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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Can I get “fail to reject the null” when testing with test statistic, and “reject the null” when testing with P-value at the same time? [duplicate]

Can I get "fail to reject the null" when testing with test statistic, and "reject the null" when testing with P-value at the same time in a same nonlinear regression model?
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Rejection sampling ineffectiveness in high dimensions

I guess I really have two questions. First, iv'e seen quoted in a couple of places that the probability of accepting a given sample in a rejection sampling algorithm (sampling from a density $f$ with ...
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25 views

Finding a proposal distribution in acceptance-rejection method

I'm learning the Acceptance-Rejection method but I am having a hard time finding a g(x) except using uniform distribution to simulate the f(x). How could we find a g(x) that has a simple pdf and is ...
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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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how to generate data from a distribution whose cdf is not in closed form? [duplicate]

I am working on a distribution whose pdf and cdf is $$f(x,\alpha,\beta)=\frac{(\frac{\beta}{\alpha})(\frac{x}{\alpha})^{\beta}}{(1+(\frac{x}{\alpha})^{\beta})^{2}}\frac{\sin(\frac{\pi}{\beta})}{(\frac{...
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29 views

Rejection region and two sided test. Absolute value of mean

Given following problem: I've solved this problem assuming two sided test and rejection region $R=\{|\bar{X_n}| > c\}$ but it seems to be incorrect because correct answer assumed (I've checked it)...
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Escape unsuccessful accept-reject step in MCMC

I have an MCMC procedure that samples latent variables $h_1, \dots, h_T$. It is based on Shephard and Pitt (1997), https://doi.org/10.1093/biomet/84.3.653. Let $f$ be the true conditional posterior ...
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75 views

Does the accepted sample based on the acceptance-rejection algorithm has the same distribution as X~$f(x)$? [duplicate]

In Bayes Statistics, does the accepted sample based on the acceptance-rejection algorithm has the same distribution as X~$f(x)$? Intuitionally it does, but how to prove it under the discrete and ...
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126 views

Accept-Reject algorithm from binomial or other non-uniform distribution

I'm currently researching monte carlo simulations and the different methods. What I'm finding is that methods such as accept-reject typically sample from a uniform distribution and then compare that ...
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Rejection sampling - total probability of acceptance [closed]

I am given the following pdf $$f(x)=3 x^{2}, \quad 0 \leq x \leq 1$$ which i need to simulate by using rejection sampling. I have used the following code below in R. ...
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180 views

Rejection Sampling when the proposal is a mixture of two distributions

Given a density $f(x; \alpha, 1) = x^{\alpha-1}\exp(-x)/\Gamma(\alpha)$ and a proposal density $q(x) = \alpha_1.q_1(x) + \alpha_2.q_2(x)$ I want to generate random samples using Rejection Sampling ...
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114 views

Integration with accept reject sampling Monte Carlo

I've got a quick question with regards to accept-reject Monte Carlo integration that I can't solve. Suppose I want to integrate some function, $f(x,y)$, with samples of $x, y$ from $p(x,y)$. Now, ...
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52 views

generating process of acceptance-rejection algorithm

The acceptance-rejection algorithm is described as follows: suppose you have RVs $X$ and $Y$ with densities $f_X$ and $f_Y$, respectively, and there exists a constant $c$ such that $\frac{f_X(t)}{f_Y(...
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Confused about the sampling method

I want to sample from a density using the rejection method. The density is defined as $$ f(x) = \frac{e^x}{e-1},~~~ 0\leq x \leq 1.$$ Following the definition of the rejection method, we can find ...
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721 views

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 ...
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Devising an acceptance sampling plan for False Negative Rate

I need to evaluate a binary classifier that classifies inputs in positives and negatives. Since all predicted positives (PP) are assessed, I have complete data on the true positives (TP) and the false ...
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101 views

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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353 views

Metropolis-Hastings - interpreting the transition kernel: alpha*proposal

I thought I had great intuition and mathematical understanding of the Metropolis-Hastings algorithm, until closer inspection... as I started compiling my notes, I realized I do not understand the ...
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Interpretation of the region of rejection in hypothesis testing in binomial distribution

The pharmacy company Life Co. has developed a new drug against insomnia. To check the effectiveness, this drug was tested with n = 10 patients. At present, the standard medication can cure 30% of the ...
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231 views

How does the Metropolis Algorithm “get off the ground”?

I'm thoroughly confused by the Metropolis Algorithm as defined in Casella and Berger's Statistical Inference. Namely, here's the definition (p.254): Let $Y \sim f_Y(y)$ and $V \sim f_V(v)$, where $...
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Acceptance-Rejection using Functional

Setup Let $X\in L^1(\Omega,\mathcal{F},\mathbb{P})$. As far as I've seen, Monte-Carlo methods generate $x_1,\dots,x_n$ from the distribution of $X$ and uses the Glivenko-Cantelli theorem to conclude ...
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541 views

Posterior of $\text{Normal}(\theta,1)$ with a Cauchy prior distribution

If $X \sim N(\theta,1)$ with Cauchy as robust prior $$\pi(\theta) = \frac{1}{\pi(1+\theta^2)} \qquad -\infty < \theta < \infty$$ What will be the posterior distribution when Cauchy is $(-2 <...
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Understanding the Delayed Rejection Metropolis algorithm (Mira, 2001a)

I'm having trouble understanding the algorithm as briefly described here, and I can't find the original paper by Mira since it seems to be from some obscure print journal (Metron Volume 59). The ...
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748 views

Metropolis-Hastings acceptance ratio for truncated proposal

I have a proposal distribution for one parameter theta_guess theta_guess = guessleft(theta_accept(1,r-1), 0.01,0) which is a ...
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225 views

Exact Sampling from Improper Mixtures

Suppose I want to sample from a continuous distribution $p(x)$. If I have an expression of $p$ in the form $$p(x) = \sum_{i=1}^\infty a_i f_i(x)$$ where $a_i \geqslant 0, \sum_i a_i= 1$, and $f_i$ ...
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Using a Random number Generator to draw samples from a Cumulative Distribution function

I am given a Rayleigh, distribution function:$$f(x)=\frac{1}{5}x\exp\left(\frac{-x^2}{10}\right)$$ with $x>0$ and asked to: Use an appropriate random number generator algorithm to draw 500 samples ...
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813 views

Proof of Rejection Sampling

I'm trying to go through the proof of rejection sampling and I found a paper ACCEPTANCE-REJECTION SAMPLING MADE EASY which provides several helpful explanations. For Lemma 2, the paper claims that if $...
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Sampling from Skew Normal Distribution

I want to draw samples from a skew normal distribution as part of a matlab project of mine. I already implemented the CDF and PDF of the distribution, but sampling from it still bothers me. Sadly, the ...