In
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, the widely applicable information criterion (WAIC), also known as Watanabe–Akaike information criterion, is the generalized version of the
Akaike information criterion
The Akaike information criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to e ...
(AIC) onto
singular statistical models.
Widely applicable Bayesian information criterion (WBIC) is the generalized version of
Bayesian information criterion
In statistics, the Bayesian information criterion (BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; models with lower BIC are generally preferred. It is based, in part, on ...
(BIC) onto
singular statistical models.
WBIC is the
average log likelihood function over the
posterior distribution
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule. From an epistemological perspective, the posterior p ...
with the
inverse temperature
In statistical thermodynamics, thermodynamic beta, also known as coldness, is the reciprocal of the thermodynamic temperature of a system:\beta = \frac (where is the temperature and is Boltzmann constant).J. Meixner (1975) "Coldness and Tempe ...
> 1/log ''n'' where ''n'' is the
sample size
Sample size determination is the act of choosing the number of observations or Replication (statistics), replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make stat ...
.
[
Both WAIC and WBIC can be numerically calculated without any information about a true distribution.
]
See also
*Akaike information criterion
The Akaike information criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Given a collection of models for the data, AIC estimates the quality of each model, relative to e ...
*Bayesian information criterion
In statistics, the Bayesian information criterion (BIC) or Schwarz information criterion (also SIC, SBC, SBIC) is a criterion for model selection among a finite set of models; models with lower BIC are generally preferred. It is based, in part, on ...
*Deviance information criterion The deviance information criterion (DIC) is a hierarchical modeling generalization of the Akaike information criterion (AIC). It is particularly useful in Bayesian model selection problems where the posterior distributions of the models have been o ...
*Hannan–Quinn information criterion In statistics, the Hannan–Quinn information criterion (HQC) is a criterion for model selection. It is an alternative to Akaike information criterion (AIC) and Bayesian information criterion (BIC). It is given as
: \mathrm = -2 L_ + 2 k \ln(\ln ...
*Shibata information criterion Shibata may refer to:
Places
* Shibata, Miyagi, a town in Miyagi Prefecture
* Shibata District, Miyagi, a district in Miyagi Prefecture
* Shibata, Niigata, a city in Niigata Prefecture
** Shibata Station (Niigata), a railway station in Niigata Pre ...
References
Model selection
Bayesian statistics
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