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

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Is sampling according to several i.i.d. random variables or to just one of them equivalent

Suppose we have n+1 random variables i.i.d. distributed $X_0,X_1,...X_{n}$. Is it the same operation if I generate n samples according to $X_0$ $\{S^0_1,S^0_2..,S^0_n\}$, or if I take from each of the ...
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29 views

How to emphasize on specific data points in Linear Regression?

I'm now solving linear regression problems. $y = wx + b + e$ So I have $(x, y)$ data set and want to learn weights $w, b$. Additionally I know that certain data points are not polluted by noise ...
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35 views

Bootstrap and MonteCarlo Method

I am trying to make sense of the bootstrap method. I am studying on Rice, "mathematical statistics and data analysis" Here it is its explanation of the bootstrap method: Imagine for the moment ...
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9 views

Subset items from a group while controlling for variables between groups

Can anyone offer solutions to the following problem?: I'm trying to extract a subset of items from multiple groups (grouped by 2 separate factors) so that the final groups are: 1) of equal size, and ...
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33 views

data are drawn from a probability distribution P?

what does it mean to say data are drawn from a probability distribution P?
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37 views

Systematic Sampling with unequal probabilities

I found the library Sampling in R to conduct a systematic random sampling with unequal probabilities. I got my sample but I really don't know how that sample is selected. Is there anyone that can ...
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1answer
27 views

How to calculate a sample size for validating correct/incorrectness of records in a data table?

I have read through existing answers on CrossValidated (plus elsewhere online) and can't find what I'm looking for, but do please point me to existing sources if I've missed them. Let's say I have a ...
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1answer
25 views

Is this a Random or Purposive Sample? Inclusion-Exclusion Criteria and the Sampling Frame

Introduction I am confused about when a sample is a random sample (i.e. probability sample) and when it is a purposive sample (i.e. non-probability sample). My understanding is that the former allows ...
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15 views

Relationships between N independent samples and a single sample

Imagine I have a population of $N=1$ million balls in a bag. I want to draw $M = 10$ independent samples, each having $S = 1\%$ of the total population. Let each ball be marked with a unique ...
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29 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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30 views

Bootstrap resampling for constructing hypothesis test

I need to use bootstrap resampling to test the significant difference between two datasets (data1 & data2). I have already used bootstrap resampling to estimate the confidence interval of the mean ...
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27 views

Confidence intervals for sample mean when estimated standard deviation is 0

I ran a Monte Carlo simulation to determine a confidence interval for the population mean based on N trials. The underlying distribution of results is not normal (the values are discrete -- 0, .5 or ...
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24 views

Observed and Observable

What is observed and what is observable? I found this two word frequently in the context of random variable and realization of ...
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24 views

Repeated sampling with outliers

I have a situation where I'm sampling a value (computer program runtimes, not that that should make a difference) where the sampled values are presumed to be distributed around an unknown "true" value ...
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13 views

A fast convergence method for inverse problem

I have an inverse problem that is very CPU demanding. In this problem I have two types of data: 1-static, 2-Dynamic. First I use a method and create some models based on the static data. Clearly, ...
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15 views

How to do Hierarchical (Nested) Elliptical Copula simulation sampling

dear researchers, I am doing a project to aggregate about 30 risks into total loss (15 of them are market risks, and 15 of them are insurance risks). The current approach is to simulate millions of ...
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Contaminated mark-recapture: estimating set size from sampled subsets

Someone poured marked balls in my urn! Simplistically, I think this is a capture-recapture problem where, after drawing and marking balls from the urn, somebody added an unknown number (approx 25% of ...
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8 views

Subsampling Dataset

Is there an algorithm to subsample a dataset such that the resulting samples span as close as possible the space spanned by the original dataset? E.g. Given a dataset S={1,2,3,4,5,6,7,8,9} and a ...
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25 views

Reducing the amount of data by extracting a representative sample of my population

I have 6 B&W images representing different wavelengths (i.e. Landsat bands) of the Alta Valtellina (Italy). I extracted from the images only the areas of bare soil. Now, I want to perform a PCA on ...
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47 views

How to make sample space of the following question

My teacher gave me a question to solve.In the book of Ronald E. Walpole (Probability and Statistics for Engineers and Scientists), chapter no#3 exercise 1,question #2 which is as below: 3.2) An ...
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Acceptance Sampling Plan

I was reading Acceptance Sampling Plan but didn't understood when should I use single sampling plan , when double sampling plan , when multiple sampling plan and when sequential sampling plan. Also ...
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1answer
54 views

Sampling Calibration

I was trying to work out by hand the first example in the following PDF link entitled The calibration software CALMAR – What is it? The example is given below for convenience: Example 1: We ...
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32 views

How to determine an appropriate sample size for a normal distributed population?

I am trying to extract a sample from a given population. Assuming the population distribution is normal (I still have to test it, but I am confident it is), since the number of observations in the ...
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Adapt sampling in Random Forest (R)

I have a number of objects ($a,b,c,...$) which are observed over time. From each object there may be multiple observations (e.g. $a_1, a_2, a_3, b_1, b_2, c_1, ...$) with a numeric outcome. Note that ...
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Estimating Size of a Set based on two Overlapping Subsets

I've searched everywhere for a similar question and many things come close but are not the same. I'm looking for a way to estimate the size of a set if two partially overlapping subsets are known ...
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38 views

Can you perform bootstrap resampling from a sampling distribution?

