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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
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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.

Marginal posterior distribution of hyperparameters.


ormally, to obtain the distribution $\mu,\gamma|y$ we would integrate the ( Hierarchical1 ) over the parameters MATH . However, in this particular situation we take a short cut. The data $\bar{y}_{\cdot j}$ was generated from MATH where the $\theta_{j}$ comes from MATH Hence, MATH . With such observation we can write the distribution $\mu,\gamma|y$ as MATH

MATH (Hierarchical2)




i. Distribution of mu conditionally on gamma.
ii. Posterior distribution of gamma.
iii. Prior distribution for gamma.

Notation. Index. Contents.


















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