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

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How a quota sample should be executed?

Let's say I have a population stratified by gender and age group. Having their proportions, how should I choose the sampling units for interview? How do I ensure the defined quotas are met? If the ...
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4 views

What is the best ensemble sampler for highly correlated parameter space?

I have a likelihood that I want to estimate the free parameters for it and I am using MCMC to estimate the parameters. Two of the free parameters are positions and I defined uniform priors and one has ...
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31 views

Simpson's Paradox with new sample

Suppose you constructing model whose training data is cumulative in nature; meaning each year you can add new observations with all prior observations being kept the same. (e.g. training set is ...
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28 views

How many samples do I need to prove that a classification algorithm is better than another?

I have two algorithms A and B, used to automatically classify each of N elements into K categories, N and K both being in the millions. Neither A or B is perfect, but it is relatively easy for a human ...
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1answer
21 views

Leave-one-subject-out cross validation in Caret

Hi Dear Colleagues, I wonder how to correctly setup a leave-one-subject-out cross validation (LOSO) for train() function in caret. Here is my example code: ...
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24 views

Estimating number of unique people

Assume from a prior experiment with have a known truth table of misclassification of logins on an individual basis. $$ \begin{array}{c|lcr} \text{Truth}/\text{Observed} & \text{Al (M)} & ...
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Birthday “Paradox” — with a different perspective

Background: Many people are familiar with the so-called Birthday "Paradox" that, in a room of 23 people, there is a better than 50/50 chance that two of them will share the same birthday. In its more ...
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19 views

How to calculate sample size? [closed]

I need to know how many people of risk group do I have to screen, to get any statistical significance? For example renal cell carcinoma is diagnosed to 25 people from 100 000 population. If they have ...
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15 views

What are the statistical implications of assigning treatment and control in time series study under 2 different approaches?

I have a project wherein my group wants to measure the effect of counseling at-risk students on their academic outcomes. There are 1,000 students who will be enrolled during the current academic ...
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39 views

What are the null and alternate hypotheses? Will you use a left, right, or two-tailed test?

Ben has a coin which he claims is weighted in a way so that when he flips it, heads appears more often than 50% of the time. He tries to prove it to you by flipping the coin 100 times, which ...
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17 views

Inclusion probabilities in a sampling with unequal probabilities with Brewer's method, n > 2

I'm trying to estimate the total of a variable in a population using an unequal probability sample with $n>2$ and the Brewer's selection method. I draw the first unit with probability ...
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1answer
64 views

Optimal Allocation

A campus population of size N=9000 is to be surveyed by a stratified sample for the prevalence of a certain disease based upon three strata of respective sizes $N_h$ = 1000, 3000, and 5000 for h = 1, ...
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26 views

Expected coverage of a set of random samples

For a set A, I'm running 8 independent random samples, each with a probability of 1/8=12.5% and is without replacement. I know that the set formed by the union of these 8 samples will be of a size ...
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31 views

Pearson Correlation for Clustered data

I have a sample that was drawn using cluster sampling. Let say I have variables x and y, and I would like to check the significance of correlation between those two variables in SPSS 20 taking into ...
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16 views

Sampling Distribution of mean for Poisson Distributions

Suppose I have random variables $X_i$ which are Poisson distributed with mean $\mu$. I m interested in the sampling distribution of the variable $\frac{X_1+...+X_n}{n}$. We now that as $n$ goes to ...
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1answer
27 views

Verifying representativeness of a sample, after simple random sampling

I just used the standard formula to determine the sample size of a sample to match the mean of a pupulation with an error margin of 3 percentage points and with a 90% probability. I know would like ...
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10 views

How to improve results when using sampling in skewed binary classification?

