mcmcrecord_gaussian {bbemkr} | R Documentation |

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 |

`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 |

`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`

[Package *bbemkr* version 2.0 Index]