# Questions tagged [sampling]

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### Alternative to the Sampling Theorem / Invertible transform with sampling criteria

I seek a transform $T$ that operates on real-valued $x(t)$, that Is perfectly invertible Has discrete counterpart with continuous reconstructor Provides conditional reconstruction guarantees ...
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### Invertibility of the sampling matrix

Given a function $f: \mathbb{R}^2\rightarrow\mathbb{C}$ sampled as a matrix $F_{ij}$ on some ractangle $[a,b]\times[c,d]\subset\mathbb{R}^2$ with steps $\Delta x$ and $\Delta y$ as the stepsizes so ...
1 vote
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### Given iid samples from the joint distribution $P$ of pair of r.v.'s $(X,Y)$, how to get iid samples from independence coupling $P_X \otimes P_Y$?

Let $(X,Y)$ be a pair of random variables on a measure space $\mathcal T \subseteq \text{"subsets of }\mathbb R^2\text{"}$, with joint probability distribution $P$. We don't assume $X$ and $Y$ are ...
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### Probability of an edge in a random graph

Consider a vertex set $V$ and a degree sequence $(d_v)_{v\in V}$. I want to know the probability that an edge exists between two given vertices $u$ and $v$ in a random graph with this degree sequence. ...
1 vote
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### Correlating two matrices $A,B$ with stochastic dependency structure imposed by cross-validation

Consider a labelled data set $$D = \{(x_1, y_1),...,(x_n, y_n)\}$$ on which we want to evaluate a machine learning algorithm using $k$-fold cross validation with $m$ different random seeds. This ...
1 vote
118 views

### Intuition of the "work" done by random variables in Monte Carlo methods (incl. MCL)

(I've tried Math SE, but have so far come up empty handed, so I'm trying my luck here.) I would like to get a better intuitive understanding of why Monte Carlo works so well in approximating a ...
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1 vote
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### Sampling from a particular multivariate probability distribution

Given $3$ real variables $x_1, x_2, x_3 \equiv \bf{x}$, consider their probability density function (PDF) \begin{equation} P({\bf x}) = C \, p(x_1) \cdots p(x_3) \exp[f({\bf x})], \end{equation} where ...
1 vote
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1 vote
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### Simulate a graph from a certain distribution

I am wondering if anyone can indicate whether the following is a solved problem. I don't care about time of the algorithm currently. Consider a general probability distribution F on simple graphs ...
For $r,d\in\mathbb{N}$, let $$C_{r,d}=\{x\in\mathbb{Z}^d: \|x\|_1\le r\}\subset\mathbb{Z}^d$$ be the set of integer points of the $d$-dimensional cross-polytope with radius $r$. What is (...