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.

Neyman-Pearson Lemma.

e are still within hypothesis testing setup ( Hypothesis_testing_section ). Let us forget about the structure of the threshold . We still perform the likelihood ration test where the threshold is chosen according to requirement that for a given level of error . The Neyman-Pearson lemma states that there is no better decision rule . Precisely, the lemma prohibits existence of such that and

 Notation. Index. Contents.