# Questions tagged [accept-reject]

Use this tag for accept-reject sampling methods. These are also known as rejection sampling methods. These methods sample a random variable from a dominating measure (h) and accepts the draw if an auxiliary random variable (a uniform) is less than the desired measure (g), so accept the draw if u<g. Otherwise draw another pair. You can think of this as sampling on a space with 1 additional dimension where the additional dimension is uniform under g.

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### How can Envelope Rejection Sampling be used to generate samples from a posterior distribution? [closed]

Say we have two independent variables: $X \sim N(\mu_1, \sigma_1^2)$ and $Y \sim N(\mu_2, \sigma_2^2)$ but these cannot be observed directly. Instead, we can observe $R = \sqrt{X^2 + Y^2} + \epsilon$ ...
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### Generating samples from a n-dimensional Epanechnikov kernel

I have successfully generated samples from the 1D Epanechnikov kernel, following the routine described on page 236 in "Nonparametric Density Estimation" by Devroye and Gyorfi (Also described ...
1 vote
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### Rejection sampling with inverse-gamma-like density [closed]

I would like use rejection sampling to sample from a density, $f_y$ on $(0, \infty)$ satisfying $$f_y(y) \propto \frac{y^{-1}}{1 + y^{-1}}e^{-by^{-1}}$$ I made a first observation that \begin{align*} ...
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### How to sample $n$ observations from a multinomial distribution using binomial (or poisson) sampling?

Context I have $n$ observations which I'd like to sample with replacement for the purpose of bootstrap. A way to think about it is that we have a multinomial distribution with $n$ classes and that we'...
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### Monte Carlo sampling ( accept/reject) for geographic dataset

I have a dataset consisting of latitude and longitude and I'm confused on which approach to use to determine the distribution of points so I can apply the monte Carlo accept/reject for sampling. this ...
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1 vote
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### Sampling from Gamma Distribution using the Rejection Method

I'm having some issues working through this practice problem. I have worked through the first portion of it, and I have the solution, but I don't understand how/why the solution does two things at the ...