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Course overview
A course in probability, Monte-Carlo simulation and stochastic processes with an eye toward data science applications.
Main topics
- random number generators, inverse-transform sampling
- probability measures, random variables, expectation, variance
- Law of Large Numbers (LLN) & Central Limit Theorem (CLT)
- Monte-Carlo methods: importance sampling, rejection sampling, variance reduction
- random networks: fundamental Concepts, models (Erdős-Rényi, Watts-Strogatz, Barabási-Albert), friendship paradox
- stochastic processes and Markov chains: transition matrices, irreducibility, periodicity, stationary distributions
- counting processes: Poisson process, from Binomial to Poisson, from Poisson to Exponential, memoryless property, Birth-Death process, Gillepsie algorithm
- diffusion processes: random walks, Brownian motion, stochastic differential equation (SDE), Itô's lemma
- stochastic optimization