DIC {BAMBI} | R Documentation |

## Deviance Information Criterion (DIC) for angmcmc objects

### Description

Deviance Information Criterion (DIC) for angmcmc objects

### Usage

```
DIC(object, form = 2, ...)
```

### Arguments

`object` |
angular MCMC object. |

`form` |
form of DIC to use. Available choices are 1 and 2 (default). See details. |

`...` |
additional model specific arguments to be passed to |

### Details

Given a deviance function `D(\theta) = -2 log(p(y|\theta))`

, and an estimate
`\theta* = (\sum \theta_i) / N`

of the posterior mean
`E(\theta|y)`

, where `y`

denote the data, `\theta`

are the unknown
parameters of the model, `\theta_1, ..., \theta_N`

are MCMC samples from the posterior
distribution of `\theta`

given `y`

and `p(y|\theta)`

is the likelihood function,
the (form 1 of) Deviance Infomation Criterion (DIC) is defined as

`DIC = 2 ( (\sum_{s=1}^N D(\theta_s)) / N - D(\theta*) )`

The second form for DIC is given by

`DIC = D(\theta*) - 4 \hat{var} \log p(y|\theta_s)`

where for `i = 1, ..., n`

, `\hat{var} \log p(y|\theta)`

denotes the estimated variance
of the log likelihood based on the realizations `\theta_1, ..., \theta_N`

.

Like AIC and BIC, DIC is an asymptotic approximation for large samples, and is only valid when the posterior distribution is approximately normal.

### Value

Computes the DIC for a given angmcmc object

### Examples

```
# illustration only - more iterations needed for convergence
fit.vmsin.20 <- fit_vmsinmix(tim8, ncomp = 3, n.iter = 20,
n.chains = 1)
DIC(fit.vmsin.20)
```

*BAMBI*version 2.3.5 Index]