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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14 views

What is the formula for obtaining the Sample Size? [closed]

I'm carrying on an audit on "credit's process" for commercial loans in order to verify if the VARIABLE , which is the "portfolio classification", is correct . The DISCRETE VALUES ...
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High-dimensional Bernoulli Factory?

I am interested in the question of simulating a coin with head probability $f(p_1, p_2)$ (for example $f(p_1, p_2) = \min\{p_1, p_2, 0.5\}$), or more generally, simulating a coin with head probability ...
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31 views

expected value of sample

Suppose we have a distribution that has some pdf, say, $f(x)= 4(3-x^3)$ for $0<x<2$, and $0$ elsewhere. I am able to find $E(X)$ and $Var(X)$ using the standard definition of expected value (i....
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When to average technical replicates to get experimental replicate value?

I'm having trouble deciding when to average technical replicates from an experiment. The scenario is this: 4 Experimental replicates (i.e. experiments done on separate days) 3 Technical replicates ...
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27 views

How to obtain histograms of non-central t distributions from a normal distribution?

My Question; I'd like to know how to generate random numbers that follows a non-central t distribution using the normal random numbers. I made a calculation code for this using R (See Box2, below), ...
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38 views

Variable-specific random sample imputation. Is it a valid method of imputation?

Is random sample imputation a valid method of imputation for categorical variables? Not randomly drawing from any old uniform or normal distribution, but drawing from the specific distribution of the ...
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Consistency of likelihood importance sampling estimator

In a lecture recently our lecturer described a method for approximating the expectation of a function over a posterior distribution using likelihood importance sampling. That is: $$ \mathbb{E}_{p(x|D)}...
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24 views

Simulations of Chi-Square Tests on 2 x 2 table without using the chi-square distribution

I'd like to simulate the chi-square test without using the chi-square distribution on the following 2×2 table. I made "chiq_2by2" function using the R (See #main function in the Box1,below)....
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+50

Inference in Normalizing Flow model: NICE(non linear independent components estimation)

I was recently reading Y. Bengio's paper on NICE (https://arxiv.org/abs/1410.8516). In the paper, authors have taken a view that a good representation involves easy learning of the data distribution. ...
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Determine the Sampling Distribution [duplicate]

Let $X_1,…, X_n$ be a sample of $iid$ $N(𝜇, 𝜎^2)$ random variables. How do you calculate or determine the sampling distribution of $\overline{X} = \frac{1}{n}\sum\limits_{i=1}^n X_i$ and $S^2 = \...
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Generating a min{p, 0.5} coin from a p-coin - Bernoulli factory type problem

Suppose we are given a coin with arbitrary (unknown) head probability $p$, I am wondering if there is an easy-to-implement algorithm for generating a $\min\{p, 0.5\}$ coin for any $p\in [0,1]$. ...
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May Skilling's Nested Sampling Estimate parameters in hierarchical model?

May Skilling's Nested Sampling integration technique Estimate parameters in hierarchical model?
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How to deal with very large degrees of freedom? [closed]

I am using a dataset from an online database and the df seems to be huge. I do understand that higher degrees of freedom generally mean larger sample sizes. But can it be so big? If yes how can I ...
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Efficiently sampling a symmetric posterior with MCMC

I am using MCMC (via emcee) to sample a posterior distribution $p(\vec\theta|Y)$ where $\vec\theta = (\theta_1, \theta_2, \ldots)$ are parameters for a physical model of the process generating an ...
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How does one sample all images uniformly when the data set is organized in hierarchies?

