Lectures related to Statistical Finite Element Method

Hypothesis Testing and Confidence Intervals: An Overview

Covers hypothesis testing, confidence intervals, and their applications in statistics.

Maximum Likelihood: Inference and Model Comparison

Explores maximum likelihood inference, model selection, and comparing models using likelihood ratios.

Explores maximum likelihood inference, comparing models based on likelihood ratios and demonstrating with a coin example.

Binary Hypothesis Testing

By Emre Telatar explores binary hypothesis testing and decision rule design.

Probabilistic Models for Linear Regression

Covers the probabilistic model for linear regression and its applications in nuclear magnetic resonance and X-ray imaging.

Probabilistic Linear Regression

Explores probabilistic linear regression, covering joint and conditional probability, ridge regression, and overfitting mitigation.

Statistical Inference

Covers likelihood ratio statistic, confidence intervals, and hypothesis testing concepts.

Probability and Statistics

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

Maximum Likelihood Estimation: Multivariate Statistics

Explores maximum likelihood estimation and multivariate hypothesis testing, including challenges and strategies for testing multiple hypotheses.

Optimization-Based Uncertainty Quantification

Explores optimization-based uncertainty quantification for ill-posed inverse problems in the physical sciences, focusing on regularization methods and interval constructions.

Steady-state Kalman Predictor: Examples and Comparison

Discusses the steady-state Kalman predictor, provides examples, and compares Luenberger and Kalman filtering.

Probability and Statistics: Independence and Conditional Probability

Explores independence and conditional probability in probability and statistics, with examples illustrating the concepts and practical applications.

Hypothesis Testing and Confidence Intervals: Key Concepts

Provides an overview of hypothesis testing and confidence intervals in statistics, including practical examples and key concepts.

Dependence and Correlation

Explores dependence, correlation, and conditional expectations in probability and statistics, highlighting their significance and limitations.

Probability and Statistics

Covers fundamental concepts in probability and statistics, emphasizing data analysis techniques and statistical modeling.

Estimation Methods in Probability and Statistics

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

Linear Regression: Estimation and Inference

Explores linear regression estimation, linearity assumptions, and statistical tests in the context of model comparison.

Sufficient Statistics: Understanding Data Compression

Explores sufficient statistics, data compression, and their role in statistical inference, with examples like Bernoulli Trials and exponential families.

Bayesian Estimation: Unsupervised Learning & MCMC

Explores Bayesian estimation for unsupervised learning and MCMC, using a Spin Glass Card game example.

Statistical Theory: Inference and Optimality Log in to Mediaspace to watch this video

Explores constructing confidence regions, inverting hypothesis tests, and the pivotal method, emphasizing the importance of likelihood methods in statistical inference.