WRUG Winter 2016
Richard Vale
University of Otago, 17/5/16
Introduction
- (from Aug-Oct 2014)
- Series of novels by G. R. R. Martin
- Noted for exciting cliffhangers and unexpected deaths
- Each chapter told from point of view of one character
- Want to know whether a particular character died or not
- Statistics exists in order to tell us what to do when we have incomplete information, so why not use it?
Data (1)
Number of point-of-view chapters of each character in each book. Character i has Xij POV chapters in book j.
24 characters; 5 books; want prediction for book 6
| AGOT | ACOK | ASOS | AFFC | ADWD | |
|---|---|---|---|---|---|
| Eddard | 15 | 0 | 0 | 0 | 0 |
| Catelyn | 11 | 7 | 7 | 0 | 0 |
| Sansa | 6 | 8 | 7 | 3 | 0 |
| Arya | 5 | 10 | 13 | 3 | 2 |
| Bran | 7 | 7 | 4 | 0 | 3 |
| Jon | 9 | 8 | 12 | 0 | 13 |
Data (2)
Data (3)
This is repeated measures data. We can predict that the next value will be the same as the current value. But to measure the uncertainty in our predictions, we require a model.
Model
Include deaths in the model by assuming that each character enters the action at a time ti,1 and leaves the action at a time ti,2 so that Xij = 0 if j < ti,1 or j > ti,2.
This means that each character has three parameters (average number of chapters, start time and end time.) This is too many, so we assume each parameter is drawn from a common underlying distribution. This is the same as assuming that the characters are exchangeable.
This gives a model with six parameters, which can be fitted using Bayesian methods.
Model
[Philosophical aside
The use of a model involving randomness does not imply a claim that the data were generated by some random process.
A model can be viewed as a way of writing down all the possible states of the information that we don't know (in this case, everything about the books apart from the table of point-of-view chapters.)
Randomness is the same as not-knowing.
Compare: coin flip. ]
Model fitting
Results
Evaluation
Is Jon Snow dead?
...No!
