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

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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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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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How to sample from this dirichlet distribution with an L1 prior?

I'd like to draw a sample from a distribution with p.d.f $$f(p,q,r,s) \sim \mathrm{e}^{-w(|p+q-r-s|+|p-q-r+s|+|p-q+r-s|)}p^aq^br^cs^d \mathbb{1}_{p+q+r+s=1}$$ $w > 0$ is a free parameter (which ...
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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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In responses collected from online survey, how to eliminate multiple representations from same company

Problem statement: In responses collected from online survey, How to eliminate multiple representations from same company Assuming that I intend to get one (and only one) response from each company ...
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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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163 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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202 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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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 ...