Lectures related to Nonparametric and Bayesian Statistics

Nonparametric Statistics: Bayesian Approach

Explores non-parametric statistics, Bayesian methods, and linear regression with a focus on kernel density estimation and posterior distribution.

Estimation and Confidence Intervals

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

Nonparametric Statistics: Estimation and Optimization

Explores nonparametric statistics, covering estimation methods and the bias-variance tradeoff.

Estimators and Confidence Intervals

Explores bias, variance, unbiased estimators, and confidence intervals in statistical estimation.

Kernel Density Estimation: Bandwidth Selection and Curse of Dimensionality

Covers Kernel Density Estimation focusing on bandwidth selection, curse of dimensionality, bias-variance tradeoff, and parametric vs nonparametric models.

Estimation Methods in Probability and Statistics

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

Basic Principles of Point Estimation

Explores the Method of Moments, Bias-Variance tradeoff, Consistency, Plug-In Principle, and Likelihood Principle in point estimation.

Confidence Intervals: Definition and Estimation

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

Estimating Parameters: Confidence Intervals

Explores estimating parameters through confidence intervals in linear regression and statistics.

Implicit Generative Models

Explores implicit generative models, covering topics like method of moments, kernel choice, and robustness of estimators.

Bayesian Inference: Gaussian Prior for Mean

Discusses Bayesian inference for the mean of a Gaussian distribution with known variance, covering posterior mean, variance, and MAP estimator.

Confidence Intervals: Gaussian Estimation

Explores confidence intervals, Gaussian estimation, Cramér-Rao inequality, and Maximum Likelihood Estimators.

Bayesian Inference: Beta-Bernoulli Model

Explores the Beta distribution, Bayesian inference, and posterior calculation in the Beta-Bernoulli model.

Model Selection Criteria: AIC, BIC, Cp

Explores model selection criteria like AIC, BIC, and Cp in statistics for data science.

Intro to Quantum Sensing: Parameter Estimation and Fisher Information

Introduces Fisher Information for parameter estimation based on collected data.

Probability Distributions in Environmental Studies

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

Monte Carlo: Markov Chains

Covers unsupervised learning, dimensionality reduction, SVD, low-rank estimation, PCA, and Monte Carlo Markov Chains.

Density of States and Bayesian Inference in Computational Mathematics

Explores computing density of states and Bayesian inference using importance sampling, showcasing lower variance and parallelizability of the proposed method.

Estimation Methods: Bias-Variance Tradeoff

Explores the MSE quality measure for estimators and the bias-variance tradeoff.

Probabilistic Models for Linear Regression

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