The quick and to-the-point question I have is: Can you perform bootstrap resampling on a sampling distribution, using the sampling distribution as if it were an original sample of observations? What ...
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48 views

How sampling works

Rattling around in my head I am trying to work out a little theoretical problem. Imagine we are doing a poll/study to find out something or other from the people across 3 cities. We want as ...
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Ideas for sampling design

I have a data base of schools per district and the number of teachers per school. I want to select a sample where between 1 an 10 schools are selected in each district. Once a school is selected, the ...
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1answer
27 views

Adaptive Sampling Design

In a pdf, the definition of adaptive sampling design is written as : "An adaptive sampling design is one in which the selection of units to include in the sample depends on ...
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42 views

Which kind of “uncertainty” is this?

I'm a bit confused about all the different "definitions" of uncertainty? One can calculate "uncertainty" of a single measurement by simply checking how accurate the tool that is being used to do the ...
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Notation for a random vector whose length depends on another random variable?

I have the following process that I'm trying to describe with random variables. First, I have a random variable $X$ that takes on values drawn from a Poisson distribution with parameter ...
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15 views

Sample calculation

I'm about to start an In vitro model experiment. I will have 3 groups to compare between them with continuous variables. I will use ANOVA for the comparison and I would like alpha to be 0.05 with ...
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5 views

Analysis of multi-stage sample with probability proportional to size sampling

I am analyzing data from a multi-stage sample to assess the usage rate of cookstoves across a population. Primary sampling unit = VDC (village), secondary sampling unit = Stoves (i.e. household). I ...
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How is the sample size for a given population determined?

The following passage is an excerpt from Thinking, Fast and Slow by Daniel Kahnemann The risk of error can be estimated for any given sample size by a fairly simple procedure. Traditionally, ...
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24 views

What is intervention?

An intervention is strategy to produce change among individuals or entire population. Is the definition of intervention correct ?
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How I can analyze a data survey obtained with non probabilistic sampling?

I got data from a survey. The survey was designed with quotas of the population in that neighborhood (near the 10% of the total population of that place). But, the people was surveyed in the ...
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10 views

Value at Risk in the Sample Vs Out of Sample

please can anyone explain to me what is the difference between the VaR in the sample and VaR out of sample. and how do i use those In what cases should we use In the sample or out the sample we it ...
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2answers
32 views

Non-Normal empirical distribution sampling

I want to determine if some sampling I have done is significantly enriched or not compared to a null empirical distribution.I have collected data for the counts of genes in a certain sized window ...
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Efficient generation of graph structured correlated random variables via MCMC/Gibbs

Sometime back I had asked this question about generating correlated random draws based on the correlation structure given by a graph. Link Here The solution there requires to create $n\times n$ ...
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22 views

Probability Distribution of Binary Operation Applied to Elements of Two Populations

Given two populations from which one can draw finite samples, how does one estimate the probability density of the result of some binary operation applied to elements of the two populations? The ...
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1answer
26 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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23 views

Naive Bayes text classification on different cardinality classes

I have written a Naive Bayes classifier (with Laplace smoothing) and am using it to classify text into a few simple classes. However, I found that the classes are not of the same vocab size -- to be ...
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61 views

How to reduce dimension of the sampling procedure?

I am stuck with this problem for a long time, hopefully I can get help here! Basically, I want to sample from a posterior distribution that looks like, \begin{align*} X &\sim ...
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7 views

How to incorporate survey margins of error in modeling

I am using data collected from the American Community Survey (ACS), which has a complex sampling design. For all estimates, a margin of error is provided. This is useful for estimating univariate ...
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52 views

Sample size calculation for proportion

I am in a doubt about using Absolute and Relative precision for sample size calculations. Suppose if I want to conduct a study to asses the prevalence of Hypertension in a general population, which ...
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How can I sample multivariate binary variables such that sum of them follows a gamma distribution?

Edit: Since the original question was confusing as whuber pointed out, let me rephrase the question with a Poisson distribution instead of a gamma distribution. The energy term of a Poisson ...
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1answer
51 views

$H_0=250g$ and $H_1\neq 250g$" [closed]

We have a sample of size $100$ with a standard deviation of $5g$ It was decided that if the sample mean is between $245g$ and $255g$ while the sample average is $250g$ if $\mu=250g$ or $\mu\neq250g$ ...
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1answer
35 views

Log posterior function in PYMC

my question concerns the logp function in the PYMC package in Python. Ultimately I want to calculate a quantity that goes by many names, namely the Bayes-factor/ evidence/ marginal-likelihood of the ...
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Symmetric Distribution for MCMC Continuous Distribution

I have a sampling distribution $g(X^{'}| X=x)$ such that $$ \log(X^{'})|X=x\sim N(\log(x), \sigma^2)$$ This ensures that our samples are in $(0, \infty)$. Now I would like to use the Metropolis ...
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How do I sample using multiple groupings?

I have a large number of tests that pass or fail, in multiple projects, and the tests can divided according to two criteria, -- Location (100 locations), and Type (15 types). Now, for calculating the ...