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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CLUSTER SAMPLING PROOF

i have one questions that referred to book "On Efficiency of Cluster Sampling" (Daroga Singh, 1956) and my problem is i don't have that book, 9.14 The following sampling schemes for estimating the ...
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12 views

Limit of multivariate hypergeometric distribution for infinite colours/categories?

The multivariate hypergeometric distribution gives the probability of drawing, without replacement and in any order, $n_1$ balls with colour (or of category) #1, $n_2$ balls with colour #2, ... $n_c$ ...
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41 views

Understanding hypothesis testing using bootstrapping and simulating the null hypothesis method

I am trying to understand the bootstrap technique to perform hypothesis testing using the following post (This is also a part of Udacity Datascientist Nanodegree course): https://towardsdatascience....
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34 views

Hypothesis test for arbitrary distribution

Given a sample of $N$ observed values I'd like to test the null hypothesis that they arose from an arbitrary PDF (for which I have the analytical form). There are tests in place that can handle some ...
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Match sample to equal men and women in factor analysis?

I have a sample of 1567 autistic participants (m = 925, f = 642) who all completed a 75 question questionnaire measuring 'Systemising' or the drive to understand systems/patterns. For my ...
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14 views

Diversity enhancing sampling from positively dependent random measures

Is there any efficient method to maximize diversity of samples when sampling from a set of positively dependent random variables?
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Inclusion probabilities in two stage cluster sampling

So, there are H total clusters, each with size N_h. Two-stage cluster sampling involves: 1. Randomly selecting n_1 <= H clusters (without replacement) 2. Randomly selecting (w/o replacement) n_2 ...
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Sampling a distribution in 3 sections

For a time series process simulation I defined an input. It's a pulse train, the height of every pulse is one of three 3 possibilities (1, 2 or 3). That input is then convoluted with a process ...
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15 views

Two stage sampling method for my research in high schools

My research will be in high schools. Sample size will be over 300 and I have to choose them among 13 schools. Total number of students is over 3000 and when I think about sampling method, two stage ...
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59 views

Two phase sampling method for stratification

Question: $\$3000$ is allocated for a survey estimated proportion. The main survey will cost $\$10$ per sampling unit. Information is available in files, at a cost \$0.25 per sampling unit, that ...
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42 views

Why does the standard deviation of the sampling distribution of the sample mean needs N >= 20n

I keep seeing sources stating, without proof, that the standard deviation of the sampling distribution of the sample mean: $$\sigma/\sqrt{n}$$ is an approximate formula that only holds if the ...
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I need to construct function that gives out data of specific pdf function and draw histogram of it [closed]

So, the given density function is: $\theta x ^{\theta - 1}, \ \ if \ \ 0<x<1 \text{ and } 0 \ \ \text{ otherwise}$. $\theta$ is given as 2. I also need to draw a line that corresponds the ...
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Stratified Sampling vs. Hand picking a “random sample”, and using Chi-Squared as justification. Dichotomous outcome methods question

Suppose I would like to evaluate "the proportion of potato farms in Idaho that use pesticides". (dichotomous yes/no outcome variable). Now let's assume I know the exact number of potato farms in Idaho,...
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sample size determination for a system with several states

I would like to ask for help to determine the sample size of systems that could stay in any of the five states that are decreasing quality ( 5, 4, 3, 2, 1). 5 is the highest quality and 1 is the ...
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25 views

What is the difference between random sampling and simple random sampling?

This is my understanding: Probability sampling refers to the situation where you know the probability of each item potentially picked. Random sampling means each item has the SAME likelihood of ...
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Sample selection SI

I have to solve this exercise: We want to know about households income. We have N individuals of all households and we select n individuals of them, then we identify which home they belong to and the ...
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Can I perturb a sample drawn from a certain gaussian such that it becomes drawn from another gaussian?

Given known $v_1$ and $v_2$ such that $v_2 > v_1$, and an unknown $\mu$: I have a single sample drawn from the distribution $\mathcal{N}(\mu, v_1)$. Can I somehow perturb this sample in a sound ...
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48 views

How to sample a total variation prior?

