Lecture

Monte Carlo: Markov Chains

Related lectures (32)

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.

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.

Supervised Learning Fundamentals

Introduces the fundamentals of supervised learning, including loss functions and probability distributions.

Spin Glasses and Bayesian Estimation

Covers the concepts of spin glasses and Bayesian estimation, focusing on observing and inferring information from a system closely.

Linear Regression: Statistical Inference Perspective

Explores linear regression from a statistical inference perspective, covering probabilistic models, ground truth, labels, and maximum likelihood estimators.

Estimation and Confidence Intervals

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

Clustering & Density Estimation

Covers dimensionality reduction, PCA, clustering techniques, and density estimation methods.

Bayesian Estimation: Unsupervised Learning & MCMC

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

Clustering & Density Estimation

Covers clustering, PCA, LDA, K-means, GMM, KDE, and Mean Shift algorithms for density estimation and clustering.

Clustering & Density Estimation

Covers dimensionality reduction, clustering, and density estimation techniques, including PCA, K-means, GMM, and Mean Shift.

Estimators and Confidence Intervals

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

Bayesian Inference: Beta-Bernoulli Model

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

Bayesian Estimation: Overview and Examples

Introduces Bayesian estimation, covering classical versus Bayesian inference, conjugate priors, MCMC methods, and practical examples like temperature estimation and choice modeling.

Learning Chemical Reaction Networks

Explores sparse learning of chemical reaction networks from trajectory data using data-based methods and learning approaches.

Probabilistic Models for Linear Regression

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

Basic Principles of Point Estimation

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

Dimensionality Reduction: PCA and LDA

Covers dimensionality reduction techniques like PCA and LDA, clustering methods, density estimation, and data representation.

Nonparametric Statistics: Bayesian Approach

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

Unsupervised Learning: Dimensionality Reduction

Explores unsupervised learning techniques for reducing dimensions in data, emphasizing PCA, LDA, and Kernel PCA.

Unsupervised Learning: PCA & K-means

Covers unsupervised learning with PCA and K-means for dimensionality reduction and data clustering.