Monte Carlo: Optimization and Estimation

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Simulation & Optimization: Poisson Process & Random Numbers

Explores simulation pitfalls, random numbers, discrete & continuous distributions, and Monte-Carlo integration.

Sampling Distributions: Estimation

Explores sampling distributions, estimation methods, and consistency in parameter estimation.

Approximate Query Processing: BlinkDB

Introduces BlinkDB, a framework for approximate query processing using sampling techniques.

Basic Principles of Point Estimation

Explores the Method of Moments, Bias-Variance tradeoff, Consistency, Plug-In Principle, and Likelihood Principle in point estimation.

Monte-Carlo Integration: Approximation and Variance

Explores Monte-Carlo integration for approximating expectations and variances using random sampling and discusses error components in conditional choice models.

MCMC with Metropolis

Covers the implementation of Markov Chain Monte Carlo (MCMC) with the Metropolis algorithm for sampling from posterior distributions.

Estimation and Confidence Intervals

Explores bias, variance, and confidence intervals in parameter estimation using examples and distributions.

Markov Chains: Applications and Sampling Methods

Covers the basics of Markov chains and their algorithmic applications.

Distribution Estimation

Covers the estimation of distributions using samples and probability models.

Markov Chains and Algorithm Applications

Covers Markov chains and their applications in algorithms, focusing on Markov Chain Monte Carlo sampling and the Metropolis-Hastings algorithm.