Bayesian Methods for Finite Population Sampling
Assuming a basic knowledge of the frequentist approach to finite population sampling, Bayesian Methods for Finite Population Sampling describes Bayesian and predictive approaches to inferential problems with an emphasis on the likelihood principle. The authors demonstrate that a variety of levels of prior information can be used in survey sampling in a Bayesian manner. Situations considered range from a noninformative Bayesian justification of standard frequentist methods when the only prior information available is the belief in the exchangeability of the units to a full-fledged Bayesian model. Intended primarily for graduate students and researchers in finite population sampling, this book will also be of interest to statisticians who use sampling and lecturers and researchers in general statistics and biostatistics.
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absolute error analysis approach approximately assume assumption auxiliary variable Bayes estimator Bayes risk Bayesian bootstrap belong to stratum consider credible interval data point defined denote density Dirichlet EB estimator estimating the population example finite population sampling follows frequentist Ghosh guessed stratum Hence interval estimators k=1 L L kth stratum labels Lemma likelihood principle median Meeden method model given nonresponders normal notation Note parameter space partition point estimator Polya posterior population mean posterior distribution posterior probability predictive distribution previous section prior distribution prior guess prior information procedure proof pseudo posterior quantile responders restricted problem sample mean sample space sensible sequence of priors set estimation simple random sampling squared error loss statistic statistician stepwise Bayes stepwise Bayes argument stepwise Bayes estimator strata strk subset Suppose Table theorem tion true stratum unbiased predictor unobserved units usual values vector yi's