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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Sampling from a hypersphere subject to a linear constraint? [duplicate]
I'm running into efficiency issues when trying to sample from a "hypercone" using rejection sampling. By a hypercone, I mean the set of vectors $C_{v,\beta} = \{w \sim N(0,1)\ |\ w^T v \geq \...
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Rejection sampling method in tail of truncated exponential distribution (answered)
See edit below as question has been answered.
I want to sample from an exponential distribution with parameter $\lambda>0$ truncated in the tail between $a>0$ and $b>0$, such that $b>a$, ...
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Rejection of samples suspected of not coming of the target population
Say, there is a stationary process that should resemble a Gaussian distribution with 'known' mean and variance. Iid samples in triplicates (or n-plicates) are taken from it. It is also known that ...
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Rejection sampling to obtain a random sample from a truncated version of a multivariate probability density
Suppose I have a multivariate probability density $f(\mathbf{y}|\boldsymbol{\theta})$ with support $\mathbb{R}^d$ that is analytically tractable, and I know how to randomly sample from $f(\mathbf{y}|\...
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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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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 ...
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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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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 ...
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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 ...
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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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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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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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