new discount function: Exponential-Power

[drbenvincent]

My version

V = reward * exp(-a*(delay^b))

This is very similar to the discount function proposed by Ebert & Prelec (2007):

V = reward * exp(-(a*delay)^b))

• [x] add to unit tests
• [x] JAGS: separate model
• [x] JAGS: mixed model
• [x] add STAN models [edit: later removed, see below]

Implement properly for JAGS at the moment.

STAN models are very poor for this discount function (as they are with others). For the moment, just focus on JAGS and come back to STAN later. There are more general issues with STAN that I'm having with other discount functions.

• 17 Jan 2017: updated priors based on analysis of real data from my lab.

Avoiding hierarchical (group level) inference with this model

Because the joint posterior over (k, tau) is complex, I've decided to skip implementing this for the moment. Sticking with just the 'separate' or the 'mixed' models

Update priors and improve model stability

We have been getting issues with VB=inf or VB=NaN because of certain parameter combinations of (k, tau).

• [x] fix it

New subplot of subjective time

• [x] Add new plot of implied prospective time perception

[drbenvincent]

This is now working pretty well on data from my lab. There is probably scope to be a bit more informed about the priors, but they seem to be working well for the data I have so far.

[drbenvincent]

The issue of numerical instability continues.