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.

Marginal distribution of mean.

e would like to simplify the previous result for the situation when the only variable of interest is the mean. We integrate over the nuisance parameter $\tau$ to obtain the marginal distribution MATH Hence, MATH We transform the above expression to the form of the gamma function: MATH We obtain MATH where MATH MATH We calculate the integral MATH Therefore, MATH The last expression is called "shifted student t-distribution".

Notation. Index. Contents.

Copyright 2007