I am interested in drawing samples from a total variation prior: $$\pi_{\mathrm{pr}}(\boldsymbol{x})=\left(\frac{\alpha}{2}\right)^n\exp\left(-\alpha\sum_{j=0}^{n-1}\vert x_{j+1}-x_{j}\vert\right)=\...
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38 views

Why is the formula for standard error of the sample mean and standard error of the sample proportion different?

Trying to understand this intuitively and haven't been able to find any explanations for this. If the formula for the standard error of the sample proportion is: $$\sigma_\hat p = \frac{\sigma_X}{n}=\...
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18 views

DIF: match sample randomly or by age?

I am carrying out a DIF analysis comparing the scores of men and women on a questionnaire. A preliminary ANOVA revealed that when comparing total scores on the test, there is a significant effect of ...
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Family members in factor analysis

I'm carrying out an exploratory PCA, followed by an CFA, to test for dimensionality of a questionnaire. I am wondering about the effect of having family members in the same sample. I have a final ...
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Are there methods or considerations for real-time Gelman-Rubin diagnosis while running multiple mcmc chains in parallel?

I have a Metropolis-Hastings algorithm in Python and I parallelized it with the multiprocessing library. However, at this moment I can only do Gelman-Rubin diagnosis when all generated parallel chains ...
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Weighing toilet paper with an imprecise scale

A practical, topical problem: Consider a typical roll of toilet paper (TP) with perforated sheets of fairly uniform size, and suppose we're interested in the distribution of a sheet's weight $W$ but ...
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22 views

Which statistical test is applicable if the variance within groups is large?

I have multiple groups, each group with 3 replicates so I performed a Kruskal-Wallis One Way Analysis of Variance on Ranks since normality was not achieved; however, post-hoc Tukey tests show no ...
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48 views

Sample Proportion $\hat p$ versus $p$ as the probability of success in a Binomial Distribution

I'm new to hypothesis testing and I have a homework problem which says: " For a certain coin test, $H_0: P = 1/2$ against $H_1: P = 1/3$ can be retained where $P$ represents the probability of ...
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Efficient sampling from a subspace of a multivariate normal distribution

I have an $N$-dimensional multivariate normal with mean vector and covariance matrix $(\mu,\Omega)$. The covariance matrix is diagonal. Thus one arbitrary draw from this distribution is an $N \times 1$...
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190 views

Minimize asymptotic variance of fintely many estimates

Let $(E,\mathcal E,\lambda)$ be a $\sigma$-finite measure space; $f:E\to[0,\infty)^3$ be a bounded function with integrable Euclidean norm on $(E,\mathcal E,\lambda)$ and $p:=\alpha_1f_1+\alpha_2f_2+\...
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Probability of filling M boxes with 2 or more elements when sampling S elements from N total elements

Similar to this question, Frequency of Item in Combination. I am randomly sampling S objects out of N=99 objects into 9 boxes labeled by a single character, "A-I". Question 1: I want to find the ...
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12 views

Choosing a representative sample for Clustering

I am doing Cluster Analysis for clickstream data. My data set has got 18 columns and over 821.000 rows. It has only numeric data. The rows represent customers, the columns Shopping baskets, number of ...
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51 views

Gibbs sampling for Multivariate: how to update?

In this page of Murphy's 'Machine Learning: a Probabilistic Perspective' it's explained how to do Gibbs sampling on a Gaussian Mixture Model. Reading this, I was trying to understand when to update ...
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15 views

Inferential statistics for multiple classes / groups

I have data regarding calls to a company. Only a small proportion of calls are classified into about a hundred different categories by a group of humans. The volume of calls is in the range of ...
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12 views

Combination of different Markov chains

Suppose I have a state space X with probability $\pi(X)$ that I want to sample via Metropolis Monte-Carlo. Suppose I have $T_1(x \rightarrow x'),...,T_n(x \rightarrow x')$ different transition ...
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30 views

How to sample a set of numbers, given the discrete probability distribution for the nth largest number

I recently saw a problem stated like this.. Generate a random set of 3 numbers, each distinct, such that The smallest number has the following pdf: {1: 25%, 2: 30%, 3: 15%, 4: 30%} The 2nd ...
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Statistically analyze path planning strategy effectiveness based on motion samples

My research concerns robot path planning. I want to demonstrate that a robot is more successful using one path planning strategy over another. In these scenarios, two robots are competing, and a ...
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145 views

Where is the error in my computation of the wrapped normal distribution density?

