# 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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• 2,103
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### Is this a correct way of resampling the MCMC chain?

Please understand I am not familiar to the statistical languages. All I want is to resample a probability distribution from an existing sample drawn from another distribution using MCMC, without ...
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1 vote
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### Tightness of rejection sampling

Hello. I'm studying the Monte Carlo Statistical Method textbook by Robert and Casella. I have a question about exercise problem 30 in Chapter 2. I've already solved parts (a)-(c), but I'm having ...
• 31
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### Sampling from $P(x) \propto \cosh^{m}(a x) e^{-x^{2}/2}$

Is there an efficient algorithm to draw samples $x \sim P(x)$ from the PDF: $$P(x) \propto \cosh^{m}(a x) e^{-x^{2}/2}$$ where $a\ge0$ is a real parameter, and $m$ a positive integer? Since this is ...
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1 vote
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### The lower bound of acceptance rate for independent Metropolis–Hastings algorithm

In comparison with rejection sampling, for independent M-H algorithm, if there is a constant C such that$$f(x)=\frac{p(x)}{\int p(x)dx} \leqslant Cg(x)$$ for all x, then the acceptance rate is at ...
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### Random correlation matrices

Suppose that we simulate random $n\times n$ correlation matrices by assigning iid $U(-1,1)$ random variables to all off-diagonal entries and accept matrices $\boldsymbol\Sigma$ that are positive ...
• 11.3k
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### Proof of Rejection Sampling: Flawed reasoning about continuous random variables

I recently studied Rejection Sampling as part of one of my University courses. When justifying why Rejection Sampling makes sense (to "prove", so to speak, that samples drawn using Rejection ...
1 vote
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### Accept Rejection Mante carlo simulation and simulation mean [closed]

I read that in Monte Carlo simulation results, the larger the sampling, the mean sample results from the simulation close to normal distribution, but does this also apply to Monte Carlo accept ...
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1 vote
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### Rejection Sampling Proposal vs Target Confusion

My understanding is that rejection sampling for some target distribution $p_{X}(x)$ and proposal distribution $\tilde p_{\tilde X} (x)$ follows the process below: If there is some scaler $c$ such ...
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### The lack of evidence to reject the H0 is OK in the case of my research - how to 'defend' this in the discussion of a scientific paper?

It is probably best if I give an example because I would like to be well-understood, and I do not know how to deal with the following situation: I analysed, using the Kruskal-Wallis test (post hoc ...
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1 vote
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### Is Metropolis-Hastings ever more efficient than rejection sampling in 2 dimensions?

I know that Metropolis-Hastings is an MCMC (Markov Chain Monte Carlo) method that is very useful in higher dimensions. The advantages it has over something like simple rejection sampling are that ...
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### Acceptance-Reject to generate a distribution proportionate to Inverse Gamma and truncate Cauchy distribution

Assume $Y_{ij} \sim N(\mu_i,\sigma^2)$, $\mu_i \sim N(\eta,\tau^2)$ for $i=1,2$ $j=1,\cdots,n_i$ and prior $\pi(\eta,\tau^2,\sigma^2) \propto Ca^+(\tau^2,0,b_{\tau}) \times Ca^+(\sigma^2,0,b_{\sigma})$...
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### How to identify the distribution being sampled by this algorithm?

I've been studying a piece of code lately that uses the Monte Carlo acceptance-rejection method to draw random samples from a distribution I'm struggling to identify. Here's a Python implementation: <...
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### Capital Y vs small y

I want to use the acceptance-rejection method to generate a sample from the following target probability density function: $$f\left(x\right)=1.25x^4+2x^3+0.25,\:0<x<1$$ Let the trial probability ...
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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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### 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 ...
53 views

### 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 ...
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1 vote
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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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### 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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### 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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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 \$...