Posterior entropy over trials: calculate, store, plot

drbenvincent / darc_toolbox

Run adaptive decision making experiments

MIT License

16 stars 2 forks source link

Posterior entropy over trials: calculate, store, plot #43

Closed drbenvincent closed 5 years ago

drbenvincent commented 5 years ago

Goal

Be able to generate figures like this

Approach

It's probably easiest/best to calculate entropy by:

[x] Take the particles for a given parameter. Calculate the parameters of the distribution using the fit method on the appropriate scipy.stats distribution object. Calculate the marginal entropy for that parameter using the fitted parameters from the previous step.
[x] store it
[x] write script to produce figure
[x] sample logk from prior for each repetition
[x] improve the look of the plotting
[x] update the plotting... use seaborn to plot the sd of the data instead of bootstrap uncertainty about the mean

NOTE: This implementation is done assuming the univariate distributions are Gaussian distributed.

drbenvincent commented 5 years ago

Progress so far. Note:

that this is for one fixed logk value, we are not yet drawing it from a distribution.
only a few repetitions
crude initial plotting effort
poor colour coding
the behaviour of the drop in entropy seems much less steep than for the Matlab implementation. This is most likely because the Matlab implementation calculated entropy over a discrete posterior density, but the Python implementation (as of now) calculates it assuming we have a normal distribution using the entropy() method on the scipy distribution object.

screen shot 2018-11-28 at 16 46 01

drbenvincent commented 5 years ago

This is approaching completion. I now use seaborn to do the plotting. It is nice. But I need to work out exactly what the error bars represent - it's slightly ambiguous from the documentation, but it looks like 95% CI on bootstrap estimates of the mean. That is, it does not represent the actual spread of the data. This is fine, but I want to know that for sure. I have an issue here: https://github.com/mwaskom/seaborn/issues/1619 screen shot 2018-11-29 at 15 43 48

Also, still need to decide between plotting posterior entropy of a normal distribution fitted to the posterior, or if I should do it based on a discrete prob density of the raw posterior samples. The latter is what I did in the original Matlab version.

drbenvincent commented 5 years ago

Now the plot conveys the spread over the various simulations. Shaded zones correspond to sd. screen shot 2018-12-22 at 09 21 56