This is a generic function that will generate the marginal likelihood of a set of observations conditioned on a given "BayesianBrick" object. i.e. for the model structure:
$$theta|gamma \sim H(gamma)$$
$$x|theta \sim F(theta)$$
Marginal likelihood is p(x|gamma), p() is the probability density/mass function for continuous/discrete x.
For a given Bayesian bricks object obj and a sample set x, marginalLikelihood_bySufficientStatistics() will calculate the marginal likelihood for different model structures:
Where
$$x \sim Gaussian(A z + b, Sigma)$$
$$z \sim Gaussian(m,S)$$
marginalLikelihood_bySufficientStatistics() will return p(x|m,S,A,b,Sigma)
See ?marginalLikelihood_bySufficientStatistics.LinearGaussianGaussian for details.
Where
$$x \sim Gaussian(mu,Sigma)$$
$$mu \sim Gaussian(m,S)$$
Sigma is known.
marginalLikelihood_bySufficientStatistics() will return p(x|m,S,Sigma)
See ?marginalLikelihood_bySufficientStatistics.GaussianGaussian for details.
Where
$$x \sim Gaussian(mu,Sigma)$$
$$Sigma \sim InvWishart(v,S)$$
mu is known.
marginalLikelihood_bySufficientStatistics() will return p(x|mu,v,S)
See ?marginalLikelihood_bySufficientStatistics.GaussianInvWishart for details.
Where
$$x \sim Gaussian(mu,Sigma)$$
$$Sigma \sim InvWishart(v,S)$$
$$mu \sim Gaussian(m,Sigma/k)$$
marginalLikelihood_bySufficientStatistics() will return p(x|m,k,v,S)
See ?marginalLikelihood_bySufficientStatistics.GaussianNIW for details.
Where
$$x \sim Gaussian(X beta,sigma^2)$$
$$sigma^2 \sim InvGamma(a,b)$$
$$beta \sim Gaussian(m,sigma^2 V)$$
X is a row vector, or a design matrix where each row is an obervation.
marginalLikelihood_bySufficientStatistics() will return p(x,X|m,V,a,b)
See ?marginalLikelihood_bySufficientStatistics.GaussianNIG for details.
Where
$$x \sim Categorical(pi)$$
$$pi \sim Dirichlet(alpha)$$
marginalLikelihood_bySufficientStatistics() will return p(x|alpha)
See ?marginalLikelihood_bySufficientStatistics.CatDirichlet for details.
Where
$$x \sim Categorical(pi)$$
$$pi \sim DirichletProcess(alpha)$$
marginalLikelihood_bySufficientStatistics() will return p(x|alpha)
See ?marginalLikelihood_bySufficientStatistics.CatDP for details.
marginalLikelihood_bySufficientStatistics(obj, ...)A "BayesianBrick" object used to select a method.
further arguments passed to or from other methods.
numeric, the marginal likelihood
marginalLikelihood_bySufficientStatistics.LinearGaussianGaussian for Linear Gaussian and Gaussian conjugate structure, marginalLikelihood_bySufficientStatistics.GaussianGaussian for Gaussian-Gaussian conjugate structure, marginalLikelihood_bySufficientStatistics.GaussianInvWishart for Gaussian-Inverse-Wishart conjugate structure, marginalLikelihood_bySufficientStatistics.GaussianNIW for Gaussian-NIW conjugate structure, marginalLikelihood_bySufficientStatistics.GaussianNIG for Gaussian-NIG conjugate structure, marginalLikelihood_bySufficientStatistics.CatDirichlet for Categorical-Dirichlet conjugate structure, marginalLikelihood_bySufficientStatistics.CatDP for Categorical-DP conjugate structure ...