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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Imputing values in new samples

For the dataset, I know that: for missing values in training dataset (and therefore for validation datasets for CV) we impute values using training samples for missing values in test dataset we ...
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How do I calculate the survey sample size using stratified sampling?

Lets say I plan to do a survey of individuals aged 40-69 years old in 5 residential complexes. It is a general social survey, and is intended to survey attitudes towards a new cultural centre that ...
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Number of dimensions practically possible when using copulas for multivariate probability distribution sampling

I have a high dimensional data set (depending on how I try to estimate it, anywhere between 6 - 100 variables) and I'm trying to sample from the underlying multivariate probability density. I can ...
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Modelling uncertainty at both the individual and population level with beta-distributions

I want to measure the distribution of a population's performance on a test. Each person takes a version of the test with a random selection of N questions from a large pool of possible questions. ...
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Adaptive Sampling techniques for SVM?

I am an Engineer interested in creating a surrogate model of a certain phenomenon in the context of reliability engineering. Essentially my quantity of interest is the Limit state function/stability ...
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Metropolis -> Metropolis-Hastings for asymmetric proposal distributions?

The below python code implements the Metropolis algorithm and samples from a single variable gaussian distribution. The initial value is sampled uniformly within 5 standard deviations of the mean. ...
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A tail bound for an unknown distribution via sampling

I know that many results exist for making an argument about the tail of a distribution, i.e., for a random variable $X$, one can find a bound $\epsilon$ such that $\Pr[X \geq a]<\epsilon$. Some ...
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What would be the probability distribution to simulate K events randomly assigned to N individuals?

I am trying to randomly simulate a population of $N$ individuals among which a predefined number $K$ of them have an outcome. The trick is that I want to assign different probabilities to the ...
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Assumptions of Randomness in Formulas for Sample Mean, Error

I am reading J. Mandel's book on Analysis of Experimental Data. He states at one point that if a sample is not random ( i.e.,$X_1, X_2,..., X_n$ are not an independent, i.d. set) then the formulas for ...
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How do you determine the time needed for a sample to get an approximate of the population mean

I am doing several tests. Each test is made under different conditions and I want to know how the different conditions affect the results. The test samples are liquids. I am doing only one test under ...
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Why “sorting” is needed for simple random sampling [closed]

Tutorials demonstrating simple random sampling, first list the full number of population members (i.e., sampling frame) in a column and then assign a random number from $0$ to $1$ from a uniform ...
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Get timing statistics from time sampled data

I have measurement data from a device that is sampled every 5 minutes. It's power level data, and I'm looking to get some statistics on it, specifically time to charge/discharge. To complicate things, ...
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Case control sampling strategy for longitudinal analysis

Does it sound plausible to use a case-control sampling strategy to then address a longitudinal question? For example, let's say I have a population of diabetics (N=100) and non-diabetics (N=9999). I ...
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estimation of KL-divergence of continuous distributions

Assume we have two independently sampled datasets, $X = \{x_{1}, \dots, x_{n}\}$ and $Y = \{y_{1}, \dots, y_{m}\}$ from continuous distributions $f$ and $g$. I aim to estimate the KL-divergence ...
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Is there a formula for the expectation and variance of a ratio of sampling variances?

I know the formulas for the expectation and variance of the sample variance, difference between two sample means and proportions. Sample Variance $E(S^2) = σ^2$ $V(S^2) = 2\sigma^4/(n-1)$ Difference ...
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Is there a detailed explanation on why multiple population sampling distributions use difference for mean and proportion, while ratio for variances?

I think that it does make conceptual sense. For means and proportions, we want to compare the amount at which their values are apart. Which is why difference is used. For variances, the factor at ...
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sampling from $\frac{1}{1+x}$ times Gamma distribution density

I am simulating a process by drawing many random variates $X$ from a Gamma distribution with parameters $\alpha$, $\beta$, $$f_X(x) = \frac{\beta^\alpha \, x^{\alpha-1} \, e^{-\beta x}}{\Gamma(\alpha)}...
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Can someone explain to me the sampling distribution of sample variance in comparison to that of the sample mean?

I have read tons of things already about the sampling distribution of the sample variance but I can't get quite a good grasp of exactly what it is like in terms of the formulas of the measurements. ...
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What is the meaning of Marginal Density of Beta_binomial Distribution

Given an Experiment with a fair coins and 20 trials prior distribution defined as Beta(5,5) likelihood defined as Binomial(20,p) as a result it give a Beta Binomial distribution The Question is if I ...
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How to generate two correlated random samples, one follows geometric Brownian motion, the other follows a beta distribution? [closed]

I'd like to conduct a Monte Carlo simulation with two random variables. One random variable is generated by geometric Brownian motion, the other random variable is sampled by drawing random values ...
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Variance and covariance of a measurement given a benchmark measurement

I have a set of 20 measurements $$(x_1, x_2, ..., x_{19}, x_{20}) $$ in which 18 of the measurements are a sort of benchmark, and two measurements are special, although obeying the same sources of ...
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Does every statistic have a sampling distribution, not just the sample mean?

I am curious because most basic undergraduate statistics reference just start out Inferential Statistics by mentioning sampling distributions and the sampling distribution of the mean. My question is ...
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Is The Jacobian Needed to Find CDF for R in Polar Coordinates?

I'm attempting to use inversion sampling to generate points on a disk according to the following PDF: $$ f(r) = \dfrac{2}{\pi(1+r^2)} $$ Here, the polar angle would just be a uniform random variable ...
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Does a sampling distribution assume iid sampling of the underlying random variables forming the statistic?

