In Uncertainty over time and Bayesian updating, David Rhys Bernard estimates how quickly uncertainty about the impact of an intervention increases as the time horizon of the prediction increases. He shows that a Bayesian should put decreasing weight on longer-term estimates. Importantly, he uses data from various development economics randomized controlled trials, and it is unclear to me how much the conclusions might generalize to other interventions.
For me the following is the most questionable assumption:
Constant variance prior: We assume that the variance of the prior was the same for each time horizon whereas the variance of the signal increases with time horizon for simplicity.
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If the variance of the prior grows at the same speed as the variance of the signal then the expected value of the posterior will not change with time horizon.
I think the rate of increase of the variance of the prior is a crucial consideration. Intuitively, I would say the variance of the prior grows at the same speed as the variance of the signal, in which case the signal would not be discounted.
Thanks for the post, Jack!
For me the following is the most questionable assumption:
I think the rate of increase of the variance of the prior is a crucial consideration. Intuitively, I would say the variance of the prior grows at the same speed as the variance of the signal, in which case the signal would not be discounted.