STAT2011: Probability and Estimation Theory

Learning Outcomes

• Statistical Modelling: Constructed probability models; computed expectations, variances, and probabilities.
• Parameter Estimation: Fitted models and quantified uncertainty via theoretical and computational methods.
• Model Evaluation: Assessed goodness-of-fit and applied standard accuracy evaluation techniques.
• Theoretical Reasoning: Applied and proved key results relevant to estimation and asymptotic theory.

Takeaways

This was one of the most mathematically demanding courses I’ve taken. We worked extensively with probability models, starting from Bernoulli and Binomial distributions, then moving into more complex ones such as Poisson, Geometric, Negative Binomial, Exponential, and Gaussian. Each distribution came with its own estimation challenges, requiring both theoretical derivations and computational approaches. Although my final grade was not high, the process gave me a much deeper appreciation for the role of probability in quantifying uncertainty. I learned how to move beyond treating statistical software as a “black box,” and instead reason about estimators, variances, and asymptotic properties in a rigorous way. This course sharpened my mathematical maturity, even if it was at times overwhelming, and it laid an important foundation for further studies in inference and applied statistics.