I. Basic math.
 II. Pricing and Hedging.
 III. Explicit techniques.
 IV. Data Analysis.
 1 Time Series.
 2 Classical statistics.
 A. Basic concepts and common notation of classical statistics.
 B. Chi squared distribution.
 C. Student's t-distribution.
 D. Classical estimation theory.
 E. Pattern recognition.
 a. Decision rule based on loss function.
 b. Hypothesis testing problem.
 c. Neyman-Pearson Lemma.
 3 Bayesian statistics.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 VIII. Bibliography
 Notation. Index. Contents.

## Hypothesis testing problem.

here is a hypothesis that may be true (state ) or false (state ). The decision is the assertion of the hypothesis. The penalty function has the property Such property enforces greater penalty for the false decision then for the correct one for every prior state.

Given the observation we choose the decision if and choose otherwise. Equivalently, Note that Hence, where the stands for ''threshold''. This result is called ''likelihood ratio test''. Note, that if and then the rule simply says ''choose if ''.

With the decision rule known one may compute an apriori probability of the correct judgement as

 Notation. Index. Contents.