I am using a data set with 18 features with True/False output (Related to mobile ad targeting). True values occurs only 0.4 % of the time. So, I have used sampling to keep the ratio of True and False ...
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1answer
24 views

sample frame representing the true population

(i) Is it true to say that if the sample frame is not a random selection (such as a convenience sample), then the sample frame is not representative of the true population? (ii) We can always do a ...
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12 views

Down-sampling with building models (specifically random forests)

I was wondering if anyone had ever used down-sampling to build random forests with data that has unbalanced classes. Basically down-sampling samples (with replacement) x*min from the population where ...
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30 views

How do I sample only non-null values in R? [migrated]

Is there was a way to sample only non-null values in R? Currently, I have this code. s <- sample(200000, replace=TRUE); m <- mydata$myvar[s] However, some ...
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19 views

Incomplete questionnaires

Is it recommented to delete the cases from a database if the responses are highly incomplete? Is there a percentage that can be taken into consideration? (for example, deleting a case if more than 50% ...
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20 views

Sobol sequence for a set of discrete numbers

Is it possible to create a sobol sequence for a set of numbers? I have 5 discrete variables x1, x2, x3, x4 and x5 and say for example x1 = {1,2,3,4,5}, x2 = {10,30,40,50,60}, x3 = {1,3,5,7,9}, x4 = ...
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44 views

Linear regression without intercept - sampling variance of coefficient

I am comparing linear regression with and without intercept for the general sampling case. For this, I have $n$ samples of two correlated random variables $X \sim N\left(0,\sigma_X^2\right)$ and $Y ...
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How to get a representative sample from a large data frame given a factor [migrated]

If one column is a factor, but each subset of the data frame has a different size -- maybe a subset has thousands of rows, while another has tens or hundreds of thousands of rows -- sampling done with ...
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78 views

Given $N$ samples from $p(x|y=y_0)$ how can I infer $y_0$?

I have $N$ samples $x_i \sim p(x|y)$ for $y = y_0$. I don't know apriori what $y_0$ is but I know its a fixed value. I do not have the analytic form of $p(x|y)$, $p(y|x)$, $p(x,y)$. Instead I have ...
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37 views

Is it true that values of parameters do not vary from sample to sample?

This is something I was told. However, it seems to me that parameters of a population can be functions of time, in certain situations, in which case the values of parameters could vary from sample ...
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1answer
49 views

burn in for Metropolis Hastings MCMC

I was wondering if there is a principled way to figure out how many samples to discard during the MH-MCMC burn-in stage. So, as I understand it, the initial samples can introduce bias in the ...
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38 views

Gibbs sampling versus general MH-MCMC

I have just been doing some reading on Gibbs sampling and Metropolis Hastings algorithm and have a couple of questions. As I understand it, in the case of Gibbs sampling, if we have a large ...
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9 views

Sampling a high dimensional function

I have a function $f$ that takes $N$ real-valued inputs and is very expensive to compute. I am studying the properties of $f$ by generating samples. Each input $n$ has a range of values $(n_{min}, ...
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1answer
23 views

Dirichlet sample by normalising Gamma RVs

I know that if you sample $K$ random variables $(X_1, X_2, \dots, X_K)$ from Gamma distributions using shape parameters $(\alpha_1, \alpha_2, \dots \alpha_K)$ and a scale parameter $\theta = 1$ such ...
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1answer
42 views

Ratio of correlated sample variances (gamma distributed)

for $N$ samples of two correlated random variables $X \sim N\left(0,\sigma_X^2\right)$ and $Y \sim N\left(0, \sigma_Y^2\right)$ with correlation $\rho$, I am analyzing the ratio of the sample ...
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2answers
36 views

Difference between Research Design and Experimental Design

What is the difference between Research Design and Experimental Design? I can't see any difference. Both of them need to establish Causality. Both of them are the arrangement for collection and ...
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recommendations to analyze a survey of the entire sample frame with a 20% response rate

we surveyed all 10,000 professionals in a particular industry. The industry is highly-regulated, so we have contact information for everyone in our population of interest. We attempted to contact ...
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28 views

Aggregation of random samples

Suppose I have two distributions $X$ and $Y$, and I have a statistic $T(X, Y)$. If I have a random sample (iid) $X_1, ..., X_N$ taken from $X$ and a random sample (iid) $Y_1, ..., Y_M$ taken from $Y$, ...
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1answer
63 views

Improving SVM classification

I have a classification problem (bioinformatics domain) where I have around 333 features. Currently, I am first selecting features (using importance feature of random forest) and then pushing the same ...
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1answer
32 views

Convenience sampling - Distribution forcing?

