Questions about the statistical process of sampling from a population, in order to obtain information for use in statistical learning, estimation, hypothesis testing about some population or process. Use this tag along with the tags (probability), (probability-theory) or (statistics).
Questions tagged [sampling]
1326 questions
34
votes
4 answers
uniform random point in triangle in 3D
Suppose you have an arbitrary triangle with vertices $A$, $B$, and $C$. This paper (section 4.2) says that you can generate a random point, $P$, uniformly from within triangle $ABC$ by the following convex combination of the vertices:
$P = (1 -…
dsg
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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 depends only on $w_i / w_\cdot$ be derived…
krlmlr
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Uniform sampling of points on a simplex
I have this problem: I'm trying to sample the relation
$$
\sum_{i=1}^N x_i = 1
$$
in the domain where $x_i>0\ \forall i$. Right now I'm just extracting $N$ random numbers $u_i$ from a uniform distribution $[0,1]$ and then I transform them into $x_i$…
LordM'zn
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14
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How does accuracy of a survey depend on sample size and population size?
Which survey is more accurate? Assume the samples are taken perfectly randomly.
A sample of 100 people out of a population of 1000 (sample is 10% of population)
A sample of 1000 people out of a population of 1000000 (sample is 0.1% of…
Colonel Panic
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14
votes
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Multivariate Inverse Transformation Sampling
Summary
Given a multivariate density distribution, I use inverse transformation sampling to sample points from this distribution. While the first dimension exhibits the correct distribution, all other dimensions contain a slight, stable…
Nico Schertler
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12
votes
2 answers
What is the distribution of gaps?
Randomly select $n$ numbers from the universe $\{1,2\dots,m\}$ with or without replacement, and sort the numbers in ascending order.
We can get a list of number $\{a_1,a_2,\dots,a_n\}$, and then we can get the difference between two consecutive…
Fan Zhang
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11
votes
4 answers
Sampling from a $2$d normal with a given covariance matrix
How would one sample from the $2$-dimensional normal distribution with mean $0$ and covariance matrix $$\begin{bmatrix} a & b\\b & c \end{bmatrix}$$ given the ability to sample from the standard ($1$-dimensional) normal distribution?
This seems like…
user57159
11
votes
3 answers
Bob took a quiz
Bob took a quiz consisting of 500 questions with two options: Yes and No. Bob did not prepare for the quiz. Flustered, he hastily reached for a fair coin in his wallet and started to toss this coin for answers. Whenever the coin landed heads, he…
Loki123
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Analytic center of convex polytope
I have a convex polytope defined by $Ax \leq b$. I want to know how to find the "analytic center" of my convex polytope, because my goal is to sample from the polytope using Markov chain Monte Carlo (MCMC) methods, and it mixes better if i start…
Andy Yao
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10
votes
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Constructing a probability measure on the Hypercube with given moments
Let $H = [-1, 1]^d$ be the $d$-dimensional hypercube, and let $\mu \in \text{int} H$.
Under these conditions, I can explicitly construct a tractable probability measure $P$, supported on on $H$, which has $\mu$ as its mean. For my purposes,…
πr8
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9
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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 $\Omega$ is finite, things make sense: we might say nature…
zenna
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8
votes
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A procedure for sampling paths in a directed acyclic graph
Consider a directed acyclic graph $\mathcal{G} = (\mathcal{N},\mathcal{E})$. Assume that the graph is very large (on the order of 10000 nodes and edges).
Let there be a set of nodes termed starting nodes denoted by…
jonem
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7
votes
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Notation for sampling random variate
Is there standard notation for sampling a value from a probability distribution? Like, if I had a random variable $X$, setting $x$ to whatever value I happened to sample from $X$ on this occasion? I was thinking just $x \gets X$, but that seems…
Sneftel
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7
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Randomly generate a sorted set with uniform distribution
I have an ordered set $S = \langle S_1, S_2, .., S_M \rangle$ from which I want to draw a sample of $N$ elements in such a way that the sample is non-strictly totally ordered (as with $\leq$ and the integers), and all the possible occur with equal…
Setzer22
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7
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How is a Halton sequence related to a Latin hypercube?
I currently use a Halton sequence to choose parameter sets for a prognostic model (e.g. using metabolic rate and protein content parameters to predict growth rate).
From my understanding, both a Halton sequence and a Latin Hypercube can be used to…
Abe
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