MATH-414: Stochastic simulation

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Lectures in this course (48)

Variance Reduction Techniques: Antithetic Variables & Importance Sampling

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

Variance Reduction: Strategies and Applications

Discusses variance reduction techniques in stochastic simulation, focusing on allocation strategies and replica generation algorithms.

Important Sampling: Monte Carlo Estimation

Covers important sampling for efficient Monte Carlo estimation of expected values using a new distribution to reduce variance.

Stochastic Simulation: LHS Estimator and Variances Analysis

Covers the analysis of the LHS estimator and variances in stochastic simulation.

Stochastic Simulation: Latin Hypercube Sampling and Quasi Monte Carlo

Covers Latin Hypercube Sampling and Quasi Monte Carlo methods for stochastic simulation, explaining the goal of stratification and generating independent permutations.

Stochastic Simulation: Variance Reduction Techniques

Covers stochastic simulation and variance reduction techniques, focusing on Courra variate and auxiliary distribution generation.

Stochastic Simulation: Uncertainty Quantification

Explores uncertainty quantification using Quasi Monte Carlo methods and discrepancy measures for integral approximation and volume estimation.

Variance Reduction Techniques

Covers variance reduction techniques in stochastic simulation to improve output quantity estimation accuracy.

Stratified Sampling: Theory and Applications

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

Stochastic Simulation: Low-Discrepancy Point Sets

Explores low-discrepancy point sets in stochastic simulation and their construction algorithms.

Error Estimation in LHS

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

Stochastic Simulation: Markov Chains and Monte Carlo

Covers Markov chains, Monte Carlo methods, low discrepancy sequences, and multidimensional integrals computation.

Discrepancy Function: Estimation and Applications

Explores estimating discrepancy functions and their practical applications in generating sets with low discrepancy.

Stochastic Simulation: Markov Chains and Transition Matrices

Explores Markov chains, transition matrices, and Bayesian statistics in stochastic simulation.

Stochastic Simulation: Theory of Markov Chains

Covers the theory of Markov chains, focusing on reversible chains and detailed balance.

Low Discrepancy Sequences

Explores low discrepancy sequences and their significance in stochastic simulation and numerical methods.

Metropolis Hastings Algorithm: Markov Chains and Transition Matrix

Covers the Metropolis Hastings algorithm and constructing Markov chains with proposal distributions for convergence.

Markov Chains: Theory and Applications

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

Markov Chains: Reversibility & Convergence

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

Markov Chains: General Concepts

Covers the general concepts of Markov chains and their applications in various fields.

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