1 MATH 5820 coursework General assessment information
This coursework is included in the assessment for MATH5820, and counts 20% towards your overall mark for the module.
Your report should be handed in on, or before, Monday 11th May, via my letterbox on Level 8.
You are encouraged to collaborate with other students, but the work that you hand in must be done independently.
The analyses in the coursework should be performed using the statistics program R. You will have an opportunity to work on related problems before the practical session, which will be held on Thursday 30th April (13:00-15:00) in the Chemical and Process Engineering Cluster GR.06. The data needed for the coursework are available from Minerva.
If you have any questions about the coursework, please email me.
Background to the problem
A few years ago a university took the decision to record all lectures and provide videos of the lectures to the students through their Virtual Learning Environment. There is a concern that the amount of hard drive space to store all the hours of lectures might far exceed what is currently available. Soon, the university decision makers will need to decide if it will be necessary to expand the hard drive capacity to enable video storage for years to come.
An IT specialist has been asked by the university to perform an analysis of some data on video lengths so that the university decision makers can decide whether to invest in new disk space. In particular, he/she will get data on the length of videos (rounded to the nearest 10 seconds) from one lecturer to use in his/her analysis. Video lengths of individual lectures are controlled by the lecturers, but (prior to starting the analysis) the IT specialist knows that lectures are supposed to be 50 minutes long and should not exceed 1 hour.
For the purposes of this coursework, you will assume the role of the IT specialist.
Analyses you need to perform
1. Propose a data generating model for the data that are going to be collected (i.e. construct a likelihood for the length of videos rounded to the nearest ten seconds) and consider any assumptions that you are making.
2. Elicit your own beliefs about the parameter(s) of the data generating process, and
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MATH 5820 coursework
3. 4.
5.
produce your prior distribution for the parameter(s) based on your beliefs.
Propose a second prior distribution that might encode ignorance in the parameter(s).
Find the data, which are available on Minerva. Use a sampling method to update both prior distributions in the light of the data. Calculate the posterior means and variances based on the different posterior samples.
Use each of the two posterior distributions to give a distribution over how long the next video produced by this lecturer will be.
Writing up
You are required to write a short report outlining the analyses you have performed (including discussions of how appropriate the techniques were) and explaining the results.
The report should be aimed at someone who has a basic knowledge of Bayesian statistics and who needs convincing of your modelling and numerical integration choices.
The report should contain relevant plots such as time series plots and histograms (which should be explained in the report). These can be copied from R, but the report should not contain any R commands or other output directly copied and pasted from theR console. The aim of this practical is to explain the analyses that you have performed and giving R commands does not do this.
The report should be word processed and should not exceed 6 sides of A4 (single spaced with at least 11 pt font size) including any plots that you wish to reproduce.
In addition to the report, attach an appendix that includes all of the R commands that you have used. There is no need to reproduce any plots in the appendix, and the appendix does not count towards the number of pages in your report.