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Correction re. Jeffreys' pseudocounts

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hyginn 2017-11-20 19:00:23 -05:00
parent 9a987c22be
commit a1b5eb7b90
1 changed files with 5 additions and 5 deletions
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FND-STA-Probability_distribution.R
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@ -25,7 +25,7 @@
#TOC> ========================================================================== #TOC> ==========================================================================
#TOC> #TOC>
#TOC> Section Title Line #TOC> Section Title Line
#TOC> ----------------------------------------------------------------------- #TOC> -----------------------------------------------------------------------
#TOC> 1 Introduction 49 #TOC> 1 Introduction 49
@ -42,7 +42,7 @@
#TOC> 4.2.1 An example from tossing dice 452 #TOC> 4.2.1 An example from tossing dice 452
#TOC> 4.2.2 An example from lognormal distributions 574 #TOC> 4.2.2 An example from lognormal distributions 574
#TOC> 4.3 Kolmogorov-Smirnov test for continuous distributions 616 #TOC> 4.3 Kolmogorov-Smirnov test for continuous distributions 616
#TOC> #TOC>
#TOC> ========================================================================== #TOC> ==========================================================================
@ -449,7 +449,7 @@ chisq.test(countsL1, countsG1.9, simulate.p.value = TRUE, B = 10000)
# be applied to discrete distributions. But we need to talk a bit about # be applied to discrete distributions. But we need to talk a bit about
# converting counts to p.m.f.'s. # converting counts to p.m.f.'s.
# === 4.2.1 An example from tossing dice # === 4.2.1 An example from tossing dice
# The p.m.f of an honest die is (1:1/6, 2:1/6, 3:1/6, 4:1/6, 5:1/6, 6:1/6). But # The p.m.f of an honest die is (1:1/6, 2:1/6, 3:1/6, 4:1/6, 5:1/6, 6:1/6). But
# there is an issue when we convert sampled counts to frequencies, and estimate # there is an issue when we convert sampled counts to frequencies, and estimate
@ -482,7 +482,7 @@ pmf
# for ordered data one could substitute the average values of the two bracketing # for ordered data one could substitute the average values of the two bracketing
# outcomes. But a simple and quite robust solution is to add "pseudocounts". # outcomes. But a simple and quite robust solution is to add "pseudocounts".
# This is called adding a Laplace prior, or a Jeffreys prior: in our case, # This is called adding a Laplace prior, or a Jeffreys prior: in our case,
# simply add 0.5 to every value that the two functions don't share. # simply add 0.5 to every category.
# pmf of an honest die # pmf of an honest die
pmfHD <- rep(1/6, 6) pmfHD <- rep(1/6, 6)
@ -571,7 +571,7 @@ abline(v = KLdiv(rep(1/6, 6), pmfPC(counts, 1:6)), col="firebrick")
# somewhat but not drastically atypical. # somewhat but not drastically atypical.
# === 4.2.2 An example from lognormal distributions # === 4.2.2 An example from lognormal distributions
# We had compared a set of lognormal and gamma distributions above, now we # We had compared a set of lognormal and gamma distributions above, now we
# can use KL-divergence to quantify their similarity: # can use KL-divergence to quantify their similarity: