Creating samples from a well-specified population using a probabilistic method and/or producing random numbers from a specified distribution.

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Sampling from matrix-normal distribution

I would like to sample from a matrix-Gaussian variable (not multivariate normal). so basically, let $X \in \mathbb{R}^{m\times n}$ be a random matrix distributed according to the matrix-normal law. ...
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24 views

Joint inclusion probability for Horvitz–Thompson estimator

There is a Wikipedia page for the Horvitz–Thompson estimator. It is an estimator for the population total. Unfortunately the page has failed to state the standard error. From here, the standard ...
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6 views

How to calculate sample size for PK/PD modeling?

I'm a PhD student of Pharmacology and would like to develop a PK/PD model on TB drugs. Of course I'm in my very early stage of learning the modeling science. But, for now what I want to ask is "Can ...
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12 views

Testing whether sampling (convex polytope) is uniform

Currently, I am sampling points from: i) a convex polytope (i.e. Ax <= b) ii) a high dimensional simplex The algorithms I am using are hit-and-run and a simple version of Bayesian bootstrap. I ...
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36 views

Sampling Distribution (Variance) of Weight Estimates

I am currently facing an issue regarding the sampling distribution of weight estimates. Problem Statement Given an estimate of a $n \times n$ covariance matrix $\hat{\Sigma}$ of $n$ random variables ...
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20 views

SRSWOR involving Weighting

A Simple Random Sample Without Replacement (SRSWOR) survey is conducted that included too many women and not enough men in the sample In the resulting weighting, each female is given a weight of 1 ...
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41 views

Calculating different Sample Errors [on hold]

A university plans to do a survey of the number of hours students spend studying each week to determine the average study time per student. It knows from previous surveys that the variability of study ...
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20 views

Box Muller vs Numpy?

I used the Box Muller transform and pythons uniform random number generator to sample random numbers in a given interval [a,b]. Here's the approach I used: Note: I know the average and the standard ...
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23 views

Choosing a sample rate for GBM models

I've created several GBM models to tune the parameters (trees, shrinkage and depth) to my data and the model performs well on the out-of-time sample. The data is credit card transactions (running into ...
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32 views

How accurate is my simple description of a confidence interval?

Here's my simple words-only description of a 95% confidence interval for the mean. How accurate is it? the sample mean comes from a distribution of possible sample means the sample mean might have ...
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2answers
51 views

Get quantile function of dynamic mixture model

I have a dynamic mixture distribution fitted to my risk data (i.e., I have all parameters) of Weibull and Generalized Pareto, with a Cauchy CDF mixing function, that can be written as: $mixture(x): ...
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26 views

Estimate population mean from sample

Population contains two independent parts: Group A & Group B with size $N_A$ nad $N_B$. $N = N_A + N_B$ Now sample from Group A and Group B separately. Sample size $n_A$, $n_B$. $n = n_A + ...
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107 views

Are the balls drawn randomly (independently of the number of balls existing in their colours)?

We have a big urn that contain $N_{Tot}$ balls. Balls are of $r$ different colours. The number of balls of the $i^{th}$ colour (before sampling) is $N_i$. John sampled $x$ balls in total (without ...
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1answer
29 views

optimal sequential sampling in gaussian process models

Let's say we have a one dimensional dataset of 24 points along with their responses. I am reserving three boundary points for testing (i=1,23,24) and i am fitting a Gaussian process model based on a ...
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62 views

Sampling from von Mises-Fisher distribution in Python?

I am looking for a simple way to sample from a multivariate von Mises-Fisher distribution in Python. I have looked in the stats module in scipy and the numpy module but only found the univariate von ...
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69 views

What is the standard error of the sample standard deviation?

I read from there that the standard error of the sample variance is $$SE_{s^2} = \sqrt{\frac{2 \sigma^4}{N-1}}$$ What is the standard error of the sample standard deviation? I'd be tempted to guess ...
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63 views

Simulate from a dynamic mixture of distributions, honoring the tail

This question is a follow-up to this other question, brilliantly answered by Xi'an. I have a dynamic mixture of Weibull and GPD distributions (with a CDF Cauchy mixing function). The mixture is ...
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34 views

Proof for the sampling variance of the Neyman Estimator

I'm going through Imbens and Rubin's new book and I just for the life of me can't figure out 1 minor detail in their proof for the sampling variance of the Neyman estimator $\bar{Y}^{obs}_{t} - ...
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92 views

Enlarging a random sample

In our project we have a population of 1000+ individuals. We picked a random sample of 107 individuals, but then we realized we needed more precision, so now we want to have a larger sample. The ...
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2answers
58 views

What is the problem of singular (non-invertible) covariance-variance matrix?

What exactly is the problem of having non-invertible covariance matrix? Why is getting the inverse of this matrix so important? This problem is often encountered when doing regressiong works on ...
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1answer
24 views

Reducing size of data sets while preserving their mathematical properties

So I'm looking at the paper $l_p$ Row Sampling by Lewis Weights in which the authors provide a method to sample the rows of a matrix while preserving their mathematical properties. More specifically ...
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19 views

Can I pool my data?

I collected some data about purchase decisions. For simplicity, lets say my IVs were Price and Quality, and DV Intent to Purchase My survey prompt was something like "Answer the survey questions ...
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29 views

Can we use normal distribution statistics on frequency distribution outputted by bootstrapping?

If I understand correctly, this is the bootstrapping procedure: Pretend sample is population Repeatedly resample from this pretend-population Calculate the mean of each resample. The output of ...
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55 views

How often will sampling distribution of the mean not be normally distributed?

Kabacoff 2015 suggests that if we're not willing to assume the sampling distribution of the mean is normally distributed, we should use bootstrapping to estimate the sampling distribution of the mean. ...
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276 views

Simulate from a dynamic mixture of distributions

I need to sample from the following mixture of two distributions: $h_{\vec{\beta}}(r)=c(\vec{\beta})[(1-w_{m,\tau}(r))f_{\vec{\beta_{0}}}(r)+w_{m,\tau}(r)g_{\epsilon,\sigma}(r)]$ where ...
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Sampling distribution of sample trimmed (truncated) mean

It is elementary probability theory that the sample mean of an i.i.d. sample follows normal distribution, if the background distribution is normal. But what about the trimmed mean? Is there any result ...
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23 views

Sample discrete multivariate normal

What is an efficient way of sampling from a discrete multivariate normal distribution with pdf $$ p(z) = \frac{1}{Z} e ^ {-\frac{1}{2}(z-\mu)^\top\Sigma^{-1}(z-\mu)} $$ such that $z \in ...
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112 views

Simulating from Kernel Density Estimate (empirical PDF)

I have a vector X of N=900 observations that are best modeled by a global bandwidth Kernel density estimator (parametric models, ...
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103 views

Nontrivially simulated distributions

I'm learning Monte-Carlo approach in sampling. There I faced with ways of how to draw samples from given distribution. But can you give me an example of a distribution which can not be trivially ...
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34 views

Adjusting Probability for oversampling

I am developing a marketing (Churn) model that has an event rate of 0.5%. So i thought to perform oversampling. I mean making the number of events equal to number of non-events by reducing non-events ...
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30 views

Analysis with unequal starting groups

Background: Our business wishes to perform an demand analysis based on two marketing treatments A and B. Due to constraints imposed from the onset, there will be a 50/50 split (receive/not-receive) ...
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49 views

How to simulate more data for machine learning?

I am attempting to analyze a small dataset using machine learning (SVM, binary problem). There are $103$ samples and $215$ variables (all variables are real numbers). Some of the variables (around ...
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52 views

Is weighing cases allowed/necessary for the Kruskal-Wallis and its post-hoc tests?

I have a dataset where I have respondents from 3 different countries (USA, NL & DE) and use the Kruskal-Wallis to determine if there are any statistically significant differences regarding ...
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133 views

How to test if social structure is non-random and resulting from genetic relatedness – and how to deal with demography effect

I am trying to construct (undirected) social network based on co-occurence of individuals. Clustering algorithm will be later applied on this network to find some distinct subgroups. Issue is that ...
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51 views

Sampling from an (almost) multivariate normal over matrices

Consider $n$ points in the euclidean plane, $p_i = (x_i,y_i)_{1\leq i \leq n}$. Now consider a $2 \times 2$ matrix $M = \left(\begin{array}{cc}a & b\\c& d\end{array}\right)$ a vector $r = ...
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21 views

How to call extreme samples in a Monte Carlo simulation for hypothesis testing?

For many hypothesis tests, Monte Carlo methods are used to estimate the empirical $p$-value which is defined as $$p=\#{(T_{sample} > T_{observed})}/N.$$ Is there a name for the samples with ...
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28 views

how to calculate sample size for quasi experimental non equivalent pretest post test design where p is not known?

I am conducting a study with one treatment group and 2 comparison groups on tobacco cessation among school children in india. The GYTS 2009 has measured intention but there is no data available on % ...
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37 views

In survey sampling, have calibration margins to be known (estimated with 0 variance)?

Calibration estimators in survey sampling (as defined by Deville and Särndal, and implemented for example in the SAS macro "Calmar") generalize many other calibration estimators, including ...
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72 views

Stratified Random Sampling Implementation how to in R?

I have a dataset of 20 million rows. it is organized into strata (groups), and I need to sample from them. I need to create a smaller sampled dataset on which I bulid a regression model. I need to ...
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30 views

Justify sample size of 30 per group is valid

I am conducting a quasi experimental study. Both my control and study groups consist of 30 participants. I wasn't able to compute for the effect size etc. beforehand. Please help me to justify that 30 ...
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66 views

Bounding the bias of standard deviation estimate for stratified sampling (MC)

I cannot find an answer to this issue: in Monte Carlo runs, if one uses stratified sampling then the unknown bias of the variance estimator ( $\bar{\sigma}^2=\frac{1}{N}\sum{(y_i-\bar\mu_y)}$ where ...
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33 views

The design effect

The design effect (deff) quantifies the extent to which the expected sampling error in a survey departs from the sampling error that can be expected under simple random sampling . My question is ...
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71 views

Consequence of violation of independence assumption on estimates of standard errors

from the first chapter , Introduction to Multilevel Analysis , p.5 of the book , it is written that : Standard statistical tests lean heavily on the assumption of independence of the ...
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99 views

Is the accessible population a random sample?

At academic institutions dedicated to teaching we often use our current students taking a specific class, the accessible population, as a random sample when our actual sample includes all students who ...
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23 views

Can you use event history analysis if your sample was selected on the dependent variable?

I have a dataset that includes a random sample of individuals who are currently in a relationship in the United States. I also have data on the date that they met their partner and the date that they ...
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1answer
18 views

Information content of a set of random variables

Suppose there is some distribution $F$ not known to us. However, we can get information about this distribution by means of samples, i.e. we have a set of random variables from this distribution. ...
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251 views

Using Uniform Distribution to Generate Correlated Random Samples in R

[On recent questions I was looking into generating random vectors in R, and I wanted to share that "research" as an independent Q&A on a specific point.] Generating random data with correlation ...
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Binary variance? Comparing two sacks of uneven coins or two heterogenous groups of people

I have two sacks of coins. In one sack, the coins are all uniform, each giving a fairly constant 0.5 chance of heads (based on tossing a few of them and also visual inspection). I then estimate the ...
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62 views

Poor sample measurement and the Central Limit Theorem

I have a fairly basic question about the Central Limit Theorem. I understand it in principle, but I like to know specifically what happens when there is poor measurement on the samples. Say for ...