Topics in design-based and Bayesian inference for surveys
Date
2012
Authors
Hernandez-Stumpfhauser, Daniel, author
Opsomer, Jean, advisor
Breidt, F. Jay, committee member
Hoeting, Jennifer A., committee member
Kreidenweis, Sonia M., committee member
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Abstract
We deal with two different topics in Statistics. The first topic in survey sampling deals with variance and variance estimation of estimators of model parameters in the design-based approach to analytical inference for survey data when sampling weights include post-sampling weight adjustments such as calibration. Under the design-based approach estimators of model parameters, if available in closed form, are written as functions of estimators of population totals and means. We examine properties of these estimators in particular their asymptotic variances and show how ignoring the post-sampling weight adjustments, i.e. treating sampling weights as inverses of inclusion probabilities, results in biased variance estimators. Two simple simulation studies for two common estimators, an estimator of a population ratio and an estimator of regression coefficients, are provided with the purpose of showing situations for which ignoring the post-sampling weight adjustments results in significant biased variance estimators. For the second topic we consider Bayesian inference for directional data using the projected normal distribution. We show how the models can be estimated using Markov chain Monte Carlo methods after the introduction of suitable latent variables. The cases of random sample, regression, model comparison and Dirichlet process mixture models are covered and motivated by a very large dataset of daily departures of anglers. The number of parameters increases with sample size and thus the need of exploring alternatives. We explore mean field variational methods and identify a number of problems in the application of the method to these models, caused by the poor approximation of the variational distribution to the posterior distribution. We propose solutions to those problems by improving the mean field variational approximation through the use of the Laplace approximation for the regression case and through the use of novel Monte Carlo procedures for the mixture model case.
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Subject
variance estimation
Dirichlet process
directional data
Bayesian analysis