Source Code for Module lib.model_selection

  1  ############################################################################### 
  2  #                                                                             # 
  3  # Copyright (C) 2003-2013 Edward d'Auvergne                                   # 
  4  #                                                                             # 
  5  # This file is part of the program relax (http://www.nmr-relax.com).          # 
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 20  ############################################################################### 
 21   
 22  # Module docstring. 
 23  """Module for the statistical concept of model selection.""" 
 24   
 25  # Python module imports. 
 26  from math import log 
 27   
 28  # relax module imports. 
 29  from lib.errors import RelaxError 
 30   
 31   
 32 -def aic(chi2, k, n): 
 33      """Akaike's Information Criteria (AIC). 
 34   
 35      The formula is:: 
 36   
 37          AIC = chi2 + 2k 
 38   
 39   
 40      @param chi2:    The minimised chi-squared value. 
 41      @type chi2:     float 
 42      @param k:       The number of parameters in the model. 
 43      @type k:        int 
 44      @param n:       The dimension of the relaxation data set. 
 45      @type n:        int 
 46      @return:        The AIC value. 
 47      @rtype:         float 
 48      """ 
 49   
 50      return chi2 + 2.0*k 
 51   
 52   
 53 -def aicc(chi2, k, n): 
 54      """Small sample size corrected AIC. 
 55   
 56      The formula is:: 
 57   
 58                             2k(k + 1) 
 59          AICc = chi2 + 2k + --------- 
 60                             n - k - 1 
 61   
 62   
 63      @param chi2:    The minimised chi-squared value. 
 64      @type chi2:     float 
 65      @param k:       The number of parameters in the model. 
 66      @type k:        int 
 67      @param n:       The dimension of the relaxation data set. 
 68      @type n:        int 
 69      @return:        The AIC value. 
 70      @rtype:         float 
 71      """ 
 72   
 73      if n > (k+1): 
 74          return chi2 + 2.0*k + 2.0*k*(k + 1.0) / (n - k - 1.0) 
 75      elif n == (k+1): 
 76          raise RelaxError("The size of the dataset, n=%s, is too small for this model of size k=%s.  This situation causes a fatal division by zero as:\n    AICc = chi2 + 2k + 2k*(k + 1) / (n - k - 1).\n\nPlease use AIC model selection instead." % (n, k)) 
 77      elif n < (k+1): 
 78          raise RelaxError("The size of the dataset, n=%s, is too small for this model of size k=%s.  This situation produces a negative, and hence nonsense, AICc score as:\n    AICc = chi2 + 2k + 2k*(k + 1) / (n - k - 1).\n\nPlease use AIC model selection instead." % (n, k)) 
 79   
 80   
 81 -def bic(chi2, k, n): 
 82      """Bayesian or Schwarz Information Criteria. 
 83   
 84      The formula is:: 
 85   
 86          BIC = chi2 + k ln n 
 87   
 88   
 89      @param chi2:    The minimised chi-squared value. 
 90      @type chi2:     float 
 91      @param k:       The number of parameters in the model. 
 92      @type k:        int 
 93      @param n:       The dimension of the relaxation data set. 
 94      @type n:        int 
 95      @return:        The AIC value. 
 96      @rtype:         float 
 97      """ 
 98   
 99      return chi2 + k * log(n) 
100