Lectures related to Statistical Finite Element Method

Statistical Theory: Inference and Optimality

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

Probability and Statistics: Basics and Applications

Covers fundamental concepts of probability and statistics, focusing on data analysis, graphical representation, and practical applications.

Hypothesis Testing and Confidence Intervals: An Overview

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

Hypothesis Testing: Q-Q Plots and Non-Parametric Tests

Covers hypothesis testing, Q-Q plots, and non-parametric tests in statistics.

Interval Estimation

Covers the construction of confidence intervals for a normal distribution with unknown mean and variance.

Maximum Likelihood: Inference and Model Comparison

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

Maximum Likelihood Inference

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.

Statistical Theory: Inference and Sufficiency

Explores statistical inference, sufficiency, and completeness, emphasizing the importance of sufficient statistics and the role of complete statistics in data reduction.

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.

Introduction to Inference

Covers the basics of probability theory, random variables, joint probability, and inference.

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.

Statistical Analysis: Data Exploration and Inference

Covers statistical analysis, emphasizing data exploration and inference to quantify uncertainty and draw conclusions.

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.