Statistical Inference for Decision Science

This course turns statistical foundations into formal tools for inference. The emphasis is on what can be learned from data, how uncertainty should be quantified, and how inferential claims should be reported when decisions are at stake.

By the end, a reader should be able to explain sampling distributions, use likelihood-based reasoning, construct and interpret confidence intervals and tests, compare frequentist and Bayesian viewpoints, handle model uncertainty, and write inference reports that are honest about assumptions and limits.

Figure: Empirical interval coverage across scenarios, illustrating that uncertainty methods must be matched to the decision setting (adapted from Lecture 04: Confidence Intervals: Wald, Likelihood, and Bootstrap).

Lecture Sequence

01. From Data to Inference

This lecture connects From Data to Inference to evidence strength, model assumptions, uncertainty, and stakeholder-facing recommendations.

02. Sampling Distributions and Asymptotics

This lecture develops Sampling Distributions and Asymptotics with examples that make assumptions, diagnostics, and interpretation visible.

03. Likelihood and Maximum Likelihood

This lecture uses Likelihood and Maximum Likelihood to clarify the analyst’s question, evidence, assumptions, and decision implications.

04. Confidence Intervals: Wald, Likelihood, and Bootstrap

This lecture compares Wald, likelihood, and bootstrap intervals through coverage, assumptions, and reporting tradeoffs.

05. Hypothesis Testing Beyond p-Values

This lecture frames Hypothesis Testing Beyond p-Values as a decision problem and asks what evidence can be trusted, challenged, and communicated.

06. Permutation, Randomization, and Exact Inference

This lecture builds intuition for Permutation, Randomization, and Exact Inference and ties the result to model choice, uncertainty, and action.

07. Multiple Testing, False Discovery, and Research Risk

This lecture applies Multiple Testing, False Discovery, and Research Risk with emphasis on diagnostics, tradeoffs, and evidence limits.

08. Linear Models as Inferential Engines

This lecture develops Linear Models as Inferential Engines as a practical pattern for analysis, diagnostics, and decision support.

09. Generalized Linear Models for Binary, Count, and Rate Data

This lecture connects Generalized Linear Models for Binary, Count, and Rate Data to evidence strength, model assumptions, uncertainty, and clear reporting.

10. Hierarchical Models, Partial Pooling, and Grouped Data

This lecture develops Hierarchical Models, Partial Pooling, and Grouped Data with examples that make assumptions, diagnostics, and interpretation visible.

11. Bayesian Inference for Decision Making

This lecture uses Bayesian Inference for Decision Making to clarify the analyst’s question, evidence, assumptions, and decision implications.

12. Model Checking, Calibration, and Posterior Predictive Logic

This lecture uses model checking and calibration to ask whether fitted models behave credibly on the data they claim to explain.

13. Missing Data, Measurement Error, and Robust Inference

This lecture frames Missing Data, Measurement Error, and Robust Inference as a decision problem and asks what evidence can be trusted, challenged, and communicated.

14. Statistical Decision Analysis and Value of Information

This lecture builds intuition for Statistical Decision Analysis and Value of Information and ties the result to model choice, uncertainty, and action.

15. Reporting Statistical Recommendations for Real Stakeholders

This lecture applies Reporting Statistical Recommendations for Real Stakeholders with emphasis on diagnostics, tradeoffs, and evidence limits.