Improved approximate Bayesian computation methods for censored and uncensored data

Advisors: Nader Ebrahimi.Committee members: Barbara Gonzalez; Alan Polansky; Chaoxiong Michelle Xia.Includes illustrations.Includes bibliographical references.Approximate Bayesian Computation (ABC) is a method of statistical inference that does not require the exact model to be known. It is generally used for complex models, where the likelihood function is intractable or computationally difficult. ABC has lately become very useful in areas such as genetics, biology, ecology, and epidemiology, due to the complex structures arising in these fields. Empirical likelihood is a nonparametric estimation approach in statistics that does not require the choice of a known distribution family for the data. Common ABC methods require the choice of summary statistic, which is very difficult to find, distance metric, and a tolerance level. Empirical likelihood allows these choices to be avoided. In this dissertation, two improved methods of the ABC algorithms via empirical likelihood for uncensored data are proposed. In simulations, it is shown that the accuracy of estimation of improved procedures is higher than of existing ABC via empirical likelihood. Furthermore, for right censored or partially observed data three new algorithms are developed: ABC via empirical likelihood, ABC via comparing survival functions, and ABC via comparing smoothed distribution functions. Consistency, asymptotically unbiasedness, and asymptotic behavior of approximate posterior distribution are established for ABC via comparing survival functions and ABC via comparing smoothed distribution functions. The last two algorithms were implemented on real data.Ph.D. (Doctor of Philosophy