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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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Are random variables sampled upon stopping rules exchangeable?

In this article from D. Berry https://www.jstor.org/stable/2684222?seq=1#page_scan_tab_contents the author uses an example to introduce some limits of p-values in frequentists analyses. He takes an ...
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Distance between points in a sample follow normal distribution

I am wondering if it is possible to create a data set of say p variables with m rows (mxp matrix) where the distance between any chosen point x (from the data set) to all other points in this data set ...
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Compare means between samples, while controlling for sampling differences - valid to use regression this way?

There are two independent samples of people, drawn from a population of a city at times $t_1$ and $t_2$, a decade apart*. The people were asked rate their preference regarding some question $Q$ on a ...
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What is the probability that two samples from a source have no overlap?

I picked 29 results from a list of 429 results. I then picked a second group of 27 (with replacement) results from the same list of 429. There was no overlap between the two samples. What is the ...
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Distribution of Maximum Likelihood Estimator

Why is the Maximum Likelihood Estimator Normally distributed? I can't figure out why it is true for large n in general. My attempt (for single parameter) Let $L(\theta)$ be the maximum likelihood ...
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Intuition about a coupon problem were we ask for the distribution of the unique coupons when the number of draws is fixed

Alternative viewpoint of the coupon collectors problem In the coupon collectors problem we draw from a collection of $n$ coupons, with replacement and ask the question how many draws $K$ it takes to ...
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Why can two subgroups from one sample be treated like two independent samples?

Assume we want to compare two subgroups of a population, say men and women, on a certain trait. We could draw two independent samples of the two subpopulations, e.g. a random sample of all men, and ...
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Determining sample size of a Gaussian subset with new std

I have N1 samples that is distributed close enough to Gaussian with 0 mean and std1. For simplicity, we can assume N1=1000 and std1 = 7. Now I want to choose a subset of those samples that is ...
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Definition of Statistic

I keep seeing conflicting definitions of a statistic. Is a statistic a random variable such that it is a function of the random variables of a random sample? Or is it the value of the function of the ...
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using attribute outcomes to define variable limits

I am working on developing a specification for peel strength of a package (looking for a minimum value, higher is better). The limit of where it is considered "good" is determined by a leak test (pass/...
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What process could lead to a sampling distribution of the mean that is approximately skew normal

I have a data set representing guest ratings of various hotels. Unfortunately, I don't have access to the ratings given by individual guests, only to the mean guest rating for each particular hotel. ...
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Central limit theorem and statistical uncertainities

I am unable to understand the statement that the statistical uncertainties associated with measured data are have to be gaussian distributed because of the CLT theorem. What I know about CLT is that ...
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Prove property of a confidence interval

How does one go about proving the characteristic of a confidence interval that: A 95% confidence interval means if you were to randomly sample the same way 1000 times and create 1000 confidence ...
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Interpreting the margin of error when it is larger than the sampled proportion

Say that I have a population of $N=500$ individuals, and I'm sampling $n=60$ of them for a certain characteristic which is expected to be quite rare (say green eyes). In my sample I find out there are ...
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How to approximately sample an unknown non-parametric joint distribution given a complete set of partial conditional distributions?

This question is related somewhat to Bayesian networks. In a BN, you have a DAG (directed acyclic graph). By supplying the root nodes with a sample, you can then follow the directed arcs to sample ...
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Stratified Sampling: Given required bound, calculated $n_h$ is bigger than $N_h$?

I'm dealing with a question that has given me a peculiar result and I would like someone's opinion on how to deal this: Say you have a population of $N=550$ objects: $N_1=75$ red and $N_2=475$ blue. ...
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Probability Two Independent Samples of Different Size Have Some Intersection

I've been working on generating a probability rule for taking two random samples without replacement and finding a given amount of overlap between the two. So far I've worked through simple cases ...
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Significance Test with dichotomous variable

I have a set of data. The data contains 30.000 observations of a set of several variables. One of those variables indicates a nominal segment classification. In total there are six different segments. ...
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Generate random sample of X1 and X2

If X2 is dependent on X1, how to generate the random sample of (X1,X2)? One scenario is that we know the prior distribution of X1 and functional relationship between X1 and X2, how to generate the ...
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Web Based Survey Sampling method

I am doing a web based research with target audience as general public. I am a student and so due to limited resource, i basically did snowball sampling. I approached all those whom i knew, some ...
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Theoretically is it better to sample with or without replacement to approximate a rank test?

Let's say we want to do a rank test since we do not know the exact distribution. Say we have 3 different sample sizes. Which of the following tests (exact permutation, sample with replacement, sample ...
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Permutation of datasets to check accuracy of class labels

Currently I am using a proteomics dataset to compare 4 different disorders to healthy controls. Ultimately, I want to find unique and overlapping factors (that are deviant from healthy controls) in ...
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Symmetry group in posterior distribution/inference

Here's a scenario: Suppose I collect a dataset $\{x_i\}_{i=1}^k\subseteq\mathbb R$ of data points $x_i$, and I wish to explain it using a mixture of two Gaussians; assume the unknown parameters are ...
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Show that $\underset{1\leq i \leq n }{\max}|X_i-\overline X|<\frac{(n-1)S}{\sqrt n}$ [duplicate]

Let $X_1, X_2, \ldots , X_n$ be a sample from some population. Show that $$\underset{1\leq i \leq n }{\max}|X_i-\overline X|<\frac{(n-1)S}{\sqrt n}$$ unless either all the $n$ observations ...
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Longitudinal Data with Equal Outcomes Within Individual Samples

I need to prepare some data for plugging into a predictive model. The data is in tidy format, but it comes from an audit table, i.e. every change made to a record is recorded and stored as a separate ...
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how least square estimation can be done for a distribution

As i have estimated parameters of geometric distribution by using MLE (maximum likelihood estimation) and MOM( Method of moment) but i have problem in estimating parameter of Geometric distribution ...
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Splitting into train and test sets keeping class proportions

I have a dataset for a binary classification task which has 90 percent 'yes' and 10 percent 'no'. Let's say I want to take 25 percent of the data as the test set (which the model will not see). How ...
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what does that mean by saying “a sample having 2 (or more) observations”? does the observation mean possible outcome from an experiment?