I have a data set with $C=64$ classes and $N_c = 600$ images and total images $N = \sum_c N_c$. Each class has a separate folder for each class. I want to be able to sample images as if they were in a ...
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Question on how to sample randomly from the given distribution

I have following distribution which looks as follows: $P\left(\kappa| u,v,\lambda,y\right) \propto \kappa^{-\frac{n}{2}}exp\left\{-\cfrac{1}{2\kappa}\left[\epsilon + (u_1-u_2)^2 + (u_2-u_3)^2 \right] \...
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Interesting question on confidence intervals

Say I conducted a sample and did the relevant processing to get a 95% confidence interval of a parameter to fall between a [10,14]. My friend did another sample, and got a x% confidence interval of a ...
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trying to understand repeated sampling with individual error terms, regression errors, intuitively

in the model $Y_i = \beta X_i + \eta_i$, for consistency unbiasedness, it is typically assumed $E[\eta_i|x_i]=0$. since each error for every i in the data is its own random variable, this then must ...
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Can dichotomous variable be used as auxiliary variable in conventional way to design an estimator?

I have a variable Y that can assume a range of values, and an auxiliary variable X that assumes value 1 if it possesses a characteristic, 0 otherwise. My first assumption here is that I can substitute ...
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Question about standard errors of regressions/means

I just had a question about standard errors of sampling statistics/estimators. Is for example, the standard error of a regression coefficient, a true population value, that is estimated? Should I ...
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Resample data from a histogram with higher resolution - assuming it follows a normal distribution

I have a problem which has me stumped on what to try next. I have some data from a farm, related to yield over a period of days, for a defined area. I have daily-resolution data, where the day's ...
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Finding the “most representative” variables of a population

Most polls use the so-called quotas method to obtain their sample. They draw candidates upon a large panel of people and add one-by-one each responding candidate to the sample unless a certain quota ...
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Interpreting $\text{Var}(\hat{p};\text{stratified}/\text{Var}(\hat{p};\text{SRS}) < 1$

I have calculated the estimated variance of the proportion $\hat{p}$ under different sampling schemes. I have found $$ \frac{\hat{Var}_\text{stratified}(\hat{p})}{\hat{Var}_\text{simple random ...
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Re-calibrate interaction matrix in population sample

Let's say I have a population {$(G, p)$} where $G$ is a group within the population, and $p$ is their proportion distributed as such: ...
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Sampling from a skewed distribution

So I have a dataset with around 40,000 unique free text descriptions of purchased goods. I also know the spend on each of these unique descriptions, and the distribution of spend is long tailed. Some ...
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Does sampling more frequently reduce variance?

Suppose you are getting a stock's prices at hourly intervals and you want to use those to model the stock's returns (relative to the day's starting price). When you get the stock price, you are also ...
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What statistical analysis do i deploy? if i have 100 survey respondents from a population of 1000

And i obtained these responses by a random mechanism. (My study sample is a random sample from my population.) And i have likert data. Do i just report it with a bar chart, and maybe a frequency table....
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Sample from parameters' posteriori distribution

Assume a linear model for the data : $y = x^T\beta + \epsilon$, with $\epsilon \sim \mathcal{N}(0,\sigma^2)$ and an a priori on the parameter: $\beta \sim \mathcal{N}(0,\Sigma^2 _p)$. Let $\mathbf{y}, ...
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Probability that the sample comes from a certain distribution

Assume we have a data sample: $x_{1}, \dots, x_{n}$ from $n$ i.i.d. continuous random variables. Then, for simplicity, let us consider two distributions, $f(x)$ and $g(x)$. Is there any statistical ...
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Does the sampling distribution for the median of a bimodal distribution depend on sample size? [duplicate]

I have a dataset of project sizes (in $) which is sometimes bimodal, sometimes not (it varies across time and I am using annual data sets). These projects are distributed across two types of project ...
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50 views

Sample size for binomial distribution for rare events

I would like to estimate the parameter p in a binomial process but need to determine the sample size required. I believe the event is fairly rare, and I have read the normal approximation may not be ...
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16 views

Why is minimum sample size not based on proportion?

