Learn Bayesian statistics

Perform a Bayesian update for a problem with discrete hypotheses using a table-based calculation.

Explain how the likelihood function quantifies the evidence provided by data for different hypotheses.

Analyze the influence of prior strength on the posterior, recognizing when strong evidence can overcome the prior.

Calculate posterior probabilities for multiple competing hypotheses to make a decision based on the evidence.

Interpret the marginal likelihood (evidence) as the probability of the observed data, averaged over all hypotheses.

Select appropriate likelihood distributions for common data types (e.g., Binomial for binary, Poisson for counts, Normal for continuous).

Explain the concept of a conjugate prior and why it enables exact analytical solutions.

Perform Bayesian inference for a population proportion using a Beta-Binomial conjugate model.

Interpret the parameters of a Beta posterior distribution as a combination of prior beliefs and observed data.

Perform Bayesian inference for a population mean using a Normal-Normal conjugate model (with known variance).

Estimate a model parameter by summarizing its posterior distribution with point estimates (mean, median, mode).

Compute and interpret a credible interval as a range of plausible values for a parameter.

Contrast the interpretation of a Bayesian credible interval with a frequentist confidence interval.

Visualize a posterior distribution to communicate uncertainty about a parameter estimate.

Distinguish between informative, weakly informative, and uninformative priors, and justify the choice of a prior for a given problem.

Explain the role of the Bayes factor in comparing two competing models or hypotheses.

Calculate a Bayes factor for a simple case (e.g., comparing two proportions) to quantify evidence.

Interpret the value of a Bayes factor as the strength of evidence for one model over another.

Compare the Bayesian approach to hypothesis testing with classical Null Hypothesis Significance Testing (NHST) and p-values.

Frame and solve a practical A/B testing problem using Bayesian methods.

Specify a simple Bayesian linear regression model, including the likelihood and priors for the intercept and slope coefficients.

Contrast the goals and outputs of Bayesian regression with classical least squares regression.

Interpret the posterior distributions of regression coefficients to understand relationships between variables.

Generate predictions with associated uncertainty using the posterior predictive distribution.

Construct and interpret credible intervals for regression parameters.

Explain why computational methods are necessary for non-conjugate or complex Bayesian models.

Describe the high-level goal of Markov Chain Monte Carlo (MCMC) as a method to sample from a posterior distribution.

Explain the intuitive idea behind a sampling algorithm like Metropolis-Hastings using an analogy.

Recognize the purpose of key MCMC diagnostics, such as trace plots and the R-hat statistic, to assess sampler convergence.

Explain the concepts of burn-in and thinning as common steps in processing MCMC output.

Specify and run a Bayesian linear regression model on a prepared dataset using a computational library.

Diagnose MCMC convergence for the model's parameters using trace plots and summary statistics.

Analyze and interpret the posterior distributions of regression coefficients from the model output.

Explain the purpose of posterior predictive checks for assessing how well a model fits the data.

Summarize and communicate the key findings from a Bayesian analysis for a non-technical audience, focusing on uncertainty.