Say, I am drawing balls. "drawing 2 balls from 3(labeled numbers from 1 to 3) with replacement" is an experiment. perform this experiment could result 9 possible outcomes. here is the list ...
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Location level a/b testing sample size

We are setting up experiments to measure impact on the city level. Customer in certain cities are treated and we have list of holdout cities with similar behavior. Measurement of lift of the ...
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30 views

Estimating probabilities from truncated set of counts?

If I have a truncated histogram like this, where the ordinate is the number of occurrences $N_X$ of each value of $X$, and the abscissa is the value of $X$, is there a way to estimate the probability $...
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Acceptance-Rejection using Functional

Setup Let $X\in L^1(\Omega,\mathcal{F},\mathbb{P})$. As far as I've seen, Monte-Carlo methods generate $x_1,\dots,x_n$ from the distribution of $X$ and uses the Glivenko-Cantelli theorem to conclude ...
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Downsample a stochastic process without losing correlation statistics?

I have a stochastic variable $X(t)$ which changes at a discrete set of random times $t_1, t_2, \dots$. I can simulate this stochastic process to obtain a series $X(t_1), X(t_2),\dots$ However, the ...
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What is expected times of sampling that a full population is covered?

There is a population with N instances. A sampling means we draw randomly M instances from the population without replacement. ...
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Win probability of a game character vs. two other characters

Clarification about original problem: Dota 2 is played in matches between two teams of five players—known as the Radiant and Dire—, with each team occupying and defending their own separate base ...
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Calculating error/confidence interval on points of a distribution

This is a beginners question, coming from an absolute beginner in statistics, but I haven't been able to find anything about this online, probably because I don't even know where to start looking. My ...
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when and where need deep stratification?

as working in sampling i understood some methods like, stratification and post stratification, as post stratification is good when simple random sampling provides underestimate results then we adjust ...
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consistency of an estimator in real data

as we know in statistics we are interested in the properties of an estimator , as my estimator is consistent , in probability sense it can be shown as $P(|estimator - true| <- positive) = 1$ as ...
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How to prove High Sampling Variance in over-fitted functions

I've been reading recently about over-fitting and it is frequently related to High Sampling Variance and Low Bias characteristics. However, what is the metric used to state the High Sampling ...
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Likelihood modification in Metropolis Hastings ratio for transformed parameter

I want to use MH to get samples from $p(\theta \mid y) \approx p(y \mid \theta) p(\theta)$. Let's assume $\theta$ is heavily constrained and I transform $\theta$ to $f(\theta)$ so I can sample from ...
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Interpretation of intercept only random effects models

I am estimating the global risk of infection risk in a population of patients, but these patients are clustered in hospitals and wards/departments. If I just take the crude prevalence (infected ...
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Attribute Sampling Math question for inventories

I hope this is the right forum for this, but I'm terrible at stats and got tasked to help a QA team do some math. I'm trying to figure out how to do the calculations to be able to say something to the ...
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Adding Bad Events from the past to the risk default model to avoid Down/Up sampling techniques

We have been trying to build a classification model for credit default prediction using two different models one being Random forest and another being the Logistic regression based scorecard model. ...
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A\B Testing with Sorting

In my company while splitting site users for AB test we do the following: we choose parameters that seem the most important for us (for example: gender, life time value, average check, etc), if they ...
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Determine frequent states

I have a distribution from which I can sample (namely, a Boltzmann Machine). Which methods exists to determine frequent states (states with high probability) / the most frequent state (state with the ...
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ML Sampling question - Can I increase sample size of current dataset with older copies that have changed over time [closed]

I am working on a multinomial machine learning algorithm that labels stocks with buy/sell signals. My code updates with the most recent quantitative data about the stocks daily, so obviously the data ...
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Effects of class imbalance on nn batch training

Say I have a binary classification task, where the positive class (1) is only 1% of the whole data set. Intuitively I can understand why this could be bad for the classifier as the model may learn ...
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Suggested noninformative hyperprior distributions?

I have a hierarchical model that includes a normal distribution and a beta distribution. For the normal distribution, it has two parameters: $\mu$ and $\tau^2$. However, I want to implement ...
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Gibbs sampler for ARIMA AR(1) parameters: division by zero

Suppose the following AR(1) model: $$ y_t = \mu + \phi (y_{t-1} - \mu) + \epsilon_t $$ with $\epsilon_t \sim \mathcal{N}(0,\sigma^2)$. Following issue arises when sampling from $P(\mu_i \;|\; \phi_{...
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Checking for group differences after randomly assigning subjects to one group or another?

If an experimenter assigns subjects to an experimental vs a control group truly randomly, is there still any point to performing baseline comparisons between the groups, after they've been so defined? ...
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Sampling from the surface of a sphere in n dimensions with specific centre

I have a point $p$ on the surface of a unit sphere. I want to sample points from the surface of the sphere, such that the probability density of a point $q$ on the surface is given by \begin{equation} ...