Re: Probability of making a choice by a person, on the basis of earlier made choices?

se16@xxxxxxxxxxxxxx wrote:

If the man randomly and independently decides whether to answer each
question truthfully, his probability of a lie on question 6 is
unaffected by how many lies he told in the first five questions. In
this case, the proportion of lies detected among questions whose answers
were checked converges to his probability of lying on any given question
as the number of questions checked increases (Weak Law of Large Numbers).
...

Let's stick with this version of the problem. The frequentist
response "ask a lot of questions" may not be practicable.

Alternatively you could take a Bayesian approach. With a symmetric
proper prior distribution, for example Beta(k,k) for some k>0, you
could say the probability that the first statement is true is 0.5.
Once there had been t true and f false statements this would modify
the posterior distribution, in the example to Beta(k+t,k+f) which
would make the posterior probability of the next statement being true
(k+t)/(2*k+t+f).


Of what is the Beta distribution a prior? As I see this version of the problem, the truthfulness of any response is a Bernoulli variable with parameter p, and p is not random. I don't see where the Beta distribution fits in.

/Paul
.

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