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Results tagged with bayesian
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user 252071
The approach and interpretation of probability associated with Bayes' theorem; usually used as opposed to the frequentist approach. It can be seen as an extension of logic that enables reasoning with propositions whose truth or falsity is uncertain. A Bayesian probabilist starts with some prior probability, and evaluates the evidence in favour of a hypothesis by combining the prior with the likelihood function of the observed data.
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Bayesian statistics - explanation of evidence
To summarize the discussion in the comments: The source is very vague and informal, though not actually inaccurate. In particular, they abuse notation in an unhelpful manner...using $P(\theta)$ to d …
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Bayesian inference about a proportion (NFL playoffs and coin flips)
Let $p_n$ be the probability that our team played exactly $n$ games.
Our prior: $$p_{16}=\frac {20}{32},\,p_{17}=\frac 4{32},\,p_{18}=\frac 6{32},\,p_{19}=\frac 2{32}$$
Now, if there were $n$ coi …
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Bayesian analysis
Your prior is $.15$ since, at the start, you have no reason to reject the hypothesis that cab color is independent of accident proclivity. That is, knowing that a cab was involved in an accident shou …
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What is the probability that a coin is fair?
Part 1: if the coin is fair, it comes up $H$ with probability $\frac 12$. If it is unfair then it comes up $H$ with probability $$\int_0^1 pdp=\frac 12$$. Thus the two cases are symmetric and the an …
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Help me with this conundrum about Bayesian\subjective probability theory.
If the fourth reviewer likes the film they would do the obvious Bayesian computation and determine that the probability that the film was actually good is $$\frac {.8\times.2^3\times .8}{.2\times .8^3\ … As a variant: if each reviewer considered their own vote, and reported the Bayesian posterior (using the last reported Bayesian posterior as their Bayesian prior) then the method would be fine. …
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Bayes Theorem Question about drawing two cards from a choice of four
There are three possible, unordered, hands: $RR,RB,BB$. Let's get the probability of each:
$P(RR)=P(BB)$ (by symmetry). The first is red with probability $\frac 12$, and the second matches with pr …
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Bayes' Rule broken?!?!
The problem is that seeing heads changes your estimate of the probability that you have seen the $HH$ or $HT$ coins.
To see this intuitively, suppose that, instead of coins, you had a pair of trillio …
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How do you interpret the answer to a Bayes' Theorem Question?
to flesh out the comments:
This is a routine application of Bayes Theorem.
Using the standard Poisson distribution, we see that the probability of observing $6$ cars given that $\lambda =2$ is $.01202 …
- 71.9k
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A priori probability in Bayesian inference problem
First, some basic calculations. let $p$ be the probability of guessing a card correctly. Then the probability of getting exactly $3$ correct is $\binom 53 p^3(1-p)^2$. If $p=.2$ this is $.0512$, if …
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