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] | 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:
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Explain what subjective probability is and how Bayesian statistical inference is the result of adopting the subjective approach to probability can be motivated;
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Explain how Bayesian statistical inference is the result of adopting the subjective approach to probability;
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Contrast the Bayesian and frequentist approaches to statistical inference, explaining the meaning of a likelihood, parameter and probability model;
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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;
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Summarise the different numerical analysis approaches to calculating the integrals involved in multi-dimensional posterior distributions or the calculation of marginal distributions from them;
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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;
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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