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.
A. Time series forecasting.
B. Updating a linear forecast.
C. Kalman filter I.
D. Kalman filter II.
a. General Kalman filter problem.
b. General Kalman filter solution.
c. Convolution of normal distributions.
d. Kalman filter calculation for linear model.
e. Kalman filter in non-linear situation.
f. Unscented transformation.
E. Simultaneous equations.
2. Classical statistics.
3. Bayesian statistics.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

General Kalman filter solution.

ince the law MATH is available from the model, we calculate MATH We calculate the components as follows MATH MATH MATH The densities MATH are calculated directly from the model ( Model equations ). Hence, we complete the recursion MATH

It is important to note that the distribution MATH is a normalization factor for the MATH . It is rarely necessary to calculate it.

Notation. Index. Contents.

Copyright 2007