waic-methods: Widely Applicable Information Criterion (WAIC)

In jrnold/mcmcStats: MCMC Postprocessing Functions

Description

Widely Applicable Information Criterion (WAIC)

Arguments

x	matrix Containing log likelihood values. Each row is an observation. Each column is an iteration.
method	Method to use when calculing the effective number of parameters.

Value

Object of class WAIC.

Notes

The WAIC is constructed as

WAIC = -2 * (lppd - p_{WAIC})

The lppd is the log pointwise predictive density, defined as

lppd = ∑_{i=1}^n \log ≤ft(\frac{1}{S} ∑_{s=1}^S p(y_i | θ^s)\right)

The value of p_WAIC can be calculated in two ways, the method used is determined by the method argument.

Method 1 is defined as,

p_{WAIC1} = 2 ∑_{i=1}^{n} (\log (\frac{1}{S} ∑_{s=1}^{S} p(y_i \ θ^s)) - \frac{1}{S} ∑_{s = 1}^{S} \log p(y_i | θ^s))

Method 2 is defined as,

p_{WAIC2} = 2 ∑_{i=1}^{n} V_{s=1}^{S} (\log p(y_i | θ^s))

where V_{s=1}^{S} is the sample variance.

References

Gelman, Andrew and Jessica Hwang and Aki Vehtari (2013), "Understanding Predictive Information Criteria for Bayesian Models," http://www.stat.columbia.edu/~gelman/research/unpublished/waic_understand_final.pdf.

Watanabe, S. (2010). "Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory", Journal of Machine Learning Research, http://www.jmlr.org/papers/v11/watanabe10a.html.

See Also

waic

jrnold/mcmcStats documentation built on May 20, 2019, 1:03 a.m.