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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.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Hierarchical analysis of normal model with known variance.


he data MATH is divided into the $J$ independent samples: MATH where the $\sigma^{2}$ is a known constant. The variables $\theta_{j}$ are treated as a non observable sample from a normal variable $\theta$ MATH where the variables $\mu,\gamma$ are also random with some prior MATH Based on the sample $y$ we would like to recover the joint and marginal posterior distributions of the parameters $\theta,\mu,\gamma$ .




a. Joint posterior distribution of mean and hyperparameters.
b. Posterior distribution of mean conditionally on hyperparameters.
c. Marginal posterior distribution of hyperparameters.

Notation. Index. Contents.


















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