# Questions tagged [sampling]

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### Distribution of a two-part sampling process

I have a known distribution $f(x)$ (in fact, I can safely assume that $f(x)$ is the Maxwell-Boltzmann distribution, i.e. $f(x)\propto x^2 \exp(-x^2)$). I take $N$ samples from the distribution, but am ...
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I am tasked with randomly sampling from the following probability density function, which is a modified Erlang Function: $$f(k,q,\nu)=\frac{(k q)^{k-1}}{[(k-1) !]^{v}} \quad \text { with } \quad q \... • 111 2 votes 1 answer 77 views ### Column subset selection with least angle optimization Given a matrix A I need to select a "representative" subset of its columns so that the each non-selected column is as close as possible to a selected one. Formally: Given A \in \mathbb{R}... • 6,922 3 votes 1 answer 192 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 ... 2 votes 0 answers 69 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 ... • 1,434 3 votes 1 answer 826 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 1 answer 152 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 "... 6 votes 0 answers 293 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 ... • 1,434 2 votes 1 answer 824 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 ... 0 votes 0 answers 33 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 ... • 461 0 votes 1 answer 103 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: ... 5 votes 2 answers 934 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. [1] there are presented two ... • 271 1 vote 1 answer 132 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 ... • 1,667 5 votes 1 answer 242 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 ... • 53 -2 votes 1 answer 47 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 ... 2 votes 0 answers 111 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 ... • 1,915 1 vote 2 answers 346 views ### Use Importance sampling for multimodal and multivariate distribution draws, how to choose proposal distribution? I'm in trouble trying to generate samples following a particular distribution which is not numerically known perfectly. Let us consider a R^n space provided with an orthonormal base ( e_{1},...,e_{... • 11 2 votes 2 answers 100 views ### Draw samples from distribitions in the neighborhood of a fixed distribution Disclaimer Sorry in advance for vagueness. I'm still trying to get my ideas right on this one. Setup So, let P be a distribution on a Euclidean space X with an \ell_p metric, and let P_\... • 6,824 8 votes 1 answer 401 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:... 4 votes 1 answer 387 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). ... • 6,824 2 votes 1 answer 797 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 ... 2 votes 1 answer 72 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 ... • 145 1 vote 1 answer 127 views ### Plancharel-Pólya inequality for functions of exponential type If f(z) is an entire function of exponential type \tau and p a positive number such that that$$\int_{-\infty}^{+\infty}|f(x)|^pdx<\infty$$then it can be proven that$$\int_{-\infty}^{+\...
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Let $M \in \{0,1\}^{m\times n}$, where $n\gg 1$ and $m\le n$. A procedure consisting of the following three steps is repeated $t\gg 1$ times: A row $\require{amsmath} \boldsymbol{r}$ of $M$ picked in ...