Content of present website is being moved to www.lukoe.com/finance . Registration of www.opentradingsystem.com will be discontinued on 2020-08-14.
 I. Basic math.
 II. Pricing and Hedging.
 III. Explicit techniques.
 IV. Data Analysis.
 V. Implementation tools.
 1 Finite differences.
 2 Gauss-Hermite Integration.
 3 Asymptotic expansions.
 4 Monte-Carlo.
 A. Generation of random samples.
 a. Uniform [0,1] random variable.
 b. Inverting cumulative distribution.
 c. Accept/reject procedure.
 d. Normal distribution. Box-Muller procedure.
 e. Gibbs sampler.
 B. Acceleration of convergence.
 C. Longstaff-Schwartz technique.
 D. Calculation of sensitivities.
 5 Convex Analysis.
 VI. Basic Math II.
 VII. Implementation tools II.
 VIII. Bibliography
 Notation. Index. Contents.

## Gibbs sampler.

ibbs sampler produces a sample that converges in distribution to a target multidimensional random variable specified by a distribution known up to a normalization constant. Bayesian analysis ( Bayesian section ) is the main field of application.

Suppose we are given a distribution . The variable is multidimensional: .

Algorithm

The first element of a sample is drawn from some distribution . We proceed to generate the subsequent draws , as follows:

Set .

For every do

1. form a vector ;

2. generate a draw from the single dimensional conditional distribution ;

3. store the result in the new .

Set .

See [Gelman] for full treatment of the subject.

 Notation. Index. Contents.