Let $\sigma\in(0,1)$ $$\phi(x):=\frac1{\sqrt{2\pi\sigma^2}}e^{-\frac{x^2}{2\sigma^2}}\;\;\;\text{for }x\in\mathbb R$$ and $$\psi(x):=\sum_{k\in\mathbb Z}\phi(x+k)\;\;\;\text{for }x\in\mathbb R$$ $\...
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Calculate Sampling Weights

I have sampled 300 respondents, stratified by zones and have conducted a survey, prior to carrying a census (ideally would have been the other way round). I would like to compute sampling weights to ...
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1answer
53 views

Sampling a changing distribution over time

I'm interested in learning more about sampling a changing population over time. For example, these statistics from the University of Washington coronavirus testing show a 7% positive rate day after ...
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101 views

Compute which of a finite number of integrals is minimal (not interested in the actual value of the integral)

Let $(E,\mathcal E,\lambda)$ be a $\sigma$-finite measure space; $f:E\to[0,\infty)^3$ be a bounded Bochner integrable function on $(E,\mathcal E,\lambda)$ and $p:=\alpha_1f_1+\alpha_2f_2+\alpha_3f_3$ ...
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23 views

How to test the representatives of a sample?

I have a data set with over 10000 measurements, then I random sample 35 measurements from this big data set. How to test that this is a representative sample. I know the central limit theory, if ...
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8 views

Inference methods for dependent samples

Hypothetically, let's say I've sampled 5 samples per subject, of 10 subjects per group (2 groups for that matter). If I want to compare between groups, I could calculate the mean of each subject, and ...
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1answer
84 views

Balancing measurement error with number of samples

Suppose I am doing a physical experiment and would like to measure the output (random variable). Inherently, I introduce measurement errors when sampling the random variable. There are also sampling ...
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17 views

Simple random sample size for large data question and appropriate strategy

I am working with a large data set from my company. I am trying to determine if using another sample would provide a better coverage compared to what I am using now. To do so, I am going to take a ...
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23 views

Is there a statistical law that can determine quantity of experiment and predict accuracy of results in my experimental context?

I designed a biological protocol A which measures a continuous variable qA for each sample I designed a biological protocol B which measures a continuous variable qB for each same sample as above ...
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5 views

Using simple random sample for large number of data with confidence interval

I am trying to see if a sample that I might use is better compared to my current results. I have sets of large data, 220k in one sample and 400k in another. I am trying to see if I use a new source to ...
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49 views

How should I compute this proposal kernel density?

Let $d\in\mathbb N$ and $$u(x,y):=\beta+(1-\beta)\prod_{i=1}^d\psi(y_i-x_i)\;\;\;\text{for }x,y\in[0,1)^d,$$ where $\beta\in[0,1]$, $$\psi(x):=\sum_{k\in\mathbb Z}\varphi(k+x)\;\;\;\text{for }x\in(-1,...
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25 views

Which statistic to choose - biased or unbiased?

In a book on introductory statistics, there is a question that goes like this: If two statistics are available for estimating a population characteristic, under what circumstances might you ...
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How do I find required sample size for my survey given the data I have from my pilot survey?

I have a data set which has a boolean variable (the question being 'Have you been the recipient of a blood transfusion?') it has either yes or no as the output. I currently have 118 replies to this ...
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57 views

Insufficient floating point precision for the correct computation of a density

I'm using the Metorpolis-Hastings algorithm in a setting where the acceptance function is essentially of the form $$\alpha(x,y)=1\wedge\frac{u(x,y)}{v(x,y)},$$ where $$u(x,y)=p+(1-p)\prod_{i=1}^mu_i(x,...
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1answer
63 views

How sampling distribution of sample proportion is related to binomial distribution

I am reading a book on introductory statistics. In the book, the author introduces the concept of the "sampling distribution of sample proportion" just after explaining the binomial distribution. I ...
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20 views

What does 'sampling from an HMM' mean?

I have an understanding of the basics Hidden Markov Models (HMM) - the transition/emission probabilities, as well as an understanding some of the algorithms used in evaluating an HMM, such as the ...

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