Unit of study_

# BSTA5002: Principles of Statistical Inference

The aim of this unit is to develop a strong mathematical and conceptual foundation in the methods of statistical inference, which underlie many of the methods utilised in subsequent units of study, and in biostatistical practice. The unit provides an overview of the concepts and properties of estimators of statistical model parameters, then proceeds to a general study of the likelihood function from first principles. This will serve as the basis for likelihood-based methodology, including maximum likelihood estimation, and the likelihood ratio, Wald, and score tests. Core statistical inference concepts including estimators and their ideal properties, hypothesis testing, p-values, confidence intervals, and power under a frequentist framework will be examined with an emphasis on both their mathematical derivation, and their interpretation and communication in a health and medical research setting. Other methods for estimation and hypothesis testing, including a brief introduction to the Bayesian approach to inference, exact and non-parametric methods, and simulation-based approaches will also be explored.

Code BSTA5002 Public Health 6
 Prerequisites: ? BSTA5100 or (BSTA5001 and BSTA5023) None None

At the completion of this unit, you should be able to:

• LO1. Calculate and interpret important properties of point and interval estimators
• LO2. Calculate and interpret p-values, power and confidence intervals correctly.
• LO3. Write a likelihood function.
• LO4. Derive and calculate the maximum likelihood estimate.
• LO5. Derive and calculate the expected information.
• LO6. Derive a Wald test, Score test and likelihood ratio test.
• LO7. Use a Bayesian approach to derive a posterior distribution.
• LO8. Calculate and interpret posterior probabilities and credible intervals.
• LO9. Apply and explain an exact method, non-parametric and sampling-based method.

## Unit outlines

Unit outlines will be available 1 week before the first day of teaching for the relevant session.