Rejection sampling is a basic technique used to generate observations from a distribution. [Wikipedia]

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Adaptive Rejection Sampling in python?

Adaptive Rejection Sampling is a sampling technique for uni-dimensional variables that takes profit of the log-concavity of the probability density. It is used, for instance, in Gibbs sampling, when ...
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55 views

Metropolis-Hastings using log of the density

Does Metropolis-Hastings work with the log of the proposal and the density to be sampled from? That is, say we want to sample from a density $\pi(x)$, using a proposal $q(x|x^{old})$, will the ...
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On accept-reject method for unknown function

My problem is this I have a posterior as $Gamma(\alpha, \beta) \times exp(\lambda)$. $$Y_{1}^{n} \sim Gamma(\alpha, \beta)$$ $$\alpha \sim Exp(\lambda)$$ $$\beta \sim Exp(\lambda)$$ Now $n=50, ...
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Generating Random Zero-truncated Negative Binomial Values using Rejection Sampling

I am interested in generating zero-truncated negative binomial random variables using some sort of rejection sampling. My first thought was to simply draw from a negative binomial distribution, and ...
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Does Accept - Reject Algorithm Monte Carlo help fit a distribution to the data?

As far as I understand the Accept - Rejection Algorithm is used to help us simulate hard to simulate densities or unknown densities by first simulating an easy density and then accepting or rejecting ...
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Rejection-Sampling of Exponential Distribution

Consider the following question. Consider the generation of random numbers following an exponential distribution with some known mean. Give three reasons why the rejection-acceptance method would ...
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Bayesian: Sampling from Truncated Distributions

When would the rejection sampling method be preferred to the inverse CDF method for sampling truncated random variables? And when would the inverse CDF method be preferred to the rejection sampling ...
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the non-rejection region in level of significance approach eqaul to the area determined by upper and lower bounds in confidence interval approach

For $H_0: \hat \beta=\beta^*$ I want to prove that the non-rejection region in level of significance approach Will be eqaul to the area determined by upper and lower bounds in confidence interval ...
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Rejection Sampling

Suppose we are using rejection sampling and we want to sample from a distribution, say $p$. In order to calculate the acceptance probability we use the ratio: $$P(u < \frac{p(x)}{Mq(x)})$$ ...
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Rejection sampling from a Gamma distribution using a Cauchy proposal

i'm trying to find the parameters $ \gamma,x_0$ of a standard Cauchy distribution : $$T(x)= \frac{1}{(\pi \gamma (1+(\frac{x-x_0}{\gamma})^2))} $$ To perform rejection sampling from a gamma ...
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610 views

How does the proof of Rejection Sampling make sense?

I am taking a course on Monte Carlo methods and we learned the Rejection Sampling (or Accept-Reject Sampling) method in the last lecture. There are a lot of resources on the web which shows the proof ...
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Question about the logic of hypothesis testing

Let us say that we have this following problem: "A government agency claims that more than 50% of US tax returns were filed electronically last year. A random sample of 150 tax returns for last year ...
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Normalizing constant & rejection sampling

I think I understand what a normalizing constant is. Say for example you have a pdf $f(x)$ with support $0 \le x \le 5$. If you wanted to truncate the pdf and only look at $0 \le x \le 3$ you would ...
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Rejection sampling - picking a g(x) distribution

Let's say I have to sample from a pdf $\pi(x) = 3x^3+\frac{3}{4}x^2, 0 \le x \le 1$. I know we have to pick some pdf $g(x)$ such that $cg(x) \ge \pi(x)$ for all x. The only thing that came to mind was ...
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135 views

Accept-reject algorithm for Beta(1,$\beta$)

Consider the pdf $$f(x)= \begin{cases} \beta x^{\beta -1 }\quad 0<x<1 \\ 0\quad \text{elsewhere} \end{cases} $$ for $\beta >1 $ Use the accept-reject algorithm to generate an observation ...
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Empirical distribution alternative

BOUNTY: The full bounty will be awarded to someone who provides a reference to any published paper which uses or mentions the estimator $\tilde{F}$ below. Motivation: This section is probably not ...
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Hypothesis Testing on Exponential distributions

Let $X_1, \dots, X_n$ be independent exponential $(\theta)$ random variables. Suppose we are interested in testing $H_0: \theta = \theta_0 = 1$ versus $H_A: \theta = \theta_1>1$. Consider two tests ...
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282 views

Estimated error variance $\sigma^2$ for MCMC estimation in a high-dimensional space

Let $f$ be a function such that: $$f~:~(x,~\theta)\in\mathbb{R}^{3}\times\mathbb{R}^{12} \rightarrow f(x,~\theta)\in\mathbb{R}^3$$ My observations $y$ are noisy values taken by the function $f(\cdot ...
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Is there any proper way to fix a sample to adjust for known demographic overrepresentation?

My spouse frequently works with (expensive, hard to obtain) data samples; for example route information for commuting bicyclists collected using a smartphone app. More often than not, these samples ...
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303 views

What is the probability of rejection in rejection sampling?

Context: I'm reading up on sampling in MCMC for Machine Learning. On page 5, it mentions rejection sampling: ...
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371 views

What is a good proposal distribution for this density (in rejection sampling)? Is mine correct?

I have this density, I want to find a density "larger" than this $f(x)=\frac{1}{c}g(x)(1-\sin (20x)/4))$ , where $g(x)$ is N(0,1). I am looking for a proposal distribution for f(x), basically find ...
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How do I sample without replacement using a sampling-with-replacement function?

I vaguely recall from grad school that the following is a valid approach to do a weighted sampling without replacement: Start with an initially empty "sampled set". Draw a (single) weighted sample ...
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How to choose the tolerance parameter for ABC?

I have the following sorted data (sampling from parametric space [1,5]) with respect to their distances of parameter Theta. i.e., Let say N = 1000, Theta : 1.1, 1.7, 1.9, 2.4, 2.8, . . . , 4.9 ...