Bayes-and-Certainty.md

@@ -74,12 +74,12 @@ So one idea to handle this is to weigh the opinions as follows:
 
 1) Use the regular Bayes equation to combine the two probabilities. This is the one limit.
 2) Use the experiment with the most evidence for it (most decimal places) to establish another limit, $P_1$.
-3) Decide on a factor for the difference in evidence between the two experiments using the decimal place of the reported probabilities. An 80.3% probability vs. 73% has one more decimal place and so gives the 80.3% opinion 10 times the weight of the 73% opinion. This leads to the equation $f = 10^{Nd1-Nd2}$. Of course, if the probability comes with the sample size used to calculate it we can just divide the sample sizes to obtain the factor.
+3) Decide on a factor for the difference in evidence between the two experiments using the decimal place of the reported probabilities. An 80.3% probability vs. 73% has one more decimal place and so gives the 80.3% opinion 10 times the weight of the 73% opinion. This leads to the equation $f = 10^{Nd_1-Nd_2}$ where $Nd_1$ is the number of decimal places of the most accurate probability. Of course, if the probability comes with the sample size used to calculate it we can just divide the sample sizes to obtain the factor.
 4) Use the factor just calculated as a weighting factor in establishing the combined opinion between the lower and upper limit.
 
 For example, using $P_1 = 0.803$ and $P_2 = 0.73$,
 
 1) $P\_{bay} = {0.803(0.73)\over {0.803(0.73) + 0.197(0.27)}} = 0.917$
-2) $P\_{lo} = 0.803$
-3) $f=10^{(Nd_1 - Nd_2)}$
-4) $P_{comb,w} = 0.803 + {(0.917 - 0.803)\over f} = 0.8144$
+2) $P\_{1} = 0.803$
+3) $f=10^{(Nd_1 - Nd_2)} = 10^{3-2} = 10$
+4) $P_{comb,w} = 0.803 + {(0.917 - 0.803)\over 10} = 0.8144$
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