Lectures related to Entropy and Sampling Theory

Sufficient Statistics: Understanding Data Compression

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

Statistical Estimation Methods

Covers statistical estimation methods, including maximum likelihood and Bayesian estimation.

Exponential Family: Maximum Entropy Distributions

Covers exponential families and maximum entropy distributions under moment constraints.

Sampling Distributions: Understanding Ancillary Statistics

Explores ancillary statistics, sufficiency, and minimally sufficient statistics in sampling distributions.

Maximum Likelihood Estimation: Theory and Examples

Covers maximum likelihood estimation, including the Rao-Blackwell Theorem proof and practical examples of deriving estimators.

Exponential Family: Definition and Properties

Covers the Exponential Family, including its definition, sufficient statistics, and distribution properties.

Special Families of Models

Explores completeness, minimal sufficiency, and special statistical models, focusing on exponential and transformation families.

Sampling Theory: Sufficiency and Ancillarity

Explores sufficiency and ancillarity in sampling theory, emphasizing the importance of sufficient statistics in compressing data without losing information.

Generalised Linear Models: Regression with Exponential Family Responses

Covers regression with exponential family responses using Generalised Linear Models.

Exponential Family: Maximum Entropy Distribution

Covers exponential families, maximum entropy, and Moxwell-Boltzmann distribution properties.

Estimation and Confidence Intervals

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

Optimality in Decision Theory: Unbiased Estimation

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

Estimation Methods in Probability and Statistics

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

Sampling Theory: Statistics and Inference

Covers sampling theory, statistics, and inference, focusing on the sampling distribution of statistics.

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.

Sampling Theory: Statistics for Mathematicians

Covers the theory of sampling, focusing on statistics for mathematicians.

Entropy and Sampling Theory

Explores entropy, exponential family, sampling theory, and statistical inference from samples.

Maximum Likelihood Estimation

Covers Maximum Likelihood Estimation in statistical inference, discussing MLE properties, examples, and uniqueness in exponential families.

Estimation: Measures of Performance

Explores estimation measures of performance, including the Cramér-Rao bound and maximum likelihood estimation.

Sampling Distributions: Theory and Applications

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