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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8 views

Repeatedly sampling with replacement between samples - producing the right distribution for monte-carlos

I have two groups; group A, and group B. Each member of group A is associated with a varying number of members from group B; i.e. each member of group A is essentially a sample from group B without ...
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Central limit theorem and normal distribution confusion

So I'm trying to study for a test and I'm stuck on two textbook questions. I'm having trouble grasping the concept of sampling distributions and when to apply certain rules/when to categorize a ...
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What is the name of this simple discrete sampling algorithm?

I have a vector of probabilities $p \in \mathbb{R}^n$ which I have never seen before. I would like a single sample from the indices $(1, 2, \ldots n)$ according to the distribution defined by $p$. ...
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Intuition for variance of mean sampling distribution

I'm having issues comprehending the reasoning behind the following formula: For a sampling distrubution $$\overline{X_1}, \overline{X_2},..., \overline{X_N},$$ The following is true $$ V(\overline{X})...
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KL divergence between two sampling?

I was wondering if it is possible to find the KL between two samplings? not probabilities. Each one sampled from a multivariate gaussian distribution.
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is this sampling from a simplex?

Simply, if I sample $n$ $X_i$s from an exponential distirbution; that is $$ X_i \sim exp(1) $$ Then prove that the vector $$ \left ( \frac{X_1}{\sum X_i}, \frac{X_2}{\sum X_i}, \cdots, \frac{X_n}{\...
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inferential approach for estimating error rate on classified population

I am looking mainly for ideas and approaches which I could not find by just Googling. I created a classification model to predict about 175 unique classes from text features. I trained the model on ...
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Is there a sampling plan for weight variation of semi-processed goods? [closed]

I only came across CODEX for prepackaged goods and was wondering if there is a similar document for partly-finished goods. Thank you!
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25 views

Distribution of inbag matrix when sampling with replacement

Say I take a random sample of size $M$ from a sample of size $N$, like, for example you'd do when bootstrapping in random forest. As you increase $M$, you're more likely to sample any particular ...
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What does this OpenStax textbook passage mean?

The following is an excerpt from OpenStax's Introductory Business Statistics text: True random sampling is done with replacement. That is, once a member is picked, that member goes back into the ...
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Metropolis-Hastings algorithm for a possibly negative probability distribution

Let $I$ be a finite nonempty set $\zeta$ denote the counting measure on $(I,2^I)$ $(E,\mathcal E,\lambda)$ be measure space $p_i:E\to[0,\infty)$ be $\mathcal E$-measurable with $$\int p_i\:{\rm d}\...
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Sampling highly imbalance multi-class response variable

I have a dataset (11000 x 117) with response variable having multiple classes. Here is a plot of class distribution: Some of the classes have only 1 sample in the entire dataset and some have 2, 3 ...
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Taking into account the variance of an estimated population size to construct confidence intervals for count statistics

I had originally posted this on the Math Stack Exchange website, but was justifiably recommended to explore this site instead. When given confidence intervals that are developed for proportions under ...
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Choosing data to compare collected data against

I currently have a sample of 30 data points of how long a specific process takes to complete when a particular issue occurs and am looking to compare these times to the times where it doesn't happen ...
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Variance analysis for state dependent mixture importance sampling estimators

Let $(E,\mathcal E,\lambda)$ be a measure space $k\in\mathbb N$ $q_i:E\to[0,\infty)$ be $\mathcal E$-measurable with $$\int q_i\:{\rm d}\lambda=1$$ and $\nu_i:=q_i\lambda$ for $i\in\{1,\ldots,k\}$ $...
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Simulations of sampling distribution of variance

I'm trying to estimate the sampling distribution of a variance from a single sample to do a certain statistical test. To test the proof of concept, I take a normal distribution $N(200,5)$ with mean ...
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51 views

Determine sample size using reversed goodness of fit

I am asked to work on a specific problem in which I have to calculate certain expenditures for an industry, consisting of a population of about 400 companies. Although I already suggested to conduct a ...
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What happens If the variables are highly correlated in multivariate sampling allocation problem

