Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Stochastic Simulation: Computation and Estimation

In course

MATH-414: Stochastic simulation

The student who follows this course will get acquainted with computational tools used to analyze systems with uncertainty arising in engineering, physics, chemistry, and economics. Focus will be on sampling methods as Monte Carlo, quasi Monte Carlo, Mark ...

Description

This lecture covers the computation and estimation in stochastic simulation, focusing on generating iid replicas, likelihood ratio, confidence intervals, and optimal importance sampling. The instructor explains practical implementations and algorithms for parameter families of pdfs.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Fabio Nobile

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics, Statistical hypothesis testing

Related concepts (32)

Credible interval

In Bayesian statistics, a credible interval is an interval within which an unobserved parameter value falls with a particular probability. It is an interval in the domain of a posterior probability distribution or a predictive distribution. The generalisation to multivariate problems is the credible region. Credible intervals are analogous to confidence intervals and confidence regions in frequentist statistics, although they differ on a philosophical basis: Bayesian intervals treat their bounds as fixed and the estimated parameter as a random variable, whereas frequentist confidence intervals treat their bounds as random variables and the parameter as a fixed value.

Confidence interval

In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level, degree of confidence or confidence coefficient represents the long-run proportion of CIs (at the given confidence level) that theoretically contain the true value of the parameter; this is tantamount to the nominal coverage probability.

Likelihood function

In statistical inference, the likelihood function quantifies the plausibility of parameter values characterizing a statistical model in light of observed data. Its most typical usage is to compare possible parameter values (under a fixed set of observations and a particular model), where higher values of likelihood are preferred because they correspond to more probable parameter values.

Interval estimation

In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a parameter of interest. This is in contrast to point estimation, which gives a single value. The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method); less common forms include likelihood intervals and fiducial intervals.

Prediction interval

In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed. Prediction intervals are often used in regression analysis.

Related lectures (38)

Estimation Methods in Probability and Statistics

Discusses estimation methods in probability and statistics, focusing on maximum likelihood estimation and confidence intervals.

Confidence Intervals: Definition and Estimation

Explains confidence intervals, parameter estimation methods, and the central limit theorem in statistical inference.

Estimation and Confidence Intervals

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

Hypothesis Testing: Wilks' Theorem

Explores hypothesis testing using Wilks' Theorem, likelihood ratio statistics, p-values, interval estimation, and confidence regions.

Confidence Intervals: Gaussian Estimation