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

learn more… | top users | synonyms

2
votes
1answer
44 views

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 ...
2
votes
1answer
94 views

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 ...
0
votes
0answers
57 views

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 ...
1
vote
1answer
48 views

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: $$P(u < \frac{p(x)}{Mq(x)})$$ ...
2
votes
0answers
123 views

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 ...
2
votes
1answer
205 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 ...
1
vote
1answer
61 views

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 ...
1
vote
1answer
66 views

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 ...
2
votes
1answer
73 views

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 ...
0
votes
0answers
79 views

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 ...
1
vote
1answer
98 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 ...
0
votes
0answers
51 views

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 ...
10
votes
2answers
543 views

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 ...
2
votes
0answers
337 views

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 ...
1
vote
1answer
208 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 ...
1
vote
2answers
62 views

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 ...
0
votes
2answers
255 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: ...
1
vote
0answers
299 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 ...
6
votes
2answers
2k views

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 ...
3
votes
2answers
362 views

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 ...