I am solving a multivariate sampling allocation problem where the variables of interests are highly correlated. Now If I take only one variable of interest and calculate the univariate sampling ...
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Sampling inclusion probability for multiple items

Suppose we sample (uniformly, with replacement) $t$ times a set of $N$ items. What is the probability $x$ that the sample contains $y$ different items? This is representative of a real-life scenario ...
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Expected Value of Naive Recommender System

Let $k, n \in \mathbb{N}$, with $k \leq n$. Let $a = (a_1, a_2, ..., a_n)$ be an unordered finite sequence of real numbers. Let $(B_1, B_2, ..., B_k)$ be an unordered sequence of random variables such ...
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Is there a reason why we should run the Metorpolis-Hastings algorithm with a target density approximating the density we're actually after?

Let $(E,\mathcal E,\lambda)$ be a measure space, $p:E\to[0,\infty)$ be $\mathcal E$-measurable with $$c:=\int p\:{\rm d}\lambda$$ and $$\mu:=\underbrace{\frac1cp}_{=:\:\tilde p}\lambda$$ denote the ...
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MC error propagation of multivariate function with variables with non-gaussian distribution

I'm trying to determine the error of $K_p$ in the following: $$K_p=\frac{a^3}{P^2}$$ $a$ derives from $a/R_s$, of which I had previously sampled the distribution using a MCMC sampler (the algorithm ...
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“Compressing” or downsampling a discrete probability distribution

I have a discrete probability distribution $P$ which I obtained by applying a softmax transformation, with an automatically-derived exponent $-\beta$, to a set of measurements (potentially large, in ...
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51 views

Machine Learning - How to Sample Test and Training Data for Rare Events

Suppose I have a data set with 1000 observations. I want to train and test a Classification Model to predict a target variable as true or false. However, in my observation set, true occurs only say 10%...
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confidence interval for population parameters

This is my second question based on the understanding from this suppose I want to estimate the mean height of all the students studying in 12th class in my state. I do not have access to the entire ...
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28 views

estimating population parameter mean and variance

I have a couple of questions, but I would go one at a time. So what exactly estimates the population parameter. I do not know the mean height and variance of my population, which is sufficiently ...
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OOB error prediction in RF if case weights are used

I have a dataset for which grossing-up factors are given. I am using these factors as case weights for a random forest (R package ranger). Until now I was using the OOB prediction error for tuning, ...
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Why do we need to sample from a maximum of 10% of the population for the CLT to hold? 10% seems like too much

One of the conditions for the CLT to hold is that your sample sizes cannot be >10% of the population. This means, if we sampled 10% of the population each time without replacement, we would have ...
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1answer
25 views

Expected value without complete sample space

The book way: Suppose, we have a bag with 8 balls numbered 1-8, we want to estimate the population parameter mean. we note down the entire sample space. (1,1)(1,2).. (8,8) calculate mean of each ...
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35 views

Estimating population mean $\mu$ based on a sampling distribution

I've learned that under certain codnitions I can assume the mean of the distribution of sample means to be approx. equal to the real mean of the underlying population. Additionaly, the standard ...
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What is best way to sample from words that is representative of original distribution of words

Suppose I have a large distribution of words with their absolute counts in documents. As an example just take five words 1. Facebook 1000 2. Google 2000 3. Twitter 300 4. Quora 40 5. Reditt 60 If I ...
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Sampling with fixed probability from two different distributions. How is the sample distributed?

Let $(\Omega,\mathcal A,\operatorname P)$ be a probability space $\mu$ be a probability measure on $(\mathbb R,\mathcal B(\mathbb R))$ $X$ be real-valued random variable on $(\Omega,\mathcal A,\...
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75 views

Sampling Correlated Binary Values

Say I have two variables X, Y. We progress through iterations 1 to i, and pull a binary TRUE/FALSE for each variable. Each variable has it's own probability of getting TRUE each period P(X) and P(Y) ...
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38 views

Sampling from multivariate normal and folding to draw correlated half-normal samples

