In this course, we will review the brief mathematical and statistical knowledge through numerical methods. See details.
Homework
- Numerical integration (Trapezoidal rule, Simpsons rule), Monte Carlo integration, and generating random variable by rejection sampling. See hw01, hw02, hw03, hw04.
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Density function estimation in the way of parametric and non-parametric (kernel method). Some discussion about mean integratrd square error (MISE). See hw05.
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Finding the root of f(x) with fixed point iteration and Newton method. See hw06, hw07.
- Find the point of maximum/minimum value of f(x) with some methods: Newton, golden-section, steepest descent, conjugate gradient. See hw08, hw09.
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Using EM algorithm to solve the maximum likelihood estimation (MLE). See hw10.
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In final exam, we discuss more about EM algorithm, the MCEM (using Monte Carlo in E-step), and further introduce Metropolis-Hasting algorithm which is used to generate random variables by Markov Chain. See final exam. Also, the convergence properties of EM algorithm was summarized here.