In different situations there are many tests or general agreements for a minimum sample size, which are usually some fixed number that is not that high, capping at <400. Common numbers include 100, ...
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Positive cases without variable data

I'm working on a classification model aimed at identifying if behavioral activity within an account (b2b - one account, many contacts) can predict or not an opportunity generation ( a salesperson ...
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Reformulation - Probability of correctly inferring whether a coin can produce heads

[This is a repost, since the original post specified a slightly different problem than I actually had in mind] Suppose you have a coin which you know could be biased towards tails with unknown ...
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21 views

Concept: Impact of Random Sampling on the Uncertainty Associated with Making Inferences

I am struggling with a concept on sampling and I was unable to find the answer here or anywhere on google where I could fully understand. Specifically, my concept question is: In what ways can ...
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Sample sizes estimation for testing two proportions (2 samples): power based vs rewriting confidence interval

As I see it there are generally two ways to estimate the required sample size(s) based on what you want to test. For this question I am interested in a two-sample proportion test, where the binomial ...
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1answer
23 views

Implementing a sampling scheme that satisfies certain probabilities

Suppose we have two boxes of balls. Balls can be blu or red. In the first box: the probability of drawing (at random with replacement - this is assumed everywhere) a red ball is $p^1_R=0.4$ the ...
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38 views

i.i.d. requirement for very large datasets

I am working with ML models where the data is plentiful: I can get billions of records for training and validating my models. In fact, I have so much data, I need to sample to reduce the data set ...
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time complexity of sampling from multivariate hypergeometric distribuiton

numpy has an implementation and the doc is here. It says it is "roughly" equivalent to: ...
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26 views

Clustering algorithm for a coordinate-based matrix

I have $1000$ scenarios, each of which is composed of $5$ users' coordinates $(x_i,y_i), \forall i \in \{1,\dots,5\}$. Now, based on users' coordinates, I want to cluster these $1000$ scenarios into ...
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How do I know whether my sample is fair?

I have a time series dataset with 500 million rows, twenty-six columns and 400 thousand unique actors. It's too much data for me to process all at once, so I want to take a fair sample of my data. I'...
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How can I estimate the distribution of sizes if I sample from the tails of that distribution?

Let’s say I have an insect farm and they lay down a lot of eggs, which I collect in a cup. Now I want to study the size distribution of those eggs, but there’s a problem: The younger eggs, which are ...
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23 views

Does up-sampling lead to lots of false positives in production?

Say we have a dataset with a binary outcome variable that takes the positive case (outcome = 1) roughly 20% of the time. Often, we would modify the training set by ...
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Does oversampling or undersampling not impact the coefficients of independent variables?

I have come across a few discussions on this site which state that random oversampling or undersampling doesn't impact the coefficients of the independent variables in logistic regression. Since the ...
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75 views

how to construct and sample from conditional multi-variate normal distribution?

The two random variables $D$ and $W$ represent the uncertainty of average price of a product in the daily (short resolution) and weekly (long resolution) time-interval . On the other hand, the ...
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1answer
76 views

No free lunch in statistics: an elaboration

James et al. "An Introduction to Statistical Learning" (2013) p. 29 states: There is no free lunch in statistics: no one method dominates all others over all possible data sets. On a ...
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1answer
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Bootstraping with R, how to find possible bootstrap samples for a given vector

Consider the vector our_names <- c("John","Ciprian","Brian") a. List all possible bootstrap samples of our_names. b. How many ...
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81 views

Probability of a unit being selected in sample

I recently studied sampling from one of online courses and got to know about various sampling methods but i'm confused regarding the probability of an element being selected in a sample. In that ...
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23 views

Simple random sampling (SRS) with vs without replacement

Why is the variance formula for sampling with replacement easier to derive than without replacement? And why is it that it is for small sample size n relative to N, the two sampling designs are not ...
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47 views

Why permutations are counted in Simple random sampling with replacement?

Why are ordered pairs counted in Simple random sampling with replacement but not in without replacement? Is there any intuition behind it as to why when we take samples(simple random sampling) with ...

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