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Fix simulation on wald chapter #341

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Fix simulation on wald chapter #341

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9 changes: 7 additions & 2 deletions lectures/dynamic_programming/wald_friedman.md
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Expand Up @@ -361,7 +361,7 @@ Later, doing this will help us obey **the don't repeat yourself (DRY)** golden r
Let's code this problem up and solve it.

We implement the cost functions for each choice considered in the
Bellman equation {eq}`new3`.
Bellman equation {eq}`new5`.

First, consider the cost associated to accepting either distribution and
compare the minimum of the two to the expected benefit of drawing again.
Expand Down Expand Up @@ -475,6 +475,11 @@ end
We can simulate an agent facing a problem and the outcome with the following function

```{code-cell} julia

function bayes_new_draw_update(p, d0, d1,v)
p * pdf(d0, v) / pdf(MixtureModel([d0, d1], [p, one(p) - p]), v)
end

function simulation(problem)
(; d0, d1, L0, L1, c, p, n, return_output) = problem
alpha, beta = decision_rule(d0, d1, L0, L1, c)
Expand All @@ -492,7 +497,7 @@ function simulation(problem)
while iszero(choice)
t += 1
outcome = rand(d)
p = bayes_update(p, d0, d1)
p = bayes_new_draw_update(p, d0, d1,outcome)
if p <= beta
choice = 1
elseif p >= alpha
Expand Down