Free online courseBayesian Statistics Lecture
Duration of the online course: 22 hours and 23 minutes
New course
Explore Bayesian Statistics online. Learn probability, inference, modeling, and more. Ideal for foundational studies in Statistics.
In this free course, learn about
- Course Orientation and Probability Foundations
- Bayesian Inference for a Proportion
- Bayesian Inference for a Mean and Monte Carlo Methods
- Gibbs Sampling, MCMC, and Model Checking
- Bayesian Hierarchical Modeling
- Bayesian Linear Regression
- Case Studies, Variational Inference, and Project Guidance
- Short Topics and Applied Bayesian Examples
Course Description
Discover the foundations of Bayesian Statistics with this extensive online course. Dive into the core concepts and principles, starting with the basics of probability and Bayes' rule. Understand Bayesian inference, exploring both discrete and continuous priors and learning to update these priors effectively.
Engage in comprehensive labs and exercises designed to reinforce learning and practical application. The course covers various crucial topics such as Bayesian inference for proportions and means, exploring continuous priors and the Gamma-Poisson conjugacy. Experience hands-on learning with Monte Carlo approximations and delve into advanced concepts like the Gibbs sampler, MCMC diagnostics, and Bayesian hierarchical modeling.
The course also introduces MCMC simulations using JAGS, providing practical insights into statistical modeling and analysis. Gain proficiency in Bayesian linear regression, including multiple linear regression, and learn how to implement Bayesian methods in real-world case studies. Extend your knowledge with video introductions on Bayesian methods as applied in diverse fields, from ecological research to economic analysis and sports statistics.
Benefit from a series of intros and poster presentations that showcase various applications and recent advancements in Bayesian methodology. Enhance your understanding further with guest lectures and a project-driven approach to learning.
This course is part of the Basic Studies category under Statistics, ideal for those looking to build a solid foundation in Bayesian Statistics.
Course content
- Video class: [Introduction] Course orientation 34m
- Exercise: When a Bayesian posterior has no closed form, which approach is taught to approximate it in this course?
- Video class: [Introduction] Interpretation of probability and Bayes' rule part 1 27m
- Video class: [Introduction] Interpretation of probability and Bayes' rule part 2 25m
- Exercise: Posterior probability after a positive screening test
- Video class: [Introduction] Bayesian inference 31m
- Video class: [Introduction] Probability review part 1 10m
- Exercise: Law of Total Probability for a Partition
- Video class: [Introduction] Probability review part 2 40m
- Video class: [Bayesian inference for a proportion] Example and discrete priors part 1 10m
- Exercise: Key drawback of using a discrete prior for a proportion p
- Video class: [Bayesian inference for a proportion] Discrete priors part 2 36m
- Video class: [Bayesian inference for a proportion] Continuous prior: the Beta distribution 24m
- Exercise: Which prior best models a binomial success probability p on 0 to 1 and avoids zero probability for unlisted values
- Video class: [Bayesian inference for a proportion] Updating the beta prior 44m
- Video class: Lab 1 10m
- Exercise: Posterior for a Bernoulli parameter with a mixture of Beta priors
- Video class: [Bayesian inference for a proportion] Bayesian inference with continuous priors 48m
- Video class: [Bayesian inference for a mean] Example 14m
- Exercise: Best Bayesian setup for highly right-skewed continuous data when inferring the mean
- Video class: [Bayesian inference for a mean] Prior and posterior for mean and standard deviation part 1 09m
- Video class: [Bayesian inference for a mean] Prior and posterior for mean and standard deviation part 2 55m
- Exercise: Posterior mean for Normal likelihood with known variance and Normal prior
- Video class: [Bayesian inference for a mean] Prior and posterior for mean and standard deviation part 3 29m
- Video class: Lab 2 04m
- Exercise: In a normal model, which function provides exact Bayesian credible interval bounds, analogous to qbeta in the beta case?
- Video class: [Bayesian inference for a mean] Gamma-Poisson conjugacy exercise 11m
- Video class: [Bayesian inference for a mean] Monte Carlo approximation 16m
- Exercise: Estimating P(p1 < p2) with Monte Carlo in a two-year proportion comparison
- Video class: [Gibbs sampler and MCMC] Example and prior and posterior derivations for mean and standard deviation 1h04m
- Video class: [Gibbs sampler and MCMC] Use JAGS and Bayesian inferences 19m
- Exercise: Which parameterization does JAGS use for the normal distribution in the model specification?
- Video class: [Gibbs sampler and MCMC] MCMC diagnostics 36m
- Video class: [Gibbs sampler and MCMC] Gamma-Gamma-Poisson exercise part 1 12m
- Exercise: Full conditional for lambda in a Gamma Gamma Poisson hierarchy
- Video class: [Gibbs sampler and MCMC] Gamma-Gamma-Poisson exercise part 2 18m
- Video class: HW 3, Lab 2, and Midterm I Q 10m
- Exercise: When should you form a product in the likelihood for Bayesian inference?
- Video class: [Gibbs sampler and MCMC] Paper discussion Q1-Q3 31m
- Video class: Lab 3 04m
- Exercise: In a model with prior p ~ Beta(a, b) and likelihood X | p ~ Binomial(n, p), what is the marginal distribution of X?
- Video class: [Gibbs sampler and MCMC] Paper discussions Q4-Q7 16m
- Video class: Project overview 06m
- Exercise: Which plan best aligns with expectations for an applied Bayesian project?
- Video class: [Gibbs sampler and MCMC] Metropolis and Metropolis-Hastings 30m
- Video class: Vassar College MATH 347 Bayesian Statistics Hierarchical Modeling Intro (by Josh de Leeuw) 10/28/17 20m
- Exercise: Why use a hierarchical Bayesian model for the learning data?
