Essays on Bayesian inference of time-series and ordered panel data models

At the heart of my dissertation is the study of Markov chain Monte Carlo algorithms and their applications. My dissertation consists of three essays as follow.;The first chapter is on MCMC algorithms for the dynamic ordered probit model with random effects. I have tried to estimate the model with four representative MCMC algorithms: two algorithms by Albert and Chib (1993) and Albert and Chib (2001), Liu and Sabatti (2000), and Chen and Dey (2000). I have found that the autocorrelations still remain high in the cutoffs compared to other parameters even though the levels of autocorrelation are reduced in the algorithms by Liu and Sabatti (2000), and Chen and Dey (2000).;In the second chapter, I have developed the dynamic ordered probit model studied in the first chapter. It is natural for panel data to have missing data problem because there is no guarantee that subjects will stay over the study periods. This chapter provides Bayesian statistical methods that permit non-ignorable missing data in panel datasets. In order to incorporate non-random missing data in the model, I jointly model observed and non-ignorable missing ordinal data with selection model approach. In the empirical section, I have used the model to examine determinants of self-rated health of old people in the Health and Retirement Study. I have concluded that in this elderly American population, the longest occupation that respondents have held over their careers is strongly associated with self-rated health.;In the third chapter of my dissertation, I analyze financial time-series data before and after the Wall Street meltdown in 2008. In this chapter, I develop MCMC algorithms for the CKLS model and examine (1) time-series characteristics of the credit default swap index, stock index and federal funds rate from January 2007 to September 2009, the highly volatile period. (2) The lead-lag relationship between the credit default swap and stock markets are examined using the CKLS model employing multivariate analysis.