Bayes-and-Certainty.md

@@ -72,14 +72,14 @@ Nevertheless, this idea asks us to consider what happens when two opinions diffe
 
 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 upper limit.
-2) Use the experiment with the most evidence for it (most decimal places) to establish the lower limit.
+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.
 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. 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 80.3% and 73%,
+For example, using $P_1 = 0.803$ and $P_2 = 0.73$,
 
-1) $`P\_{bay} = {0.803(0.73)\over {0.803(0.73) + 0.197(0.27)}} = 0.917$ (upper limit)
-2) $P\_{lo} = 0.803$ (lower limit)
-3) $f=10$
-4) $P_{comb,w} = 0.803 + 
\ No newline at end of file
+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) $P_{comb,w} = 0.803 + {(0.917 - 0.803)\over f} = 0.8144$
\ No newline at end of file