BCauchy {bmstdr}

Cauchy prior simulation example.

Description

Cauchy prior simulation example.

Usage

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.

Value

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)