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.

## Distribution of mu conditionally on gamma.

ssume a non-informative prior for : . The above distribution may be regarded as where the distribution is the function of interest in this section. We replace the dependence of ( Hierarchical2 ) on the sample with the dependence on the statistic : and keep only the terms depending on . We conclude that hence,

 Notation. Index. Contents.