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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.
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 $\omega_{1}$ ) or false (state $\omega_{2}$ ). The decision $\alpha$ is the assertion of the hypothesis. The penalty function MATH has the property MATH Such property enforces greater penalty for the false decision then for the correct one for every prior state.

Given the observation $x$ we choose the decision $\alpha_{1}$ if MATH and choose $\alpha_{2}$ otherwise. Equivalently, MATH MATH Note that MATH Hence, MATH where the $T$ stands for ''threshold''. This result is called ''likelihood ratio test''. Note, that if MATH and MATH then the rule simply says ''choose $\omega_{1}$ if MATH ''.

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

Notation. Index. Contents.

Copyright 2007