# 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.

54 questions
Filter by
Sorted by
Tagged with
0 votes
0 answers
15 views

### 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 ...
• 131
1 vote
0 answers
109 views

### 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 ...
8 votes
3 answers
260 views

### 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 ...
• 4,420
1 vote
0 answers
42 views

### 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 ...
• 11
3 votes
0 answers
117 views

### 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 ...
• 10.9k
2 votes
1 answer
100 views

### 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
0 answers
19 views

### 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 ...
• 11
1 vote
1 answer
47 views

### 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 ...
• 33
12 votes
4 answers
2k views

### 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 ...
• 103
1 vote
1 answer
242 views

### 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 ...
• 13
0 votes
1 answer
87 views

### 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 $\pi(\eta,\tau^2,\sigma^2) \propto Ca^+(\tau^2,0,b_{\tau}) \times Ca^+(\sigma^2,0,b_{\sigma})$...
• 33
1 vote
1 answer
25 views

• 420
0 votes
0 answers
59 views

### 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: <...
0 votes
0 answers
26 views

### 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 ...
• 113
0 votes
0 answers
34 views

### 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?
4 votes
1 answer
708 views

### 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 ...
• 43
0 votes
1 answer
200 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 ...
0 votes
0 answers
52 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 ...
-1 votes
0 answers
50 views

1 vote
1 answer
218 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
1 answer
2k 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 ...