BPSpostSample: Function to Sample Hazard Rates from BPS Posteriors
In BayHaz: R Functions for Bayesian Hazard Rate Estimation

Description Usage Arguments Details Value Note References See Also Examples

A function to generate a random sample of hazard rates from the posterior distribution originated by a first order autoregressive BPS prior through the observation of a sequence of possibly right censored times to event.

1	BPSpostSample(hyp, times, obs = NULL, mclen = 10, burnin = 0, thin = 1, df = 10, etastar = NULL)

`hyp`	list of hyperparameters (as generated by `BPSpriorElicit`)
`times`	vector of (possibly right censored) times to event
`obs`	vector of censoring indicators (0 = censored, 1 = exact)
`mclen`	requested sample size
`burnin`	burn-in parameter
`thin`	thinning parameter
`df`	degrees of freedom for the multivariate Student-t proposal distribution
`etastar`	posterior mode and corresponding hessian in list format (as generated by `optim` with `hessian = TRUE`)

A Markov chain sample of length mclen from the posterior distribution originated by hyp through the observation of times and obs is generated using a taylored proposal density Metropolis-Hastings sampler (starting at the posterior mode); see Chib \& Greenberg (1995).

The first burnin states of the Markov chain are discarded, then one every thin is kept.

If obs is NULL, it is assumed that all observations are exact (no censoring).

A list with seven components:

`hyp`	list of hyperparameters identifying the BPS prior that originated the posterior distribution from which the sample was extracted (copy of the input argument)
`dat`	dataframe with two variables (`times` and `obs`) containing the observations on which the posterior distribution is based
`burnin`	burn-in parameter used (copy of the input argument)
`thin`	thinning parameter used (copy of the input argument)
`df`	degrees of freedom used for the multivariate Student-t proposal distribution (copy of the input argument)
`etastar`	posterior mode and corresponding hessian in list format (copy of the input argument or computed via `optim` if the input argument was NULL)
`eta`	matrix with `mclen` rows (and `length(hyp$knots)-hyp$ord` columns) containing the spline weights

If mclen is equal to zero eta will be a chain of length one containing the posterior mode.

Chib, S. \& E. Greenberg (1995). Understanding the Metropolis-Hastings algorithm. American Statistician 49, 327–335.

BayHaz-package, BPSevalHR, BPSplotHR, BPSpost2mcmc

# set RNG seed (for example reproducibility only)
set.seed(1234)

# select a BPS prior distribution
hypars<-BPSpriorElicit(r0 = 0.1, H = 1, T00 = 50, ord = 4, G = 3, c = 0.9)
# load a data set
data(earthquakes)

# find the posterior mode
postmode<-BPSpostSample(hypars, times = earthquakes$ti, obs = earthquakes$ob, mclen = 0)
# evaluate the posterior mode hazard rate at year multiples
BPSevalHR(time = seq(0,50), sample = postmode)

# generate a posterior sample
post<-BPSpostSample(hypars, times = earthquakes$ti, obs = earthquakes$ob, etastar = postmode$etastar)
# plot some posterior hazard rate summaries
BPSplotHR(post, tu = "Year")