MCMCpoissonChangepoint {MCMCpack}R Documentation

Markov Chain Monte Carlo for a Poisson Multiple Changepoint Model

Description

This function generates a sample from the posterior distribution of a Poisson model with multiple changepoints. The function uses the Markov chain Monte Carlo method of Chib (1998). The user supplies data and priors, and a sample from the posterior distribution is returned as an mcmc object, which can be subsequently analyzed with functions provided in the coda package.

Usage

MCMCpoissonChangepoint(data,  m = 1, burnin = 1000, mcmc = 1000,
        thin = 1, verbose = 0, seed = NA, c0, d0, a = NULL, b = NULL,
        marginal.likelihood = c("none", "Chib95"), ...) 

Arguments

data The data.
m The number of changepoints.
burnin The number of burn-in iterations for the sampler.
mcmc The number of MCMC iterations after burn-in.
thin The thinning interval used in the simulation. The number of MCMC iterations must be divisible by this value.
verbose A switch which determines whether or not the progress of the sampler is printed to the screen. If verbose is greater than 0, the iteration number and the posterior density samples are printed to the screen every verboseth iteration.
seed The seed for the random number generator. If NA, current R system seed is used.
c0 c0 is the shape parameter for Gamma prior on lambda (the mean).
d0 d0 is the scale parameter for Gamma prior on lambda (the mean).
a a is the shape1 beta prior for transition probabilities. By default, the expected duration is computed and corresponding a and b values are assigned. The expected duration is the sample period divided by the number of states.
b b is the shape2 beta prior for transition probabilities. By default, the expected duration is computed and corresponding a and b values are assigned. The expected duration is the sample period divided by the number of states.
marginal.likelihood How should the marginal likelihood be calculated? Options are: none in which case the marginal likelihood will not be calculated, and Chib95 in which case the method of Chib (1995) is used.
... further arguments to be passed

Details

MCMCpoissonChangepoint simulates from the posterior distribution of a Poisson model with multiple changepoints.

The model takes the following form:

Y_t ~ Poisson(lambda_i), i = 1,...,k.

Where k is the number of states.

We assume Gamma priors for lambda_i and Beta priors for transition probabilities:

lambda_i ~ Gamma(c0, d0)

p_ii ~ Beta(a, b), i = 1,...,k.

Where k is the number of states.

Note that no default value is provided for Gamma priors.

The simulation in this model-fitting is performed in R.

Value

An mcmc object that contains the posterior sample. This object can be summarized by functions provided by the coda package. The object contains an attribute prob.state storage matrix that contains the probability of state_i for each period, and the log-likelihood of the model (log.like).

Author(s)

Jong Hee Park, jhp@uchicago.edu, http://home.uchicago.edu/~jhp/.

References

Siddhartha Chib. 1995. "Marginal Likelihood from the Gibbs Output." Journal of the American Statistical Association. 90: 1313-1321.

Siddhartha Chib. 1998. "Estimation and comparison of multiple change-point models." Journal of Econometrics. 86: 221-241.

Martyn Plummer, Nicky Best, Kate Cowles, and Karen Vines. 2002. Output Analysis and Diagnostics for MCMC (CODA). http://www-fis.iarc.fr/coda/.

See Also

plotPostState, plotPostChangepoint

Examples

    ## Not run: 
    ## generate event count time series data with two breakpoints at 100 and 200
    set.seed(1973)
    n           <-  300
    true.lambda <-  c(3, 2, 4)
    y1          <-  rpois(100, true.lambda[1]) 
    y2          <-  rpois(100, true.lambda[2]) 
    y3          <-  rpois(100, true.lambda[3]) 
    y           <-  c(y1, y2, y3)
   
    ## run the example   
    model1 <-  MCMCpoissonChangepoint(y, m=1, burnin = 100, mcmc = 100, 
                thin=1,  verbose=5, c0=3, d0=1,  marginal.likelihood =
                c("Chib95"))  
    model2 <-  MCMCpoissonChangepoint(y, m=2, burnin = 100, mcmc = 100, 
                thin=1, verbose=5, c0=3, d0=1,  marginal.likelihood =
                c("Chib95"))
    model3 <-  MCMCpoissonChangepoint(y, m=3, burnin = 100, mcmc = 100,
                thin=1, verbose=5, c0=3, d0=1,  marginal.likelihood =
                c("Chib95"))
    model4 <-  MCMCpoissonChangepoint(y, m=4, burnin = 100, mcmc = 100,
                thin=1, verbose=5, c0=3, d0=1,  marginal.likelihood = 
                c("Chib95"))
                
    ## perform model comparison  
    BayesFactor(model1, model2, model3, model4)
       
    ## Draw plots using the "right" model
    plotPostState(model2, y, m=2, legend.control=NULL) 
    plotPostChangepoint(model2, y, m=2)    
    
## End(Not run)

[Package MCMCpack version 0.8-1 Index]