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

Structure of the model with unknown parameters.

e have seen in the previous section that the precision MATH is more natural then $\sigma^{2}$ for Bayesian computations involving normal distribution. We are given a sample MATH from MATH , where the parameters $\mu$ and $\tau$ are unknown. Assume the following prior for the mean $\mu$ and precision $\tau$ :

MATH (Normal distribution with unknown parameters 1)
MATH where the gamma distribution has the following form:
MATH (Gamma distribution)
and the constants MATH are known. As usual in Bayesian computation, we disregard multiplicative constants. The expression for the prior distribution takes the form MATH MATH We multiply it with the likelihood MATH and obtain the joint posterior distribution of MATH : MATH
MATH (Normal distribution with unknown parameters 2)

Notation. Index. Contents.

Copyright 2007