BCauchy function

Cauchy prior simulation example.

BCauchy(
  method = "exact",
  true.theta = 1,
  n = 25,
  N = 10000,
  rseed = 44,
  tuning.sd = 1
)

Arguments

• method: Which method or package to use. Possibilities are:

  • "exact": Use exact numerical integration.
  • "importance": Use importance sampling with the prior distribution as the importance sampling distribution.
  • "rejection": Use rejection sampling with the prior distribution as the importance sampling distribution.
  • "independence": Use the Metropolis-Hastings independence sampler with the prior distribution as the proposal distribution.
  • "randomwalk": Use the Metropolis-Hastings random-walk sampler with normal distribution with mean 0 and variance (tuning.sd)^2 as the increment distribution.

• true.theta: True value of theta with a default value of 5.

• n: Data sample size; defaults to 100.

• N: is the number of Monte Carlo samples.

• rseed: is the random number seed for drawing data samples.

• tuning.sd: is the standard deviation of the proposal increment distribution for the random walk sampler.

Returns

A list containing the estimated posterior mean, ybar (the data mean) and the values of the numerator and the denominator integrals The routine simulates n observations from N(theta, 1). Mean of the simulated data values are returned as ybar.

Examples

BCauchy(true.theta = 1, n=25) 
BCauchy(true.theta = 5, n=100) 
BCauchy(method="importance", true.theta = 1, n=25) 
BCauchy(method="importance", true.theta = 1, n=25, N=20000) 
BCauchy(method="rejection", true.theta = 1, n=25) 
BCauchy(method="independence", true.theta = 1, n=25) 
BCauchy(method="randomwalk", true.theta = 1, n=25, tuning.sd =1)