Deviance Information Criterion of Multivariate Time Series Model

Compute DIC of BVAR and BVHAR.

Usage

compute_dic(object, ...)

# S3 method for class 'bvarmn'
compute_dic(object, n_iter = 100L, ...)

Arguments

object: Model fit
...: not used
n_iter: Number to sample

Value

DIC value.

Details

Deviance information criteria (DIC) is

$$- 2 \log p(y \mid \hat\theta_{bayes}) + 2 p_{DIC}$$

where $p_{DIC}$ is the effective number of parameters defined by

$$p_{DIC} = 2 ( \log p(y \mid \hat\theta_{bayes}) - E_{post} \log p(y \mid \theta) )$$

Random sampling from posterior distribution gives its computation, $\theta_i \sim \theta \mid y, i = 1, \ldots, M$

$$p_{DIC}^{computed} = 2 ( \log p(y \mid \hat\theta_{bayes}) - \frac{1}{M} \sum_i \log p(y \mid \theta_i) )$$

References

Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2013). Bayesian data analysis. Chapman and Hall/CRC.

Spiegelhalter, D.J., Best, N.G., Carlin, B.P. and Van Der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64: 583-639.