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.
 D. Hierarchical analysis of normal model with known variance.
 a. Joint posterior distribution of mean and hyperparameters.
 b. Posterior distribution of mean conditionally on hyperparameters.
 c. Marginal posterior distribution of hyperparameters.
 i. Distribution of mu conditionally on gamma.
 ii. Posterior distribution of gamma.
 iii. Prior distribution for gamma.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 VIII. Bibliography
 Notation. Index. Contents.

Posterior distribution of gamma.

n conclusion, we compute the distribution The last expression does not depend on . Hence, we set and obtain

 Notation. Index. Contents.