Lectures related to Special Families of Models

Covers the basics of statistical theory, including probability models, random variables, and sampling distributions.

Exponential Family: Maximum Entropy Distributions

Covers exponential families and maximum entropy distributions under moment constraints.

Probability Distributions in Environmental Studies

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

Statistical Theory: Maximum Likelihood Estimation

Explores the consistency and asymptotic properties of the Maximum Likelihood Estimator, including challenges in proving its consistency and constructing MLE-like estimators.

Optimality in Decision Theory: Unbiased Estimation

Explores optimality in decision theory and unbiased estimation, emphasizing sufficiency, completeness, and lower bounds for risk.

Statistical Models: Basics & Applications

Covers statistical concepts like probability, estimation, hypothesis testing, and confidence intervals for mathematicians.

Generalised Linear Models: Regression with Exponential Family Responses

Covers regression with exponential family responses using Generalised Linear Models.

Likelihood Ratio Tests: Optimality and Applications

Explores the theory and applications of likelihood ratio tests in statistical hypothesis testing.

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.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Generalized Linear Models

Covers probability, random variables, expectation, GLMs, hypothesis testing, and Bayesian statistics with practical examples.

Sufficient Statistics: Understanding Data Compression

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

Continuous Random Variables

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

Sampling Distributions: Theory and Applications

Explores sampling distributions, estimators' properties, and statistical measures for data science applications.

Statistical Theory: Cramér-Rao Bound & Hypothesis Testing

Explores the Cramér-Rao bound, hypothesis testing, and optimality in statistical theory.

Probability and Statistics

Covers probability distributions, moments, and continuous random variables.

Air Pollution Analysis

Explores air pollution analysis using wind data, probability distributions, and trajectory models for air quality assessment.

Exponential Family

Covers the properties of the exponential family and the estimation of parameters.

Advanced Probabilities: Random Variables & Expected Values

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Introduction to Continuous Random Variables: Probability Distributions

Introduces continuous random variables and their probability distributions, emphasizing their applications in statistics and data science.