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

Basic idea of Bayesian analysis.


here is a sample MATH and there is an unknown parameter $\theta$ . However, unlike the classical approach, the $\theta$ is regarded as a random variable. The nature selects $\theta$ from some "prior" population MATH , then it selects the sample $X$ according to MATH . The goal is to recover the distribution MATH . Such recovery is accomplished by the repeated application of the ( Bayes formula ):

MATH (Bayesian technique)
The MATH is the likelihood function, MATH is called the "prior" distribution and the $p\left( X\right) $ is a normalization constant: MATH The MATH may hold some prior knowledge about the $\theta.$ There are at least three general strategies to choose the prior distribution: non-informative (diffuse) prior, invariant prior (Jeffrey's principle) and hierarchical modelling. For analytical convenience one should try and choose prior so that the posterior distribution MATH , likelihood MATH and the prior MATH would belong to the same class of functions (normal, binomial, exponential and so fourth). Such prior distribution is called "conjugate".

The principal technical tool is to drop normalization constants from all calculations and track only the essential part. The normalization constant is then recovered from the final solution according to MATH . In particular, we write ( Bayesian technique ) as MATH





Notation. Index. Contents.


















Copyright 2007