# STU34508 – Statistical Inference II

**Source**: https://teaching.scss.tcd.ie/module/stu34508-statistical-inference-ii/
**Parent**: https://www.maths.tcd.ie/undergraduate/modules/minor-stats.php

**Offered in 2023/24**

|  |  |
| --- | --- |
| **Module Code** | STU34508 |
| **Module Name** | Statistical Inference II |
| **ECTS Weighting****[**[1]**](#_ftn1)** | 5 ECTS |
| **Semester taught** | Semester 2 |
| **Module Coordinator/s** | Prof. Jason Wyse |

## Module Learning Outcomes

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| --- |
| On successful completion of this module, students will be able to:   LO1. Use moment generating functions to understand sums of iid random variables   LO2. Derive method of moments and maximum likelihood estimators   LO3. Describe the properties of an estimator using bias and mean square error   LO4. Derive approximate sampling distributions for maximum likelihood estimators   LO5. Construct confidence intervals for unknown parameters   LO6. Construct tests of hypothesis of unknown parameters |

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## Module Content

This module provides an overview of key topics in classical statistical theory. It begins with the study of sums of independent and identically distributed random variables, proceeding to a proof of the Central Limit Theorem using moment generating functions. Estimation of the parameters of statistical models based on observed data is then dealt with. The method of moments and maximum likelihood are examined. Properties of the estimators these methods produce are defined and explored. The Central Limit Theorem proved earlier is used to derive asymptotic properties of maximum likelihood estimators. Throughout the module, the basic inferential techniques of constructing confidence intervals and conducting hypothesis tests are revisited, and then discussed formally at the end.

## Teaching and learning Methods

Three classes per week. Some of these classes will be used for tutorials and code demos.

## Assessment Details

|  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- |
| **Assessment Component** | **Brief Description** | **Learning Outcomes Addressed** | **% of total** | **Week set** | Week Due |
| Exam | End of semester exam (2 hours) | LO1-LO6 | 90% |  |  |
| Assignments | Four assignments throughout semester | LO1-LO6 | 10% | 3,5,7,9 | 4,6,8,10 |

## Reassessment Details

100% Examination

## Contact Hours and Indicative Student Workload

|  |  |
| --- | --- |
| **Contact Hours (scheduled hours per student over full module), broken down by**: | 33 **hours** |
| Lecture | 29 hours |
| Laboratory | 0 hours |
| Tutorial or seminar | 4 hours |
| Other | 0 hours |
| **Independent study (outside scheduled contact hours), broken down by:** | 82 **hours** |
| Preparation for classes and review of material (including preparation for examination, if applicable | 42 hours |
| completion of assessments (including examination, if applicable) | 40 hours |
| **Total Hours** | 115 **hours** |

## Recommended Reading List

Statistical Inference (second edition), George Casella and Roger Berger, Duxbury Press

Computer Age Statistical Inference, Algorithms, Evidence and Data Science, Bradley Efron and Trevor Hastie, Cambridge University Press

Introduction to the Theory of Statistics, Alexander Mood, Franklin Graybill and Duane Boes, McGraw Hill

## Module Pre-requisites

**Prerequisite modules:** STU23501

**Other/alternative non-module prerequisites:** NA

## Module Co-requisites

None

## Module Website

[Blackboard](https://tcd.blackboard.com/webapps/login/)