# Questions tagged [sampling]

Creating samples from a well-specified population using a probabilistic method and/or producing random numbers from a specified distribution. As this tag is ambiguous, please consider [survey-sampling] for the former and [monte-carlo] or [simulation] for the latter. For questions regarding creating random samples from known distributions, please consider using the [random-generation] tag.

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### How to generate 2 correlated Beta random variables

I was wondering if it might be possible to generate 2 correlated $Beta$ random variables? In other words, I want to generate two Beta random variables which can be said to have come from two Beta ...
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### Tuning MALA (Metropolis-adjusted Langevin) proposal

I'd like to implement a version of Metropolis-adjusted Langevin sampling, but I'm unsure how to go about tuning the parameters of the proposal density. My understanding is that in MALA, a proposal ...
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### Assessing the representativeness of population sampling

I am looking for some suggestions about assessing the representativeness of a particular dataset I am analyzing. In this dataset I am looking at the relationship between two variables (e.g., X and Y)...
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### Probabilities arising from permutations

Certain interesting probability functions can arise from permutations. For example, permutations that are sorted or permutations that form a cycle. Inspired by the so-called von Neumann schema given ...
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### Expected value of a "logistic uniform" multivariate

Let $\mathbf{a}_1,\ldots,\mathbf{a}_n \in \mathbb R^d$ and $b_1,\ldots,b_n \in \mathbb R$ be fixed. For $\mathbf{x} \sim \mathcal U([0,1]^d)$ and $j \in \{1,\ldots,n\}$, consider the real variable ...
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### Weighing toilet paper with an imprecise scale

A practical, topical problem: Consider a typical roll of toilet paper (TP) with perforated sheets of fairly uniform size, and suppose we're interested in the distribution of a sheet's weight $W$ but ...
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### Detailed Balance for Hamiltonian Monte Carlo

I am trying to understand the detailed balance proof present in this paper: https://arxiv.org/abs/hep-lat/9208011v2 (page 4). My question: Why do we consider the volume of a neighborhood of points ...
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### How Does Variance Propagate From Likelihood Function To MCMC Posterior?

Suppose we are trying to obtain the posterior distribution of three parameters that influence a discretely observed population. The likelihood function is unfortunately intractable, as it is a mix of ...
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### Estimate number of duplicate items in a population by sampling

I have a data source that allows me to pull big sets of numbers (~1e12) with unknown distribution. let's define Mostly distinct as more than MD percent of the population is distinct numbers. For each ...
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### When will bootstrapping struggle to provide an accurate distribution?

Can someone give an example of a statistic for which bootstrapping might struggle to provide an accurate sampling distribution?
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### Does this sampling without replacement have a name?

There can be many ways and ad hoc variants to perform sampling without replacement from a limited population. Consider we have $k$ categories (types of objects) and the k-length vector of their ...
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### Expectation and variance of sample mean with random sample size

I have a question regarding sampling where the sample size itself is a random variable. Say I have two sub-populations $A$ and $B$ from which I can sample a real valued random variable with ...
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### Calculating the standard deviation of the mean of average rates of speed

Is it possible to determine the mean value of a point by averaging the average rate of ranges that contain that point, and if so, how can the uncertainty of that value be accurately determined? I ...
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### Sampling vector so they will have a given euclidean distances matrix

Given a matrix $M\in\mathbb{R}^{P\times P}$ , is it possible to sample $P$ vectors $u_i\in\mathbb{R}^N$, $i=1..P$ so that $\|u_i-u_j\|=M_{ij}$. Obviously for not any $M$ this is possible, i.e. it has ...
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### Bayesian inference with unequal sampling

I have a "two-column" data set, with a multi-class categorical variable A, and two-class variable B. It is assumed that each observation is independent. For each category of variable $A$, I want to ...
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### rejection sampling in high dimensions

I read that rejection sampling might fail in high dimensional settings, as the rejection rate becomes too low. Intuitively - i can understand this - but i would like to understand the formal proof as ...
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### Bayesian inference with sampling and mixture models

I'm having some trouble doing Bayesian inference on an experience I have in hands. I apologize in advance if it is too complex, but I couldn't find a trivial way to split it in several parts. Let ...
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### How to validate a random sample

I have been given two sets of data, one with 10,000 observations which is a subset of the other with 100,000 observations. It is claimed that the small dataset is a random sample of the large dataset. ...
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### Should the mean of the bootstrapped distribution always be asymptotically equal to the sample estimate?

Suppose I bootstrap the distribution of the sample mean. Normally, one would use the mean of the bootstrapped distribution as point estimate of the parameter and the s.d. as its standard error. The ...
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### Generating samples from Copula in R

Suppose I want to model dependence between $d$ r.v.´s $Y_1,...,Y_d$ with the copula $C_\theta$, where $\theta$ are the corresponding parameters of that copula. I've also determined the correlation ...
The convergence theorem for Gibbs sampling states: Given a random vector $X$ with components $X_1,X_2,...X_K$ and the knowledge about the conditional distribution of $X_k$ we can find the actual ...