waic.angmcmc {BAMBI} | R Documentation |

## Watanabe-Akaike Information Criterion (WAIC) for angmcmc objects

### Description

Watanabe-Akaike Information Criterion (WAIC) for angmcmc objects

### Usage

```
## S3 method for class 'angmcmc'
waic(x, ...)
```

### Arguments

`x` |
angmcmc object. |

`...` |
additional model specific arguments to be passed to waic from loo. For example, |

### Details

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

, and an estimate
`\eta* = (\sum \eta_i) / n`

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

, where `y = (y_1, ..., y_n)`

denote the data, `\eta`

is the unknown
parameter vector of the model, `\eta_1, ..., \eta_N`

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

given `y`

and `p(y|\eta)`

is the likelihood function,
the Watanabe-Akaike Information Criterion (WAIC) is defined as

`WAIC = LPPD - p_W`

where

`LPPD = \sum_{i=1}^n \log (N^{-1} \sum_{s=1}^N p(y_i|\eta_s) )`

and (form 1 of)

`p_W = 2 \sum_{i=1}^n [ \log (N^{-1} \sum_{s=1}^N p(y_i|\eta_s) ) - N^{-1} \sum_{s=1}^N \log \:p(y_i|\eta_s) ].`

An alternative form (form 2) for `p_W`

is given by

`p_W = \sum_{i=1}^n \hat{var} \log p(y_i|\eta)`

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

, `\hat{var} \log p(y_i|\eta)`

denotes the estimated variance
of `\log p(y_i|\eta)`

based on the realizations `\eta_1, ..., \eta_N`

.

Note that waic.angmcmc calls waic for computation. If the likelihood contribution of each data
point for each MCMC iteration is available in `object`

(can be returned by setting `return_llik_contri = TRUE`

)
during fit_angmix call), `waic.array`

is used; otherwise `waic.function`

is
called. Computation is much faster if the likelihood contributions are available - however, they are very
memory intensive, and by default not returned in fit_angmix.

### Value

Computes the WAIC 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, return_llik_contri = TRUE)
library(loo)
waic(fit.vmsin.20)
```

*BAMBI*version 2.3.5 Index]