution, the multivariate hypergeometric distribution, the binomialbeta distribution, the binomial distribution, and determination of prior model probabilities. The recommended objective priors for the first, third and fourth problems are new.