I am conducting some experiments on a data set that was collected by convenience. It is a data set based on historical data, most of which is not digitized. I know the exact distribution of the ...
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89 views

Confidence interval for a proportion estimated through stratified sampling

When estimating the confidence interval for a binomial proportion $p$, with $\hat{p}$ near 0 or 1, one has to use something other than the Wald interval to get a reasonable estimate (see for instance ...
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29 views

Drawing a random Sample on a Probability Distribution

Say I have multiple normal or beta distributions. So I have two questions. How do I Draw a random sample from a distribution? How do I compare determine which of my distributions has the largest ...
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1answer
44 views

Error Bars for Monte Carlo Experiment

Suppose we have a random variable $X$, where $\mathbb{E}(X)$ and $\text{Var}(X)$ are known. I have computed $N$ number of MC-type samples from the distribution of $X$. Let $\bar{x} = \frac{1}{N}\sum ...
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Calculating power for a survey to compare different metrics

I am currently planning a survey. The data will be used to test which of three metrics best captures some "true" underlying characteristic of the respondents. Getting data on the "true" underlying ...
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23 views

Injective uniform distribution on an n-sphere

For an application I'm working on, I need to go from some uniformly distributed variables to an uniform distribution on an n-sphere. The standard way to do this seems to be choose (n+1) normal ...
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20 views

Cholesky decomposition and confidence ellipsoid

I'm trying to construct an error ellipsoid from a covariance matrix (which exists for a 3D point) and then sample consistent xyz points in this region. (This question succeeds this one.) What I'm ...
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1answer
85 views

Sampling distribution of regression coefficients for normally distributed random variables

Based on $N$ realizations of two random variables $X \sim N(0,\sigma_X^2)$ and $Y \sim N(0, \sigma_Y^2)$ with correlation $\rho$, I conduct a simple linear regression $Y = \beta_0 + X\beta_1 + ...
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1answer
31 views

How to estimate the change in prevalence of a trait in the population from non-random samples?

Suppose I am interested in the prevalence of drug use in a population over time, but I am unable to conduct audits (sample some transactions at random and check to see if drugs were exchanged). I do ...
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39 views

Iterative or Lazy Reservoir Sampling

I'm fairly well acquainted with using Reservoir Sampling to sample from a set of undetermined length in a single pass over the data. One limitation of this approach, in my mind, is that it still ...
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49 views

Trying to use Cholesky decomposition of covariance matrix to sample error ellipsoid

I'm trying to construct an error ellipsoid from a covariance matrix (which exists for a 3D point) and then sample consistent xyz points in this region. In a previous question when I asked about this ...
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1answer
30 views

Sampling brownian motions

I wish to sample standard linear Brownian motions on the interval $[0,1]$. I do this by dividing the interval into $n$ equal sub-intervals, deciding $B(0)=0$, and letting ...
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What is the name of the statistical fallacy whereby outcomes of previous coin flips influence beliefs about subsequent coin flips?

As we all know, if you flip a coin that has an equal chance of landing heads as it does tails, then if you flip the coin many times, half the time you will get heads and half the time you will get ...
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218 views

Is the sampling distribution for small samples of a normal population normal or t distributed? [closed]

If I know that the population is normally distributed, and then take small samples from this population, is it more correct to claim that the sampling distribution is normal or instead follows the t ...
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26 views

Determining characteristics of sampling sets for EFA/CFA/SEM

Dividing sample data into several sets seems to be a common approach in statistics. This is especially evident in predictive modeling, where samples are traditionally divided into two sets, usually ...