AM_mix_hyperparams_uninorm {AntMAN}R Documentation

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 μ and variance σ^2. The prior on (μ,σ^2) the Normal-InverseGamma:

π(μ,σ^2\mid m_0,κ_0,ν_0,σ^2_0) = π_{μ}(μ|σ^2,m_0,κ_0)π_{σ^2}(σ^2\mid ν_0,σ^2_0),

π_{μ}(μ|σ^2,m_0,κ_0) =\frac{√{κ_0}}{√{2πσ^2},} \exp^{-\frac{κ_0}{2σ^2}(μ-m_0)^2 }, \qquad μ\in\mathcal{R},

π_{σ^2}(σ^2\mid ν_0,σ^2_0)= {\frac {σ_0^{2^{ν_0 }}}{Γ (ν_0 )}}(1/σ^2)^{ν_0 +1}\exp ≤ft(-\frac{σ_0^2}{σ^2}\right), \qquad σ^2>0.

Usage

AM_mix_hyperparams_uninorm(m0, k0, nu0, sig02)

Arguments

m0

The m_0 hyperparameter.

k0

The κ_0 hyperparameter.

nu0

The ν_0 hyperparameter.

sig02

The σ^2_0 hyperparameter.

Details

m_0 corresponds m0, κ_0 corresponds k0, ν_0 corresponds nu0, and σ^2_0 corresponds sig02.

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

Value

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

Examples

     
     #### 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)
     

[Package AntMAN version 1.1.0 Index]