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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31 views

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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38 views
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coverage index?

Suppose I have a space of potential outcomes X with a probability distribution on it. I assume that there is a distance function between elements of X (e.g. X is a metric space). I also have a set S ...
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52 views

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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1answer
278 views

Sampling on a logarithmic scale

I have to draw samples (variance parameter) based on a Gaussian kernel but on a logarithmic scale. I have no clue how to implement that as a part of the Metropolis-Hastings algorithm. In particular, ...
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1answer
23 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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2answers
384 views

Simple Random sampling with replacement - Variance

If just a single unit is drawn at random from the whole population and $y_1$ is the value of $y$ for this sampled unit, how can I prove that the $\mathbb{V}(y_1)= (1 − 1/N)\sigma^2$ (where $N$ is the ...
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222 views

Margin of Error of Sample Variance

For $N$ samples of normally distributed data $X_i \sim \mathcal{N}(\mu,\sigma^2)$, the $1-\alpha$ confidence interval for the sample mean $\bar{X}$ is $$ \left[\bar{X} - z_{\alpha/2}\frac{\sigma}{\...
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1answer
12 views

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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17 views

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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27 views

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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54 views

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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1answer
22 views

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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10 views

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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30 views

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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1k views

Perfect sampling from a huge dataset

I am working with a binary predictive model for data that belongs to A and B. The learning sample that I am using contains 6000 row that belongs to group A and 1000 row that belongs to group B. I ...
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1answer
151 views

How to create a distribution and sample?

Suppose we are given some small set of data on bundles of electrical wires and increasing voltages run through them, and we note how many of the individual wires fail. So for example, a large data ...
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1answer
154 views

Universal approximation of probability distribution with latent variable model

I want to show that under certain circumstances this form can approximate any probability distribution. For that, I came up with the following argument. Consider a directed graphical model of the ...
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13 views

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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2answers
95 views

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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1answer
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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1answer
270 views

What are some techniques to augment tabular data?

As we know we can perform data augmentation to "image dataset". We can apply random rotation, shifts, shear and flips over images. Are there techniques to augment tabular small dataset? I know the ...
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16 views

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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15 views

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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35 views

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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44 views

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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5 views

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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3answers
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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22 views

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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8 views

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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17 views

“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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5answers
8k views

Why do political polls have such large sample sizes?

When I watch the news I've noticed that the Gallup polls for things like presidential elections have [I assume random] sample sizes of well over 1,000. From what I remember from college statistics ...
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42 views

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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3answers
47 views

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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2answers
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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1answer
180 views

How can I tell whether sample size is inadequate or not?

I am given sample size of 15322 students and our research topic is to find out a relationship between students academic performance and participation in sports team. The question asks " do you think ...
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1answer
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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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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2answers
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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23 views

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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0answers
9 views

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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42 views

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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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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1answer
13 views

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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1answer
227 views

Why use envelope function for rejection sampling?

What is the purpose of envelope function? Say, for single random variable, why can't we just sample x coordinate and y coordinate (representing probability) and reject all those y's which lay above ...
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1answer
37 views

A model to suggest salient examples to annotate

I have a very large dataset of items that are all initially unlabeled. A user picks at random 5-20 items, labels them and creates an initial training set for a model. The model is trained and is ready ...
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1answer
20 views

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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3answers
6k views

How to re-sample an XTS time series in R?

I have an irregularly spaced XTS time series (with POSIXct values as index type). How can I build a new time series sampled at ...
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1answer
163 views

Simplest possible (uniform) sampling of the interval [0,1] with n points

The simplest possible sampling of a function in the region [0,1] for the purpose of finding the area under the curve, for instance, could be just take the left offsets of the bars. That is, you have ...
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24 views

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\...