A message from our CEO about the future of Stack Overflow and Stack Exchange. Read now.

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.

Filter by
Sorted by
Tagged with
0
votes
1answer
27 views

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 ...
1
vote
1answer
102 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 ...
1
vote
0answers
30 views

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 ...
0
votes
0answers
28 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 ...
2
votes
1answer
113 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 ...
3
votes
1answer
65 views

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 ...
3
votes
1answer
216 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 $...
1
vote
0answers
31 views

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 ...
1
vote
2answers
328 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 <...
1
vote
1answer
55 views

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 ...
1
vote
1answer
304 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 ...
10
votes
2answers
167 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 $f_i$ ...
2
votes
2answers
988 views

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 ...
1
vote
1answer
485 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 $...
7
votes
2answers
2k views

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 ...