Sampling functions for Bayesian analysis of mixture autoregressive models

Sampling functions for Bayesian analysis of mixture autoregressive models. Draws observations from posterior distributions of the latent variables Z_ts and the parameters of mixture autoregressive models.

Usage

sampZpi(y, pk, prob, mu, AR, sigma, nsim, d)
sampMuShift(y, pk, prec, nk, shift, z, AR, nsim)
sampSigmaTau(y, pk, prec, nk, AR, mu, z, a, c, nsim)

Arguments

y

a time series (currently a numeric vector).

pk

numeric vector of length g. The autoregressive order of each component.

prob

numeric vector of length g. Current mixing weights.

mu

numeric vector of length g. Current mean parameters.

shift

numeric vector of length g. Current shift parameters.

AR

list of g elements. Autoregressive coefficients for each component.

sigma

numeric vector of length g. Current scale parameters

nsim

dessired sample size.

d

numeric vector of length g. Hyperparameters for Dirichlet prior. If missing, a vector of 1s is generated. If length is 1, creates a vector of length g with given number.

prec

numeric vector of length g. Current precision parameters.

nk

output from sampZpi. Component sum of latent variables Z_t.

z

output latentZ from sampZpi. A matrix containing the simulated latent variables.

a,c

hyperparameters.

Details

sampZpi draws observations from posterior distributions of the latent variables Z_ts and mixing weights of a Mixture autoregressive model.

sampSigmaTau draws observations from posterior distributions of the precisions tau_k of a Mixture autoregressive model, and obtains scales sigma_k by transformation.

sampMuShift Draws observations from posterior distributions of the means mu_k of a Mixture autoregressive model, and obtains shifts phi_k0 by transformation.

Value

for sampZpi, a list containing the following elements:

mix_weights

matrix with nrow = nsim and ncol = g: sampled mixing weights.

latentZ

matrix with nrow = n - p and ncol = g, n equal to length(y) and p equal to max(pk: the simulated latent variables Z_t at the last of nsim iterations (functional). Specifically, each row contains 1 for exactly one component, and is filled with 0.

nk

Vector of length g. Column sums of latentZ.

for sampMuShift, a list containing the following elements:

shift

matrix with nrow = nsim and ncol = g: simulated shift parameters, obtained by transformation of the means.

mu

matrix with nrow = nsim and ncol = g: simulated mean parameters.

for sampSigmaTau, a list containing the following elements:

scale

matrix with nrow = nsim and ncol = g: scale parameters, obtained by transformation of precisions.

precision

matrix with nrow = nsim and ncol = g: precision parameters.

lambda

numeric vector of length nsim simulated values of hyperparameter lambda, due to hierarchical setup.

Author

Davide Ravagli

Examples

model <- new("MixARGaussian",
             prob   = exampleModels$WL_At@prob,      # c(0.5, 0.5)
             scale  = exampleModels$WL_At@scale,     # c(1, 2)        
             arcoef = exampleModels$WL_At@arcoef@a ) # list(-0.5, 1.1)
             
prob  <- model@prob
sigma <- model@scale
prec  <- 1 / sigma ^ 2
g     <- length(model@prob)
d     <- rep(1, g)
pk    <- model@arcoef@p
p     <- max(pk)
shift <- mu <- model@shift
         
AR <- model@arcoef@a       

model
#> An object of class "MixARGaussian"
#> Number of components: 2 
#>        prob shift scale order ar_1
#> Comp_1 0.5    0     1     1   -0.5
#> Comp_2 0.5    0     2     1    1.1
#> 
#> Distributions of the error components:
#> 	standard Gaussian
#> 

set.seed(1234)
n <- 50 # 500
nsim <- 50

y <- mixAR_sim(model, n = n, init = 0)
x  <- sampZpi(y, pk, prob, shift, AR, sigma, nsim = nsim, d)
x1 <- sampMuShift(y, pk, prec, nk = x$nk, shift, z = x$latentZ, AR, nsim = nsim)
x2 <- sampSigmaTau(y, pk, prec, nk = x$nk, AR, mu = x1$mu, z = x$latentZ,
                   a = 0.2, c = 2, nsim = nsim)