I. Basic math.
 II. Pricing and Hedging.
 III. Explicit techniques.
 IV. Data Analysis.
 1 Time Series.
 2 Classical statistics.
 3 Bayesian statistics.
 A. Basic idea of Bayesian analysis.
 B. Estimating the mean of normal distribution with known variance.
 C. Estimating unknown parameters of normal distribution.
 a. Structure of the model with unknown parameters.
 b. Recursive formula for posterior joint distribution.
 c. Marginal distribution of mean.
 d. Marginal distribution of precision.
 D. Hierarchical analysis of normal model with known variance.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 VIII. Bibliography
 Notation. Index. Contents.

Marginal distribution of mean.

e would like to simplify the previous result for the situation when the only variable of interest is the mean. We integrate over the nuisance parameter to obtain the marginal distribution Hence, We transform the above expression to the form of the gamma function: We obtain where We calculate the integral Therefore, The last expression is called "shifted student t-distribution".

 Notation. Index. Contents.