mcmcrecord_gaussian: MCMC iterations
In bbemkr: Bayesian bandwidth estimation for multivariate kernel regression with Gaussian error

Description Usage Arguments Details Value Note Author(s) References See Also

Estimated averaged bandwidths of the regressors and averaged variance parameter of the normal error density

mcmcrecord_gaussian(x, inicost, mutsizp, warm = 100, M = 100, prob = 0.234, 
           num_batch = 10, step = 10, data_x, data_y, xm, 
           alpha = 0.05, prior_p = 2, prior_st = 1, 
           mlike = c("Chib", "Geweke", "LaplaceMetropolis", "all"))

`x`	Log of square bandwidth
`inicost`	Initial cost value
`mutsizp`	Step size of random-walk Metropolis algorithm. At each iteration, the value of `mutsizp` will alter depending on acceprance or rejection. As the number of iteration increases, the final acceptance probability will converge to the optimal rate, which is 0.234 for multiple parameters
`warm`	Burn-in period
`M`	Number of MCMC iteration
`prob`	Optimal acceptance rate of random-walk Metropolis algorithm
`num_batch`	Number of batch samples
`step`	Recording value at a specific step, in order to achieve iid samples and eliminate correlation
`data_x`	Regressors
`data_y`	Response variable
`xm`	Values of true regression function
`alpha`	Quantile of the critical value in calculating Geweke's log marginal likelihood
`prior_p`	Hyperparameter of inverse-gamma prior
`prior_st`	Hyperparameter of inverse-gamma prior
`mlike`	Method for calculating log marginal likelihood

Akin to the burn-in period, it determines the retained bandwidths for the regressors and the variance of the error density for finite samples. It also calculates the simulation inefficient factor (SIF) value, R square, mean square error, and log marginal density by Chib (1995), Geweke (1999) and the Laplace Metropolis method describe in Raftery (1996).

`sum_h`	Estimated parameters in an order of the bandwidths of the regressors, the variance parameter of the error density and cost value
`h2`	Estimated parameters in an order of the square bandwidths of the regressors, the square variance parameter of the error density
`sif`	Simulation inefficient factor. The small it is, the better the method is in general
`mutsizp`	Step size of random-walk Metropolis algroithm for each iteration of `MCMCrecord`
`cpost`	Simulation output of square bandwidths and square normal error variance obtained from MCMC
`accept`	Acceptance rate of random-walk Metropolis algorithm
`marginalike`	Log marginal likelihood
`R2`	R square
`MSE`	Mean square error

Time-consuming for large iterations.

Han Lin Shang

H. L. Shang (2013) Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density, Computational Statistics and Data Analysis, 67, 185-198.

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 and I. Jeliazkov (2001) Marginal likelihood from the Metropolis-Hastings output, Journal of the American Statistical Association, 96, 453, 270-281.

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.

J. Geweke (1998) Using simulation methods for Bayesian econometric models: inference, development, and communication, Econometric Reviews, 18(1), 1-73.

A. E. Raftery (1996) Hypothesis testing and model selection, in Markov Chain Monte Carlo In Practice by W. R. Gilks, S. Richardson and D. J. Spiegelhalter, Chapman and Hall, London.

logdensity_gaussian, logpriors_gaussian, loglikelihood_gaussian, warmup_gaussian

bbemkr documentation built on May 1, 2019, 10:53 p.m.