Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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

Rejection Sampling

32 questions
10
votes
2 answers

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 $f_i$ are distributions which can easily be sampled from,…
πr8
  • 1,286
  • 5
  • 22
9
votes
3 answers

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 description of this process from the…
deemel
  • 2,402
  • 4
  • 20
  • 37
4
votes
0 answers

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 and $g$ a proposal density, and $h_{i:j}$ the…
hejseb
  • 2,298
  • 1
  • 15
  • 26
4
votes
1 answer

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 treated patients. The treatment with the new…
ecjb
  • 539
  • 1
  • 5
  • 16
3
votes
1 answer

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 $f_Y$ and $f_V$ have common support. To generate $Y…
Ryker
  • 171
  • 6
2
votes
1 answer

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 an envelope $g$) is $1/k$, where $k$ is the…
Student
  • 23
  • 3
2
votes
1 answer

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 rejection step of the algorithm. Here is what I…
user
  • 2,010
  • 8
  • 23
2
votes
2 answers

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 from F(x). What I thought on doing is using the…
Patrick
  • 161
  • 9
1
vote
1 answer

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) $R=\{\bar{X_n} > c\}$. Is a two sided test (check…
Sharov
  • 251
  • 1
  • 10
1
vote
2 answers

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 to someone criteria that meets a target…
Seve Martinez
  • 35
  • 4
1
vote
1 answer

Rejection sampling - total probability of acceptance

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. PDF_function <- function(x){3*x^2} c <- PDF_function(1) curve(PDF_function, 0,…
Thanos Pantos
  • 57
  • 5
1
vote
1 answer

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, with Monte Carlo integration the integral can be…
AlphaBetaGamma96
  • 248
  • 1
  • 8
1
vote
1 answer

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 end. Problem: Use the rejection method to sample…
mdawgig
  • 43
  • 6
1
vote
0 answers

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 positives (FP). However, predicted negatives…
st1led
  • 187
  • 9
1
vote
0 answers

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 that $$ \frac1{n}\sum_{i=1}^N \delta_{x_i}…
N00ber
  • 143
  • 4
1
2 3