Lectures related to Stochastic Simulation: Variance Reduction Techniques

Markov Chain Monte Carlo

Covers the Markov Chain Monte Carlo method and the Metropolis-Hastings algorithm for generating samples from a target probability distribution.

Estimating Relaxation Time: Variance and Chains

Covers the estimation of relaxation time in chains and the importance of sample sizes.

Markov Chains: Theory and Applications

Covers the theory and applications of Markov chains, focusing on key concepts and properties.

Geometric Ergodicity: Convergence Diagnostics

Covers the concept of geometric ergodicity in the context of convergence diagnostics for Markov chains.

Error Estimation in LHS

Covers error estimation in Latin Hypercube Sampling, emphasizing the importance of accurate variance estimation.

Markov Chains: Reversibility & Convergence

Covers Markov chains, focusing on reversibility, convergence, ergodicity, and applications.

Stratified Sampling: Theory and Applications

Explores stratified sampling, dividing a population into subgroups for more accurate sampling.

Efficient Stochastic Numerical Methods

Explores efficient stochastic numerical methods for modeling and learning, covering topics like the Analytical Engine and kinase inhibitors.

Common Distributions: Moment Generating Functions

Explores common probability distributions, special distributions, and entropy concepts.

Simulation & Optimization: Poisson Process & Random Numbers

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

Stochastic Simulation: Markov Chains and Metropolis Hastings

Introduces Markov chains and Metropolis Hastings algorithm in stochastic simulation.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Differential Amplifier Design

Covers the design of a differential amplifier with key parameters like gain and bias current.

Fundamental Limits of Gradient-Based Learning

Delves into the fundamental limits of gradient-based learning on neural networks, covering topics such as binomial theorem, exponential series, and moment-generating functions.

Linear Combinations: Moment-Generating Functions

Explores moment-generating functions, linear combinations, and normality of random variables.

Continuous Random Variables

Covers continuous random variables, probability density functions, and distributions, with practical examples.

Stochastic Models for Communications: Continuous-Time Stochastic Processes

Covers examples of continuous-time stochastic processes in communications.

Probability and Statistics

Covers probability distributions, moments, and continuous random variables.

Probability and Statistics

Introduces probability, statistics, distributions, inference, likelihood, and combinatorics for studying random events and network modeling.

Variance Reduction Techniques: Antithetic Variables & Importance Sampling

Explores variance reduction techniques like antithetic variables and importance sampling in Monte Carlo estimation.