Handout on Bayes’ theorem: calculator 1

 

The following form uses Bayes’ theorem to calculate the effects an observation should have on the probability of a hypothesis.

The probabilities are shown with sample values. You can change these by entering a new value in any of the three boxes in the shaded area at the center below or by clicking on one of the numbers listed to the right of each of the boxes.

1) The prior probability of the hypothesis. The probability you initially assign to the hypothesis H given your knowledge K. Choose any value from 0 to 1.

prob(H) =

[0.001] [0.01] [0.05]

[0.0] [0.1] [0.2] [0.3] [0.4] [0.5] [0.6] [0.7] [0.8] [0.9] [1.0]

[0.95] [0.99] [0.999]

2) The probability of the evidence given the hypothesis. The probability you would initially assign to an observation report E on the assumption that H is true. Choose any value from 0 to 1.

prob(E given H) =

[0.001] [0.01] [0.05]

[0.0] [0.1] [0.2] [0.3] [0.4] [0.5] [0.6] [0.7] [0.8] [0.9] [1.0]

[0.95] [0.99] [0.999]

3) The probability of the evidence given the denial of the hypothesis. The probability you would initially assign to an observation report E on the assumption that H is false. Choose any value from 0 to 1.

prob(E given not-H) =

[0.001] [0.01] [0.05]

[0.0] [0.1] [0.2] [0.3] [0.4] [0.5] [0.6] [0.7] [0.8] [0.9] [1.0]

[0.95] [0.99] [0.999]

The value calculated by Bayes’ theorem is as follows:

prob(H given E) = prob(E given H)prob(E) × prob(H)

           = ×

One of the values used in Bayes’ theorem is the prior probability of the evidence--the probability you would initially assign to the observation report E without any assumptions about the truth of H. That is calculated as follows from the values you entered:

prob(E) = ( prob(E given H) × prob(H) )

+ ( prob(E given not-H) × (1 - prob(H)) )

= (  × )

+ (  × ( 1- ))