Essays on Bayesian Time Series and Variable Selection

Estimating model parameters in dynamic model continues to be challenge. In my dissertation, we have introduced a Stochastic Approximation based parameter estimation approach under Ensemble Kalman Filter set-up. Asymptotic properties of the resultant estimates are discussed here. We have compared our proposed method to current methods via simulation studies. We have demonstrated predictive performance of our proposed method on a large spatio-temporal data.

In my other topic, we presented a method for simultaneous estimation of regression parameters and the covariance matrix, developed for a nonparametric Seemingly Unrelated Regression problem. This is a very flexible modeling technique that essentially performs a sparse high-dimensional multiple predictor(p), multiple responses(q) regression where the responses may be correlated. Such data appear abundantly in the fields of genomics, finance and econometrics. We illustrate and compare performances of our proposed techniques with previous analyses using both simulated and real multivariate data arising in econometrics and government.