I'm trying to draw samples from a bivariate half-normal distribution whose variances and covariances I want to specify. I tried using scipy.stats, but it only offers a univariate half-normal. My ...
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K-fold partitioning for dataset consisting of discrete, sampled sub-datasets

I can observe full system dynamics from some deterministic start to some deterministic end, in order to collect a sub-dataset $\boldsymbol{X}_i$ with $m$ examples, where the distribution of these $m$ ...
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Metropolis Sampling sample order

I am new to Metropolis sampling, here is a question that confuses me. Assume that there are two sets of variables $a$ and $b$ we want to sample. Let $X$ denote the observations and $p(X|a,b)$ denote ...
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Approximate a density function from sampled data

Let $(E,\mathcal E,\mu)$ be a measure space $E_0\in\mathcal E$ with $\mu(E_0)\in(0,\infty)$ and $\mathcal E_0\subseteq\left.\mathcal E\right|_{E_0}$ be finite and disjoint with $$E_0=\biguplus\...
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Sampling from joint distribution by writing its density as a product of conditional densities

In Gelman et al. "Bayesian Data Analysis Ed3" the authors often do the following (e.g. on pg. 65): Given two parameters $\mu$ and $\sigma^2$ and data y joint posterior density $p(\mu,\sigma^2)$ is ...
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Sampling from a mixture of product of Gaussians

I have the following density: $$p(y_*)=\int N(y_*\mid \mu(x_*),\Sigma(x_*) )\cdot N(x_*\mid Ax,Q)p(x,\theta)\ dx \ d\theta \ dx_*$$ with $\theta=(A,Q,\mu(\cdot),\Sigma(\cdot))$. How can I sample ...
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Random sampling from a probability density distribution?

From what I learned in introductory statistics, the probability of getting any single value for a variable described by a probability density distribution is 0, since the integral under a single value ...
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1answer
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Sampling: When is it better to use Simple Random Sampling rather than Stratified Random Sampling?

I know that stratified random sampling is almost always preferred over simple random sampling, but I have also read that the Variance of sample mean (x-bar) from stratified random sampling could ...
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Is systematic sampling outdated?

From what I can gather from lists of "pros and cons" like this one, systematic sampling is roughly equivalent to simple random sampling when the list is randomly sorted. If not, it leads to sampling ...
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Generating new(fake) probability distributions based on many sample probabilty distributions

I wish to be able to generate new probability distributions that incorporate the characteristics of many sample distributions available to me. I currently have data for the individual daily return ...
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Can I use a stratified random sample to avoid getting a random sample that is clearly not representative?

This is a follow-up to a question of what to do if you get a sample that is clearly not representative [What if your random sample is clearly not representative? ] I have a population of 800 in 25 ...
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Sample sizes: stratified random vs simple random sampling

In general, how does the total sample size for stratified random sampling compare with sample size for simple random sampling? The variable involved is binary: yes-no. The population parameter to ...
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Does random sampling from a dataset produce the same distribution as the original space?

Let's say we have a dataset $D$ with $N$ rows and $M$ columns. Each column is a feature. And for each feature $X_1, X_2,..., X_N $~ iid $F_p$ where $F_p$ is the distribution for feature p. Now let's ...
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Feature engineering procedure using optimism corrected bootstrap

I have a dataset with ~600 datapoints, 49 categorical features (five possible categories), and a binary outcome variable. The dataset is incredibly imbalanced, with just over 3% of the outcomes in the ...
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Randomly sampling snippets from a video

So I am working with traffic cam feed, and I have videos of ongoing traffic travelling at different velocities over the duration of feed. I have an object detection and tracking algorithm in place ...
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Estimating a sample size $n$ such that $\mu' n < y$

It seems like a pretty standard statistics question, but I couldn't find the answer. I have a sample from a population, from which I can estimate $\mu$ the population mean. I don't know the real ...
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Do both Bootstrap with and without replacement create a distribution?

I'm having a "noisy debate" with colleagues about whether sampling without replacement can still create a distribution. Methodology: A bootstrap (iterative process where I calculate Somers' D for new ...