Optimal Bayesian Regression With Vector Autoregressive Data Dependency

In this study, we derive a closed-form analytic representation of the optimal Bayesian regression when the data are generated from $\text{VAR}(p)$, which is a multidimensional vector autoregressive process of order $p$. Given the covariance matrix of the underlying Gaussian white-noise process, the developed regressor reduces to the conventional optimal regressor for a non-informative prior and setting $p=0$, which implies independent data. Our empirical results using both synthetic and real data show that the developed regressor can effectively be used in situations where the data are sequentially dependent.
Source: IEEE Transactions on Signal Processing - Category: Biomedical Engineering Source Type: research