# Questions tagged [rejection-sampling]

Rejection sampling is a basic technique used to generate observations from a distribution. [Wikipedia]

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### Accept-reject algorithm , why is c>1?

In an accept-reject algorithm, we need to find c such that pj/qj≤ c for all j for which pi > 0 . And, the probability of accepting in any iteration is 1/c. Why is c guaranteed to be more than 1?
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### How the conditional probability is being calculated in Rejection sampling

In a class lecture, the "Acceptance-rejection algorithm" was presented as follows: To generate $𝑋 \sim 𝑓(𝑥)$, Find density $g$ satisfying $\frac{f(t)}{g(t)}<=c$ for some constant $c$ for ...
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### How does the rejection sampling method work in layman's terms?

Suppose that I have no knowledge of sampling methods and that I have some knowledge of probability theory (e.g. probability distribution and marginal distribution). How would you explain the ...
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### Proving the Accepted Samples from Rejection Sampling follows our Posterior Distribution

I get confused how the author gets to line $(1)$ using the indicator functions. If someone can explain this to me or give me a hint that would be greatly appreciated. Thanks! Define the following: ...
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### Optimal distribution for Acceptance Rejection Sampling

For some project I have been sampling from the Gamma distribution. I have been using the exponential distribution intensively. One method I have employed is the Acceptance rejection sampling, ...
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### Can't understand why rejection sampling works

I want to generate sample points $\{z_i\}$ in an arbitrary 2D shape, e.g. a circle centered at the origin with radius 1. Rejection sampling says: Look at 2 uniform random variables over $[0,1]$, $X$ ...
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