Bayesian Predictive Inference for Nonprobability Samples

Cao, Hanqi

Etd

Bayesian Predictive Inference for Nonprobability Samples

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Generally, sampling methods are classified as either probability or non-probability. A probability sample is based on the mathematical theory of probability, assigning each individual in the population a known non-zero probability of selection. A non-probability sample is a sample in which the probabilities of selection are unknown, and not all individuals in the population have a chance of being selected. Since a probability sample is very expensive, \ntime-consuming and difficult to implement, many surveys use non-probability samples (e.g., web surveys). \n\nIn this thesis, the propensity score matching is used to help to make the prediction. Based on Bayes' theorem and Metropolis-Hastings sampler, we can get several groups of propensity scores, and in each group, each individual in the population has one propensity score. Then, the subclassification matching procedure depending on propensity score can match the sampled individuals with the non-sampled ones. The unknown responses in non-sampled groups can be predicted by Bayesian Bootstrap. As having several groups of propensity scores, we can get an H.P.D. interval of the proportion of interest, comparing to the actual value. Furthermore, we compare our method with the interval got from Hurvitz-Thompson and Hajek estimators. The result of using our method is more precise than by using Hurvitz-Thompson and Hajek estimators. To improve the prediction, we have attempted a new idea that considers the spatial correlation between neighboring subclass. The Gibbs sampler, Metropolis-Hastings sampler, empirical logistic transformation, and grid method have been applied in the prediction. Compared with the first prediction model, the model with spatial correlation performs better.

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