by Kardi Teknomo

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Bayes Rules

In learning Bayes rule or Bayes theorem, most people usually get difficulty to determine which one is a priori, posteriori, and likelihood probability. Bayes theorem itself is actually very simple. This tutorial will help you to understand Bayes theorem with an example of tabular data. If you are still confused with notation like Data Analysis from Questionnaires , you may read first the previous section of this tutorial on conditional probability . You can also download the spreadsheet file companion of this tutorial here.

Bayes' Rule: Data Analysis from Questionnaires

  • Data Analysis from Questionnaires is called prior probability of our hypothesis Data Analysis from Questionnaires . It is our state of knowledge about hypothesis Data Analysis from Questionnaires before we get the data Data Analysis from Questionnaires .
  • Data Analysis from Questionnaires is called likelihood probability. It is the probability based on our observation data Data Analysis from Questionnaires given that our hypothesis Data Analysis from Questionnaires is hold.
  • Data Analysis from Questionnaires is the prior probability that the data Data Analysis from Questionnaires will be observed. It is the probability of data Data Analysis from Questionnaires without knowledge of any hypothesis.
  • The ratio Data Analysis from Questionnaires is called irrelevance index. If the irrelevance index is 1, any knowledge about B is not relevance to A. Any value below 1 measures the relevancy between A and B.
  • Data Analysis from Questionnaires is called posterior probability. It is our state of knowledge about hypothesis Data Analysis from Questionnaires after we know data Data Analysis from Questionnaires .

Data Analysis from Questionnaires

In many applications, however, we usually have several mutually exclusive hypotheses Data Analysis from Questionnaires . Since the data Data Analysis from Questionnaires is a subset of our hypotheses set, we can decompose the data into

Data Analysis from Questionnaires

Because Data Analysis from Questionnaires and Union operation is equivalent to summation, we obtain

Total Probability Theorem :

Data Analysis from Questionnaires

Input the total probability theorem into Bayes' rule we get Bayes' Theorem

Data Analysis from Questionnaires

We use the same example as in section Conditional Probability . Refresh again your understanding about that section where you have the data and then you compute the percentage by row, percentage by column and percentage by total.

Bayes theorem problem is somewhat reversed from what we compute in section Conditional Probability . Now suppose you know only the percentage by row and the marginal percentage (from the percentage by total ), as shown in the tables below.

Data Analysis from Questionnaires

Data Analysis from Questionnaires

The question is: can you get the percentage by column only based on the information of these two tables?

To answer this kind of question is what the Bayes theorem help.

The two tables above can be put into notational table as follow:

Data Analysis from Questionnaires

And

Data Analysis from Questionnaires

While table percentage by column , can be put into notation as table below

Data Analysis from Questionnaires

Using Bayes rule Data Analysis from Questionnaires we can easily compute the percentage by column. For example Data Analysis from Questionnaires and Data Analysis from Questionnaires . The full table of percentage by column is presented below

Data Analysis from Questionnaires

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Preferable reference for this tutorial is

Teknomo, Kardi. Data Analysis from Questionnaires. http:\\people.revoledu.com\kardi\ tutorial\Questionnaire\

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