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Chris Wilson
Question for 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:
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Chris Wilson 1 Jan 19
Replying to @WilsonCattle
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(p|y), and then obtain distro over
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Chris Wilson 1 Jan 19
Replying to @WilsonCattle
time-average returns. This is an ensemble (of sorts) of time-average possibilities! What do we do now? Normal Bayesian decision-theory says to take the expectation here. What do you think? We could generalize even further to uncertainty in returns, etc.
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Ole Peters 1 Jan 19
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Chris Wilson 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,r|y). Do we want <[lim(t->Inf)f(p,r,t)]*P(p,r|y)>?
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