Forward-looking model

[imccart]

• Calculate gittins index
• basic descriptive states of index and distribution

[sethrs-jhu]

Assessing the Gittins index

First, let's look at the distribution of the underlying variables: running success rate / the index (m), and running referrals / familiarity (e)

• histograms of each
• histogram of bottom tail of m (say, bottom 10%) (if short on time, just a 'summarize, details' of each should be good enough)

Then look at how these two variables relate to the Gittins index. Recall: Gittins is a fn of mean (m) and variance (v). Recall: variance v = m (1-m) / (e+1), where e is "experience" or "familiarity" (i.e., number of past patients referred). So ideally it's a 3D plot: Gittins as fn of m and e. Is there a 2D contour plot, easy to construct, that would show the mass clearly? (e.g, via shading) Not worth much time, only if this is easy and automatic. Otherwise, bin on ranges of m and make scatter plots of Gittins vs e. (possible bins: m = 1.00, m = [0.95, 1.00), m = [0.90, 0.95), etc...) Mark the x-axis with percentiles of the x variable (e), so we know where most of the observations are.

Note for programming -- the argument inside Psi in the Gittins formula should simplify to 1/[-ln(beta)*e]