Bayesian Statistical Inference

This site is a part of the JavaScript E-labs learning objects for decision making. Other JavaScript in this series are categorized under different areas of applications in the MENU section on this page.

Professor Hossein Arsham   


The following JavaScript performs the Bayesian inference by combining the sample information with prior information to estimate the mean of a normal population.

Suppose that we draw a random sample x1, x2,....xn of size n from a normal (m, s2) population. We then take the sample mean as our estimate of m and sample variance as our estimate of s2.

Notice that before using this JavaScript it is necessary to perform the Test for Normality.

In the Bayesian inference we have also prior information on m. This is expressed in terms of a probability distribution known as the prior distribution. Suppose that the prior distribution is normal with mean m0 and variance s02, we now combine this with the sample information to obtain what is known as the posterior distribution of . This distribution is normal with posterior mean and variance.

Enter your up-to-80 sample data, a confidence level, a prior value for the mean and the variance, and then click the Calculate button. Blank boxes are not included in the calculations but zeros are.

In entering your data to move from cell to cell in the data-matrix use the Tab key not arrow or enter keys.

To edit your data, including add/change/delete, you do not have to click on the "clear" button, and re-enter your data all over again. You may simply add a number to any blank cell, change a number to another in the same cell, or delete a number from a cell. After editing, then click the "calculate" button.

For extensive edit or to use the applet for a new set of data, then use the "clear" button.


Enter a Confidence Level
Enter a Mean's Prior Value
Enter a Variance's Prior Value
Mean Estimate Using the Sample
Point Estimate
Lower Confidence Limit
Upper Confidence Limit
Variance Estimate Using the Sample
Point Estimate
Lower Confidence Limit
Upper Confidence Limit
Standard Deviation Estimate Using the Sample (for n>31)
Point Estimate
Lower Confidence Limit
Upper Confidence Limit
Posterior Statistics for the Mean
Posterior Mean
Lower Tolerance Limit
Upper Tolerance Limit
Variation of the Posterior Mean
Posterior Variance
Lower Tolerance Limit
Upper Tolerance Limit


For Technical Details, Back to:
Statistical Thinking for Decision Making


Kindly email your comments to:
Professor Hossein Arsham


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Kindly e-mail me your comments, suggestions, and concerns. Thank you.

Professor Hossein Arsham   


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