0
votes
0answers
22 views

Difficult Survey Sampling question

Question: A Secretary of State wants to survey the primary owners of motorcycles registered in the state to estimate the proportion who want the license plates redesigned. (Primary owner means that ...
4
votes
1answer
59 views

Uniform sampling with replacement item frequency

Suppose we are sampling from $N$ distinct items uniformly with replacement $M$ times. What can be said about the distribution of frequencies of items drawn? For example, if I sort all the frequencies ...
1
vote
0answers
7 views

Sampling with an “oversampling” factor, in K-Means||

I'm trying to understand K-Means||, a scalable version of K-Means++, which itself is an "improved" version of the clustering algorithm K-Means. Please find here the link to K-Means|| paper ...
3
votes
2answers
61 views

What does it mean to sample, in measure theoretic terms?

Suppose I have some random variable $X$ defined on some probability space $(\Omega, \mathcal{F}, \mathbb{P})$. What does it mean, in measure theoretic terms, to draw a sample from $X$? When $\Omega$ ...
1
vote
1answer
69 views

The mean and variance of the sample median

The population and the median of a sample sized $2k+1$ should have the same mean and variance. Why is that? Will the result still be so tidy for a sample sized $2k$?
0
votes
0answers
77 views

Sampling uniformly from n-sphere using spherical coordinates

It has been explained here why sampling from n-sphere is not achievable with naive parametrization. And it explains how to correct it for 3 dimensions. Can somebody please guide me what is the correct ...
3
votes
1answer
83 views

Is it possible to sample the Dirac delta function?

The Dirac delta function can be a probability measure with the unit/Heaviside step function as its cumulative distribution function. Is it possible to sample such a distribution? If a random variable ...
3
votes
1answer
87 views

Maximum likelihood estimation - why is $\mathcal{L}$ not the joint pdf?

Here's an excerpt from my notes: Define the likelihood function: $$\mathcal{L}(\vec{x};\theta)=\prod_{i=1}^{n} f(x_i;\theta)$$ Where $f$ is the pdf of the distribution we're sampling the $x$'s ...
1
vote
0answers
34 views

Suitable change of measure with importance sampling

I'm working on a project on Importance Sampling. When one tries to estimate the small probability $\alpha:=\mathbb{P}(X \in A)$, one can do a change of measure. There is change of measure which ...
1
vote
0answers
54 views

Continuous random sampling with replacement.

Construct a set $s\subseteq[0,1]$ by sampling points in $[0,1]$ with uniform probability density $x\leq1$ so that $|s|=x$. Interpret this as a sampling frame during which data is captured. Now, ...
4
votes
1answer
1k views

Probability to choose specific item in a “weighted sampling without replacement” experiment

Given $n$ items with weight $w_n$ each -- what is the probability that item $i$ is chosen in a $k$-out-of-$n$ "weighted random sampling without replacement" experiment? Can a closed-form solution that ...
2
votes
1answer
163 views

Sampling from discrete probability distribution from first principles

I have a set $S=\{a_1,a_2,\dots,a_n\}$. The probability with which each of the element is selected is $\{p_1,p_2,\dots,p_n\}$ respectively (where of course $p_1+p_2+\cdots+p_n=1$). I want to ...
1
vote
0answers
45 views

Bias in Resampling

I'm currently doing some work with Particle Filters, a sampling-based method for computing expectations of functions with respect to dynamic (ie: time-variant) random variables. For example, consider ...
4
votes
4answers
161 views

Sample: don't confuse measurements with actual values?

In Wikipedia's article on Sample there is the following remark: ''Note that a sample of random variables (i.e. a set of measurable functions) must not be confused with the realizations of these ...