Predictive criterion computed from the posterior, pointwise

AIC and DIC both need a point estimate of the parameters; WAIC does not, which makes it usable for singular models. The effective parameter count falls out as the posterior variance of the pointwise log likelihood, and a large variance for some observation is a warning that the posterior is being stretched by that point.

Usage

Waicd(log_lik)

Arguments

log_lik

Pointwise log likelihood, draws by observations.

Value

List with estimate, lppd, p_waic, elpd, n_high_var, S, n.

Details

Formula: lppd = sum_i log mean_s exp(ll_is), p_WAIC = sum_i Var_s(ll_is), WAIC = -2(lppd - p_WAIC).

References

Watanabe, S. (2010). JMLR 11:3571-3594; Vehtari, Gelman & Gabry (2017) Statist Comput 27:1413-1432.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Waicd(V)
#> $estimate
#> [1] -0.7577962
#> 
#> $lppd
#> [1] 6.378898
#> 
#> $p_waic
#> [1] 6
#> 
#> $elpd
#> [1] 0.3788981
#> 
#> $n_high_var
#> [1] 1
#> 
#> $S
#> [1] 8
#> 
#> $n
#> [1] 1
#> 
#> $method
#> [1] "WAIC with effective parameter count"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"