IPMbook (version 0.1.5)

demoMCMC: Demonstration of a random-walk sampler for a single parameter

Description

Generates an MCMC chain for the probability of success on the logit scale, ltheta = logit(theta), for binomial data with y successes in N trials. The prior for ltheta is a Normal distribution with mean mu.ltheta and SD sd.ltheta. Proposal values are drawn from a Normal distribution with mean = current value and SD = prop.sd.

Usage

demoMCMC(y = 20, N = 50, niter = 25000, mu.ltheta = 0, sd.ltheta = 100,
    prop.sd = 1, init = 0, quiet = FALSE, show.plots = TRUE)

Value

A list with the values of the input arguments and the following additional elements:

ltheta

a vector with the MCMC draws.

acc.prob

the proportion of proposed values accepted.

Arguments

y

number of successes.

N

number of trials.

niter

the number of MCMC draws required.

mu.ltheta

the mean of the Normal prior distribution for logit(theta).

sd.ltheta

the SD of the Normal prior distribution for logit(theta).

prop.sd

the SD of the Normal distribution for the proposals.

init

initial value for logit(theta).

quiet

if TRUE, console output is suppressed.

show.plots

if FALSE, plotting is suppressed.

Author

Adapted from code in Ntzoufras (2009), p. 48.

References

Ntzoufras, I. (2009) Bayesian Modeling Using WinBUGS, Wiley, Hoboken NJ.

Schaub, M., Kéry, M. (2022), Integrated Population Models, Academic Press, section 2.5.

Examples

require(graphics)
# Default settings
str(tmp <- demoMCMC(y = 20, N = 50, niter = 25000,
  mu.ltheta = 0, sd.ltheta = 100, prop.sd = 1, init = 0))

# Show convergence
str(tmp <- demoMCMC(prop.sd = 0.1, init = 10))

# Show convergence: no convergence
str(tmp <- demoMCMC(prop.sd = 0.1, init = 100))

# Very, very small step size: very inefficient
str(tmp <- demoMCMC(prop.sd = 0.01))

# Very small step size: inefficient
str(tmp <- demoMCMC(prop.sd = 0.1))

# Default step size: pretty good for this case
str(tmp <- demoMCMC(prop.sd = 1))

# Larger than default step size: efficiency goes down again
str(tmp <- demoMCMC(prop.sd = 10))

# Muuuuch larger ..... brrrrr !
str(tmp <- demoMCMC(prop.sd = 100))