# STU34507 – Statistical Inference I

**Source**: https://teaching.scss.tcd.ie/module/stu34505-modern-statistical-methods-i/
**Parent**: https://www.maths.tcd.ie/undergraduate/modules/minor-stats.php

|  |  |
| --- | --- |
| **Module Code** | STU34507 |
| **Module Name** | Statistical Inference I |
| **ECTS Weighting[**[1]**](https://teaching.scss.tcd.ie/wp-admin/post.php?post=375&action=edit#_ftn1)** | 5 ECTS |
| **Semester taught** | Semester 1 |
| **Module Coordinator/s** | Prof. Simon Wilson |

## Module Learning Outcomes

On successful completion of this module, students will be able to:

1. Explain what subjective probability is and how Bayesian statistical inference is the result of adopting the subjective approach to probability can be motivated;

1. Explain how Bayesian statistical inference is the result of adopting the subjective approach to probability;

2. Contrast the Bayesian and frequentist approaches to statistical inference, explaining the meaning of a likelihood, parameter and probability model;

3. Apply Bayes’ Law to a given model and prior distribution to form a posterior distribution, and recognise the functional form of the common probability distributions;

4. Summarise the different numerical analysis approaches to calculating the integrals involved in multi-dimensional posterior distributions or the calculation of marginal distributions from them;

5. Describe the Monte Carlo approaches of rejection or importance sampling to approximate a given posterior distribution and estimate the normalising constant of a posterior distribution;

6. Demonstrate methods of elicitation of prior distributions.

## Module Content

This module will describe the theoretical and practical aspects of Bayesian statistics inference.

Specific topics addressed in this module include: Quantifying Uncertainty, Some Laws of Probability, Probability Models and Prior Distributions, Statistical Inference, Simple Examples: Conjugate Priors, A More Complex Example, Point and Interval Estimates, Numerical Methods of Computing Posterior Distributions, Basic Simulation Methods, Markov chain simulation, Prior Elicitation, Some Real Applications.

## Teaching and learning Methods

Lectures and tutorials. Lectures include some programming demonstrations.

## Assessment Details

|  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- |
| **Assessment Component** | **Brief Description** | **Learning Outcomes Addressed** | **% of total** | **Week set** | Week Due |
| Examination | In person | All | 100 |  |  |
| Group project | – | – | 0 | – |  |

## Reassessment Details

 Examination (In person, 100%)

## Contact Hours and Indicative Student Workload

|  |  |
| --- | --- |
| **Contact Hours (scheduled hours per student over full module), broken down by**: | **33 hours** |
| Lectures | 27 |
| Tutorial or seminar | 6 |
| **Independent study (outside scheduled contact hours), broken down by:** | **67 hours** |
| Preparation for classes and review of material (including preparation for examination, if applicable | 62 |
| completion of assessments (including examination, if applicable) | 5 |
| **Total Hours** | **hours** |

## Recommended Reading List

Lee, P.M., “Bayesian Statistics: an Introduction”, 2nd edition, published by Edward Arnold, 1997.

de Finetti, B., “Theory of Probability (Volumes 1 and 2), published by Wiley, 1990.

Lindley, D.V., ” Making Decisions”, 2nd edition, published by Wiley, 1985.

Ross, S.M. , ” Simulation”, 2nd edition, published by Academic Press, 1997.

## Module Pre-requisites

**Prerequisite modules:** STU12501, STU12502, STU23501, STU22005

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

## Module Co-requisites

None

## Module Website

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