hmmr (version 1.0-0)

FFBS_BinomialNormal: Posterior (MCMC) samples for a hidden Markov model with a Binomial and Normal response using the forward-filtering backward-sampling algorithm.

Description

Posterior (MCMC) samples for a hidden Markov model with a Binomial and Normal response using the forward-filtering backward-sampling algorithm.

Usage

FFBS_BinomialNormal(bin,norm,nstates,hyperPars=list(),ntimes,niter=1000,nburnin=0)

Arguments

bin

the Binomial response variable. As in the glm function, this can be a binary vector with 1 indicating success and 0 failure, a factor where the first level is considered a failure and all other leves success, or a matrix with the number of successes and failures in the columns.

norm

the Normal response variable. This should be a numeric vector.

nstates

the required number of states in the hidden Markov model.

hyperPars

a named list with values of the hyper-parameters. See details.

ntimes

the lengths of time series in arguments bin and norm; it defaults to assuming a single time series of length length(bin).

niter

number of iterations to run the sampler for.

nburnin

number of initial samples to discard as burnin,

Value

A named list with samples of the different parameters.

Details

This function runs the forward-filtering backwards-sampling MCMC algorithm for a hidden Markov model with a Binomial and Normal response variable. The response variables are assumed conditionally independent given the states.

The following conjugate prior distributions are used:

For the initial state probabilities, a Dirichlet prior with parameter vector init_alpha

For each row in the transition probability matrix, a Dirichlet prior is used. The parameters of these Dirichlet distributions are contained in the matrix trans_alpha.

For the probability of correct in the Binomial response, a Beta prior is used, with parameters bin_alpha and bin_beta.

For the mean and variance of the Normal response, a Normal-inverse-Gamma prior is used.

This function was written mainly for didactive purposes, not for speed (or compatibility with other packages which provide posterior samples).

References

Visser, I., & Speekenbrink, M. (in preparation). Mixture and hidden Markov models in R.

Examples

# NOT RUN {
# }
# NOT RUN {
  data(speed)
  set.seed(1)
  hyperPars <- list(norm_invsigma_scale=.01,norm_invsigma_shape=.01,norm_mu_sca=.1)
  mcmc_samples <- FFBS_BinomialNormal(speed$corr,speed$rt,nstates=2,
        ntimes=c(168,134,137),niter=500,hyperPars = hyperPars)
        
  plot(mcmc_samples$mu[,1])
  hist(mcmc_samples$mu[,1])
# }
# NOT RUN {
# }