AIC BIC CIC DIC介绍

基础知识

    极大似然估计

    贝叶斯系数  bayes factor (Jeffreys 1961; kass & Raftery 1995)

AIC 简介 (Akaike 1974)

  由 Kullback-Leibler Information Entropy 的 approximate minimization 衍生而来

  AIC = -2ln Lmax  + 2k

  其中 Lmax 是所选模型的极大似然估计 k 是模型参数的数量

  它的表示了实际数据分布与模型分布见的差异有多大

   所以AIC值越小，实际数据与模型数据匹配度越高

 

BIC 简介 (Schwarz 1978)

  BIC  由approximate the evidence ratios of models (bayes factor) 假设数据是独立的而且是identically distributed

  BIC = -2ln Lmax  + k lnN

  其中N是用来拟合的数据的数量

CIC 简介

DIC 简介

参考资料

 [1] WIKI Akaike information criterion Bayesian information criterion;

 [2] information criteria for astrophysical model selection

 [3] information criteria and model selection

 [4] on the derivation of the Bayesian information crieria

 【5】 Akaike, H. (1974). ``A new look at the statistical model indentification''.IEEE Transactions on Automatic Control, 19:716--722.

    http://wenku.baidu.com/view/2dfd135bbe23482fb4da4c22.html

Estimating the Dimension of a Model

LIKELIHOOD OF A MODEL AND INFORMATION CRITERIA.pdf

Methods for Determining the Order of an Autoregressive-Moving Average Process A Survey.pd

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A New Look at the Statistical Model Identification
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On the Likelihood of a Time Series Model
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