mcmcrecord_admkr: 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 of the kernel-form error density

1
2
3

mcmcrecord_admkr (x, inicost, mutsizp, errorsizp, warm = 100, M = 100, prob = 0.234, 
    errorprob = 0.44, num_batch = 10, step = 10, data_x, data_y, xm, alpha = 0.05, 
      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
`errorsizp`	Step size of random-walk Metropolis algorithm. At each iteration, the value of `errorsizp` 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 0.44 for single parameter
`warm`	Burn-in period
`M`	Number of MCMC iteration
`prob`	Optimal acceptance rate of random-walk Metropolis algorithm for the regression function
`errorprob`	Optimal acceptance rate of random-walk Metropolis algorithm for the error density
`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
`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 obtained from MCMC
`ghost`	Simulation output of square bandwidths obtained from MCMC
`accept_nw`	Acceptance rate of random-walk Metropolis algorithm for the regression function
`accept_erro`	Acceptance rate of random-walk Metropolis algorithm for the kernel-form error density
`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 semi-functional partial linear regression model with unknown error density, Computational Statistics, in press.

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_admkr, logpriors_admkr, loglikelihood_admkr, warmup_admkr

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