Igor Babuschkin

Composition of random variables and parameters

8

Users should be able to pass combinations of random variables and parameters to a model. This would allow them to build more models, e.g. for fitting a function to data....

Users should be able to specify discrete values as their data variables.

What would be a good name for this? Example: `Prod(dist1, dist2)` would be the product of distributions `dist1` and `dist2`. If they depend on different random variables, the resulting distribution...

Users should be able to create custom PDFs conventiently. These could be specified using a Theano expression. They would then be compiled and optimized like any other distribution.

Users should be able to print the structure of their model or display it using dot.

Example: `Mix2E(N1, dist1, N2, dist2)`

Implement a large number of distributions

1

We can use pymc and Wikipedia (http://en.wikipedia.org/wiki/List_of_probability_distributions) for inspiration.

Users will need more functionality than just the model's likelihood when they want to create plots comparing model and data. Multi-dimensional plots are awkward to work with, which is why...

Implement convolution of PDFs

2

Theano implements fast convolution via FFT. We could implement a `Conv` distribution that takes two distributions and represents their convolution.

Implement statistical tests

2

We should implement various ways to test for goodness of fit.