@WilsonCattle  
Question for @ole_b_peters I have enjoyed reading about ergodicity economics considerable  the distinction between time average and ensemble expectation is powerful! Q: how do you handle uncertainty in the parameters of gamble in this framework? e.g. take coin flip gamble:



Chris Wilson
@WilsonCattle

1 Jan 19  
if heads > multiple wealth by 1.5, if tails > 0.6. Given known p = 0.5, this is a powerful example showing time average != ensemble average. But what if you have uncertainty in p? My (Bayesian) answer is: given data y, estimate posterior p(py), and then obtain distro over


Chris Wilson
@WilsonCattle

1 Jan 19  
timeaverage returns. This is an ensemble (of sorts) of timeaverage possibilities! What do we do now? Normal Bayesian decisiontheory says to take the expectation here. What do you think? We could generalize even further to uncertainty in returns, etc.


Ole Peters
@ole_b_peters

1 Jan 19  
Chris Wilson
@WilsonCattle

2 Jan 19  
Trying to notate a little: we have a dynamic f(p,r,t) with probabilities p, returns r, over time t. We have uncertainty in {p,r}, but can constrain with data y. Distro: [lim(t>Inf)f(p,r,t)]*P(p,ry). Do we want <[lim(t>Inf)f(p,r,t)]*P(p,ry)>?