Does the definition of a sampling distribution always assume our (theoretical) ability to generate i.i.d samples of the underlying RVs (together, as a collection of RVs) forming the statistic? From ...
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Problems with central limit theorem and bigger SE with bigger samples [duplicate]

It is said that “the finite population correction factor is used when you sample without replacement from more than 5% of a finite population. It’s needed because under these circumstances, the ...
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Extremely basic question: how are data assumed to be generated in machine learning?

Given a dataset $\mathcal{D} = \{x_i\}, i = 1, \ldots, N, x_i \in \mathbb{R}$ In machine learning, what assumption is made as to how data are generated? I've seen two basic ideas circulating around, ...
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When picking k from a population n, with replacement, how do I determine the optimal n where all of k will be unique?

Let say I pick k number of particles from a population n, with replacement, and the population n is derived from picking i number of particles from a pool of 1.0995116e+12 unique particles, with ...
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Binary Classification with almost no positives

I have a dataset with 121 features and 7176 data points. Only 11 of these are positive, the rest is negative. If I want to train a SVM on this data set, what would be the best strategy to do this? ...
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Statistical Analysis over different samples - Prediction for the number of objects

This may be a really simple question but here's my problem: I have different boxes with soil (wet sandy kind) and big stones in it. Each box is around 10kg and I want to estimate the number of big ...
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Select a sample size form the infinite population

I have a list of every store chain in the US with at least 100 locations in the US. a) What number of those do I have to pick in order to have a representative sample of the number of locations across ...
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Unbiased estimatior for $\bar{x} $ from a Random Sample with unequal selection probability

I have the following population: Where the left column is the age of our individuals and the right column is their weight (in kg). The exercise tells us that we use Random Sampling with no ...
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Covariance between sample mean of two simple random samples

Suppose that we have two simple random samples without replacement $A$ and $B$ from a population $P$ of size $N$ such that $B = P-A$ where $n$ is the size of $A$ and $m$ is the size of $B$. I want to ...
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What is the difference between “greedy selection” and “sampling according to a distribution?”

I'm currently studying language generation and had a question regarding some concepts. The paper I'm reading states that they formulate the task of next-token generation as conditionally generating ...
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Mini-Batch Gradient Descent - Why does sampling with replacement work?

When sampling the data, either one at a time (as in online learning), or in mini-batches, there exist gradient descent methods which sample with replacement and without replacement. For Mini-Batch ...
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Limits of oversampling

I have a dataset with an event rate of less than 0.3 percent. To improve the modeling results, I did some oversampling using SMOTE. I initially oversampled so that the event rate increases 10 times to ...
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1answer
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Is there a central limit theorem for random variables with a bounded interval? [duplicate]

Is there any theorem which states the asymptotic distribution for the sample mean when the samples are drawn from a random variable which has a bounded interval?
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Finding the covariance of two random sums

I am trying to derive the covariance of two sample sums. Some notation and details: $x_i$ and $y_i$ are numeric values of two characteristics corresponding to member i of a finite population of N ...
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1answer
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Easy vs difficult distributions for sampling

Many sampling methods (e.g. rejection sampling) approach the sampling of a distribution $p$ as a problem of sampling from a different and somehow easier distribution $q$ and then correcting or ...
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Empirical Bootstrap, Quantile Vs. Sd

I am trying to understand the different approaches to calculate the empirical bootstrap for a test statistic. During my research I came across two different approaches to calculate the empirical ...
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Stratified Sampling Total Statum

I wish to find the number of total population by each specification. I have the following results: \begin{array}{|c|c|} class & n_h \\\hline Positive & 5872 \\\hline Neutral & 6771 \\\...
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How many repetitions to establish difference

(Real-world Context: I often make changes to code, which I suspect will have small impacts on the performance. i.e. improvements that lie within the natural variation of the code's runtime. How many ...
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Sampling Technique: Categorical Data, Many Levels

I have a data set that has a categorical variable with almost half the number of observations as categories. Certain categories have only one observation. A minimal reproducable example in R would ...
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What is the name for this type of sensitivity measure in regression analysis?

I have a way of calculating sensitivity of a regression that is very useful for my particular domain, but I don't know what it is called. I would like a name for it so I can look up additional ...
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How to interpret multiple calls of rnorm() function in R?

I'm using rnorm() to generate data for a trainng set. The target is to generate a matrix X with n rows and p columns to represent n sets of p features, and I did so ...
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Running several MCMC chains after convergence?

I am running a MCMC Gibbs sampler for a computationally expensive model. It takes ~12 hours to obtain 1000 iterations of this MCMC sampler. I have tested the sampler, and I found that the chain seems ...
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How to get matched pairs from CEM

I am using Coursened Exact Matching to improve balance in my sample. The summary matching results after applying CEM are that 11,128 pixels have been matched: ...
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How do I generate a confidence region for a set of sample from a bivariate posterior?

I have a set of samples generated from a posterior function as shown below: I want to generate a bivariate High Posterior Density (HPD) credible region for the samples as in the below example ($\...
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How can I sample from a copula with a given correlation in python?

How can I sample from a normal copula with a given correlation in python? I know how to sample from a multivariate normal distribution with a given covariance matrix using numpy and scipy, but I don't ...
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Sample size cutoff for agreement coefficients

New poster here. Would love some help thinking through this. Suppose I am observing individuals in public space, and I am recording the number of occurrences of a target behavior (e.g., looking at a ...
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Sample from a distribution and plot in python

I am trying to understand Particle Filter and Importance Sampling Principle from a UniFreiburg Course and this USNA document on particle filters. Simultaneously, I am also trying to write a document ...

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