Illustration of discounting as Bayesian inference. Mental simulation generates a noisy value signal ( = 1), which is combined with a prior distribution to form a posterior distribution over value. The black line denotes the true underlying value , and the shaded region shows the standard deviation of the noise corrupting the value at each possible delay (in arbitrary units). Similarly, the blue line is the posterior mean, and the shaded region is the posterior standard deviation. Because the standard deviation of (simulation noise) increases with delay, the posterior mean is pulled more strongly towards the prior mean for longer delays. Same simulation as in but with a smaller signal variance, demonstrating a reduction in discounting. Discount factor under the rational inattention model as a function of the sensitivity parameter ( ) and reward magnitude. Choice stochasticity under the rational inattention model as a function of the sensitivity parameter ( ) and reward magnitude.
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