bbemkr (version 1.1)

bbeMCMCrecording: MCMC iterations

Description

Select the final bandwidths of the regressors and the variance parameter of the error density

Usage

bbeMCMCrecording(data_x, data_y, x, costpara, num_batch = 50, 
                 M = 10000, step = 20, sizep = 1.2)

Arguments

data_x

Regressors

data_y

Response variable

x

Retained log bandwidths of the regressors, after the warmup or burnin period

costpara

Retained cost value, after the warmup period

num_batch

Number of batch samples

M

Number of iterations

step

Recording value at a specific step, in order to achieve i.i.d. samples and and eliminate or reduce correlation

sizep

Tuning parameter of the bandwidths

Value

• accept_raterecording
  Acceptance rate of the random-walk Metropolis algorithm
• sum_h
  Selected parameters in an order of bandwidths of the regressors, variance parameter of the error density, likelihood and cost values
• std_h
  Standard deviation of the selected parameters
• batch_h
  Standard deviation of the selected parameters from different draws (equal to num_batch)
• total_sd
  Total standard deviation of the selected parameters
• sif
  Simulation inefficient factor. The small it is, the better the method is in general
• R2
  R square value for determining the goodness of fit
• data_post
  Gibbs output useful for calculating the Chib's (1995) log marginal density
• logmarginalNR
  Newton-Raftery log marginal density
• loglikelihoods
  Log likelihood for the Chib's (1995) log marginal density
• logprior
  Log prior for the Chib's (1995) log marginal density
• logdensity
  Log posterior density calculated from the Gibbs output
• logmarginalChib
  Chib's (1995) log marginal density

Details

Similar to the warmup period, it determines the optimal bandwidths for the regressors and the variance of the error density for finite sample size. It also calculates the SIF value, R square and log marginal density by Newton and Raftery (1994) and Chib (1995).

References

X. Zhang and R. D. Brooks and M. L. King (2009) A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation, Journal of Econometrics, 153, 21-32. S. Chib (1995) Marginal likelihood from the Gibbs output, Journal of the American Statistical Association, 90, 432, 1313-1321. M. A. Newton and A. E. Raftery (1994) Approximate Bayesian inference by the weighted likelihood bootstrap (with discussion), Journal of the Royal Statistical Society, 56, 3-48.

See Also

bbelogdensity, bbelogpriors, bbeloglikelihood

Examples

dummy = bbewarmup(nrr(data_x), bbecost(data_x, data_y, nrr(data_x)), warm = 2)
bbeMCMCrecording(data_x, data_y, dummy$xh, dummy$cost, num_batch = 2, M = 4, step = 2)