marginalLikelihood_bySufficientStatistics.CatDP

Sufficient statistics of x. In Categorical-DP case the sufficient statistic of sample x can either be an object of type "ssCatDP" generated by sufficientStatistics(), or x itself(if x is a integer vector with all positive values).

Return the log density if set to "TRUE".

Additional arguments to be passed to other inherited types.

Generate the marginal likelihood of the following model structure:
 $$pi|alpha \sim DP(alpha,U)$$
 $$x|pi \sim Categorical(pi)$$
where DP(alpha,U) is a Dirichlet Process on positive integers, alpha is the "concentration parameter" of the Dirichlet Process, U is the "base measure" of this Dirichlet process, it is an uniform distribution on all positive integers.Categorical() is the Categorical distribution. See <code>dCategorical</code> for the definition of the Categorical distribution. 
In the case of CatDP, x can only be positive integers. 
The model structure and prior parameters are stored in a "CatDP" object. 
Marginal likelihood = p(x|alpha).

A set of frequently used Bayesian parametric and nonparametric model structures, as well as a set of tools for common analytical tasks. Structures include linear Gaussian systems, Gaussian and Normal-Inverse-Wishart conjugate structure, Gaussian and Normal-Inverse-Gamma conjugate structure, Categorical and Dirichlet conjugate structure, Dirichlet Process on positive integers, Dirichlet Process in general, Hierarchical Dirichlet Process ... Tasks include updating posteriors, sampling from posteriors, calculating marginal likelihood, calculating posterior predictive densities, sampling from posterior predictive distributions, calculating "Maximum A Posteriori" (MAP) estimates ... See <https://chenhaotian.github.io/Bayesian-Bricks/> to get started.

marginalLikelihood_bySufficientStatistics.CatDP: Marginal likelihood of a "CatDP" object, using sufficient statistics

Description

Usage

Arguments

Value

See Also