AntMAN (version 1.1.0)

AM_mix_hyperparams_uninorm: univariate Normal mixture hyperparameters

Description

Generate a configuration object that specifies a univariate Normal mixture kernel, where users can specify the hyperparameters of the Normal-InverseGamma conjugate prior. As such, the kernel is a Gaussian distribution with mean \(\mu\) and variance \(\sigma^2\). The prior on \((\mu,\sigma^2)\) the Normal-InverseGamma: $$\pi(\mu,\sigma^2\mid m_0,\kappa_0,\nu_0,\sigma^2_0) = \pi_{\mu}(\mu|\sigma^2,m_0,\kappa_0)\pi_{\sigma^2}(\sigma^2\mid \nu_0,\sigma^2_0),$$ $$\pi_{\mu}(\mu|\sigma^2,m_0,\kappa_0) =\frac{\sqrt{\kappa_0}}{\sqrt{2\pi\sigma^2},} \exp^{-\frac{\kappa_0}{2\sigma^2}(\mu-m_0)^2 }, \qquad \mu\in\mathcal{R},$$ $$\pi_{\sigma^2}(\sigma^2\mid \nu_0,\sigma^2_0)= {\frac {\sigma_0^{2^{\nu_0 }}}{\Gamma (\nu_0 )}}(1/\sigma^2)^{\nu_0 +1}\exp \left(-\frac{\sigma_0^2}{\sigma^2}\right), \qquad \sigma^2>0.$$

Usage

AM_mix_hyperparams_uninorm(m0, k0, nu0, sig02)

Arguments

m0

The \(m_0\) hyperparameter.

k0

The \(\kappa_0\) hyperparameter.

nu0

The \(\nu_0\) hyperparameter.

sig02

The \(\sigma^2_0\) hyperparameter.

Value

An AM_mix_hyperparams object. This is a configuration list to be used as mix_kernel_hyperparams argument for AM_mcmc_fit.

Details

\(m_0\) corresponds m0, \(\kappa_0\) corresponds k0, \(\nu_0\) corresponds nu0, and \(\sigma^2_0\) corresponds sig02.

If hyperparameters are not specified, the default is m0=0, k0=1, nu0=3, sig02=1.

Examples

# NOT RUN {
     
     #### This example ...
     
     data(galaxy)
     y_uvn = galaxy
     mixture_uvn_params = AM_mix_hyperparams_uninorm  (m0=20.83146, k0=0.3333333,
                                                       nu0=4.222222, sig02=3.661027)
     
     mcmc_params        = AM_mcmc_parameters(niter=2000, burnin=500, thin=10, verbose=0)
     components_prior   = AM_mix_components_prior_pois (init=3,  a=1, b=1) 
     weights_prior      = AM_mix_weights_prior_gamma(init=2, a=1, b=1)
     
     fit <- AM_mcmc_fit(
       y = y_uvn,
       mix_kernel_hyperparams = mixture_uvn_params,
       mix_components_prior =components_prior,
       mix_weight_prior = weights_prior,
       mcmc_parameters = mcmc_params)
     
     summary (fit)
     plot (fit)
     
# }