- Video class: [Bayesian hierarchical modeling] Example 12m
- Video class: [Bayesian hierarchical modeling] Observations in groups: approaches to modeling 11m
- Exercise: Which modeling strategy best handles grouped observations with small group sizes while preserving group differences in a Bayesian analysis
- Video class: [Bayesian hierarchical modeling] A two-stage prior for a hierarchical model 21m
- Video class: [Bayesian hierarchical modeling] MCMC simulation by JAGS part 1 15m
- Exercise: In a hierarchical normal model coded in JAGS, what does dnorm expect as its second argument?
- Video class: [Bayesian hierarchical modeling] MCMC simulation by JAGS part 2 38m
- Video class: Lab 4 05m
- Exercise: Enforcing positive group means in a hierarchical Bayesian model
- Video class: Midterm evaluation feedback 12m
- Video class: [Bayesian hierarchical modeling] Derivation notes for a Gibbs sampler 09m
- Exercise: Conjugacy and Gibbs Updates in a Normal-Normal Hierarchical Model
- Video class: [Bayesian hierarchical modeling] Exercise for schedule-specific means and standard deviations 19m
- Video class: [Bayesian linear regression] Adding a continuous predictor and the CE example 23m
- Video class: [Bayesian linear regression] A simple linear regression for the CE sample 09m
- Video class: [Bayesian linear regression] MCMC simulation by JAGS for the SLR model 14m
- Exercise: Setting the Normal prior in JAGS dnorm using precision
- Video class: [Bayesian linear regression] Bayesian inferences with SLR 26m
- Video class: [Bayesian linear regression] More priors 25m
- Exercise: After standardizing X and Y in linear regression, what does beta1 represent and how should an informative prior be chosen?
- Video class: [Bayesian linear regression] A multiple linear regression and JAGS simulation 50m
- Video class: Case studies 1 and 2 overview 22m
- Exercise: Choosing a Bayesian model to detect guessing versus knowledge groups in true false exam scores
- Video class: Case study 1 36m
- Video class: Guest lecture on introduction to variational inference by Dr. Vojta Kejzlar 47m
- Exercise: Why is maximizing the ELBO central to variational inference?
- Video class: Final project poster session info 06m
- Video class: Case study 2 16m
- Exercise: Choosing the likelihood for total scores in a two-class Bayesian model
- Video class: [2-min intro] Revisiting the Gelman-Rubin Diagnostics 02m
- Video class: [2-min intro] How Bayesian Methods are Used in Ecological Research 02m
- Exercise: When is Approximate Bayesian Computation most appropriate in ecological modeling?
- Video class: [2-min intro] Non-parametric Density Estimation with Dirchlet Process 02m
- Video class: [2-min intro] A Bayesian Logistic Regression Analysis of Unemployment and Age during Covid-19 01m
- Exercise: Appropriate likelihood-link choice for binary employment status in Bayesian logistic regression
- Video class: [2-min intro] A Bayesian Hierarchical Model for Evaluating Fielding in Major League Baseball 02m
- Video class: [2-min intro] A Hierarchical Bayesian Analysis of the 2012-2013 Pell Grant 03m
- Exercise: Why is a hierarchical Bayesian model suitable for analyzing the Pell Grant data by institution type?
- Video class: [2-min intro] Analyzing Larynx Cancer Deaths with Bayesian Logistic Regression 01m
- Video class: [2-min intro] Bayesian Approaches to Mendelian Randomization 02m
- Exercise: Which Bayesian approach estimates the causal effect in Mendelian randomization?
- Video class: [2-min intro] Need Based Scholarships and Student Body Demographics 02m
- Video class: [2-min intro] The Gender Wage GAP 02m
- Exercise: Select the statement that best describes the hierarchical Bayesian model for analyzing the wage gap
- Video class: [2-min intro] Beta-MPT: A Bayesian Hierarchical Model for Learning Cognitive Events 03m
- Video class: [12-min poster] BART: Bayesian Additive Regression Trees - A Methodology Study 14m
- Exercise: In BART, what is the main purpose of the regularization prior?
- Video class: [2-min video] Measure Theory and Probability 02m
- Video class: [2-min intro] All-Nighters @ Vassar in the 2021-22 Academic Year 02m
- Exercise: Selecting a Bayesian hierarchical model for group-level count data over a fixed period
- Video class: [12-min poster] Effect of Extra Home Game on Home Team Winning NBA Playoff Series 13m
- Video class: [12-min poster] A Bayesian Multivariate Linear Regression on the Effects of Wealth on Well-Being 13m
- Exercise: Why use Bayesian multivariate linear regression to study income, wealth, and financial satisfaction effects on happiness, health, and life satisfaction?
- Video class: [12-min poster] Adjusted-OBP Metric for the MLB - Bayesian Hierarchical Modeling 13m
- Video class: [12-min poster] Bayesian Analysis of Lacrosse Scores 13m
- Exercise: Effect of group sigma on shrinkage in a hierarchical Poisson goal model
- Video class: [12-min poster] Review of Composite Poisson Models for Goal Scoring 18m
- Video class: [12-min poster] Evaluating MLB Career Path and Trajectories 14m
- Exercise: Why adopt a hierarchical Bayesian model when analyzing player OBP trajectories by age?
- Video class: [2-min intro] Extending Bayesian MLR with DAGs 13m
- Video class: [12-min poster] Bayesian Applications in Finance 14m
- Exercise: Key advantage of Bayesian methods for return predictability in finance
This free course includes:
22 hours and 23 minutes of online video course
Digital certificate of course completion (Free)
Exercises to train your knowledge
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