# Questions tagged [sampling]

The tag has no usage guidance.

78 questions
Filter by
Sorted by
Tagged with
40 views

205 views

### Is there something like a "self-avoiding Markov chain" on a continuous space?

If stumbled accross self-avoiding walks. They seem to be deterministically generated, but from a quick google search term seem to be randomly generated variants. However, as far as I can see they are ...
1 vote
34 views

250 views

133 views

### Fast sampling of matroids

In his classic paper, Donald E. Knuth described how random matroids of fixed rank can be generated. What is the currently the fastest (in terms of mixing behaviour) known way to sample matroids of ...
65 views

### Are two degree sequences compatible, for random simple graph generation?

Consider a set $V$ of $n$ vertices, and three degree sequences $a_i$, $b_i$ and $c_i$ such that $c_i = a_i+b_i$, $i=1..n$. Assume these degree sequences are graphical: there exist simple graphs (no ...
546 views

### Relation between signal derivative and frequency spectrum

I want to sample a signal whose derivative I know to be bounded by physical constraints. The sampling is disturbed by gaussian noise, hence I need to filter the sample with a lowpass filter. Since I ...
1 vote
133 views

### Sampling i.i.d. variables with restrictions

General Problem: Suppose $X_1,\ldots,X_n \sim \mathbb{P}_X^{\otimes n}$ is a finite sequence of i.i.d. (real- or integer-valued) random variables. Suppose $A\subseteq \mathbb{R}^n$ is a set of "...
257 views

### Probability that a random multigraph is simple

Question. Consider a given sequence of $n$ integers $d_1$, $d_2$, $\cdots$, $d_n$ with $\sum_i d_i$ even and $d_i\le n$ for all $i$. One may sample a random multi-graph having this degree sequence ...
616 views

### Interior point of a convex polytope

Suppose the convex polytope is the set of feasible solutions $\mathbf{x}\in\mathbb{R}^n$ for the linear system $\mathbf{A}\mathbf{x}=\mathbf{b}\,,\; \mathbf{A}\in\mathbb{R}^{m\times n}$ subject to ...
32 views

### Condition on the point cloud matrix making the points "generic" in the uniform sense

For a matrix $X\in\mathbb{R}^{d\times n}$, what condition can I impose on $X$ to make the collection of its columns generic in the sense that they look like the result of uniformly sampling a convex ...
47 views

### Yates-Grundy draw-by-draw sampling inclusion probabilities

Is there an efficient algorithm to calculate the inclusion probabilities (the probability that an item will be included in a sample) in the Yates-Grundy draw-by-draw sampling? Sampling description: ...
682 views

### Invariant measure vs Riemannian measure on Stiefel manifold

I'm interested in sampling uniformly from the Stiefel manifold $V(k, n)$, but while researching how to do this I came to wonder the following. In Edelman et al.  there are presented two ...
1 vote
125 views

### Random optimization problem

Let $V$ be a set of $n$-dimensional vectors such that, for each ${\bf v}\in V$ and for each index $i\in [n-1]$, we have $0\le v_{i+1}\le v_i$. Let $P(\cdot)$ be a discrete probability distribution ...
213 views

### What is the pdf of Laplace distribution conditioned on a plane? How can I sample from it?

Our goal is to sample from the Laplace distribution conditioned on a linear subspace. Here are the details of this problem. Let $$p(x) \propto \exp(-\|x\|_1/\sigma)$$ be the pdf of the Laplace ...
45 views

### Using common samples to numerically estimate pairwise equality of three random variables

Let $X,Y,Z$ be three discrete random variables which I can numerically sample. I need to numerically estimate the probability that $X=Y$ and the probability that $X=Z$. I would like to know whether ...
107 views

### Can computers take uniform samples from a polytope?

For each $r \in \mathbb N$ write $\mathbb Z/ 10^r = \{a/10^r: a \in \mathbb Z\}$ and $P(r)$ for the lattice $(\mathbb Z/10^r)^N \subset \mathbb R^N$. Suppose the plane $P \subset \mathbb R^N$ is ...
1 vote
297 views

375 views

### Expectation inequality for sampling without replacement

Is the following proposition correct? $X_1, X_2, X_3$ are uniformly at random sampled from a finite set $\mathcal X$ without replacement. $f : \mathcal X^2 \rightarrow \mathbb R_{\ge0}$ is symmetric:...
366 views

### Minimize the variance of a Boltzmann distribution

N.B.: Sorry for cross-posting from https://stats.stackexchange.com/posts/347804/edit (I realized it was the wrong venue for the question, but couldn't find an easy way to transfer the question here). ...
1 vote
643 views

### Uniform sampling of random connected graph with given number of vertices/edges

I am looking for algorithms for the exact uniform sampling of connected labelled graphs with $n$ vertices and $m$ edges. By "exact" I mean that every such graph should be generated with precisely (not ...
68 views

### Sampling with non-uniform probabilities

Let $p_1,p_2,...,p_n$ are given probabilities. ($\sum_{i=1}^n p_i =1, p_i \geq 0$). Is there any distribution, which picks $k\leq n$ distinct elements from $1,2,...,n$ such that $P(i \in S) = k p_i$ ...
1 vote