MCMCregress(formula, data = list(), burnin = 1000, mcmc = 10000,
thin = 5, verbose = FALSE, seed = 0, sigma2.start = NA,
b0 = 0, B0 = 0, nu = 0.001, delta = 0.001, ...)MCMCregress simulates from the posterior density using
standard Gibbs sampling (a multivariate Normal draw for the betas, and an
inverse-Gamma draw for the conditional error variance). The simulation
proper is done in compiled C++ code to maximize efficiency. Please consult
the coda documentation for a comprehensive list of functions that can be
used to analyze the posterior density sample.
The model takes the following form:
$$y_i = x_i ' \beta + \varepsilon_{i}$$
Where the errors are assumed to be Gaussian:
$$\varepsilon_{i} \sim \mathcal{N}(0, \sigma^2)$$
We assume standard, conjugate priors:
$$\beta \sim \mathcal{N}(b_0,B_0^{-1})$$
And:
$$\sigma^{-2} \sim \mathcal{G}amma(\nu/2, \delta/2)$$
Where $\beta$ and $\sigma^{-2}$ are assumed
a priori independent. Note that only starting values for
the conditional error variance are allowed because
$\beta$ is the first block in the sampler.plot.mcmc,summary.mcmc, lmline <- list(X = c(1,2,3,4,5), Y = c(1,3,3,3,5))
line$X <- line$X - mean(line$X)
posterior <- MCMCregress(Y~X, data=line)
plot(posterior)
summary(posterior)Run the code above in your browser using DataLab