AM_mix_components_prior_pois

The shape parameter <code>a</code> of the $Gamma(a,b)$ prior distribution.

The rate parameter <code>b</code> of the $Gamma(a,b)$ prior distribution.

It allows to set the hyperparameter $\Lambda$ to be assigned a fixed value.

Lambda

The initial value for $\Lambda$, when specifying <code>a</code> and <code>b</code>.

init

This function generates a configuration object for a Shifted Poisson prior on the number
of mixture components such that
$$q_M(m)= Pr (M=m)= \frac{e^{-\Lambda}\Lambda^{m-1} }{(m-1)!} , \quad m=1,2,3,\ldots$$
The hyperparameter $\Lambda$ can either be fixed using <code>Lambda</code>
or assigned a $Gamma(a,b)$ prior distribution with <code>a</code> and <code>b</code>.
In AntMAN we assume the following parametrization of the Gamma density:
$$p(x\mid a,b )= \frac{b^a x^{a-1}}{\Gamma(a)} \exp\{ -bx \}, \quad x&gt;0.$$

Prior

Fits finite Bayesian mixture models with a random number of components. The MCMC algorithm implemented is based on point processes as proposed by Argiento and De Iorio (2019) <arXiv:1904.09733> and offers a more computationally efficient alternative to reversible jump. Different mixture kernels can be specified: univariate Gaussian, multivariate Gaussian, univariate Poisson, and multivariate Bernoulli (latent class analysis). For the parameters characterising the mixture kernel, we specify conjugate priors, with possibly user specified hyper-parameters. We allow for different choices for the prior on the number of components: shifted Poisson, negative binomial, and point masses (i.e. mixtures with fixed number of components).

AM_mix_components_prior_pois: Generate a configuration object for a Poisson prior on the number of mixture components

Description

Usage

Arguments

Value

Details

See Also

Examples