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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Why does a 95% Confidence Interval (CI) not imply a 95% chance of containing the mean?
It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our ...
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Central limit theorem for sample medians
If I calculate the median of a sufficiently large number of observations drawn from the same distribution, does the central limit theorem state that the distribution of medians will approximate a ...
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Statistical inference when the sample "is" the population
Imagine you have to do reporting on the numbers of candidates who yearly take a given test. It seems rather difficult to infer the observed % of success, for instance, on a wider population due to the ...
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Why is the sampling distribution of variance a chi-squared distribution?
The statement
The sampling distribution of the sample variance is a chi-squared distribution with degree of freedom equals to $n-1$, where $n$ is the sample size (given that the random variable of ...
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Explanation of finite population correction factor?
I understand that when sampling from a finite population and our sample size is more than 5% of the population, we need to make a correction on the sample's mean and standard error using this formula:
...
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4
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Calculating required sample size, precision of variance estimate?
Background
I have a variable with an unknown distribution.
I have 500 samples, but I would like demonstrate the precision with which I can calculate variance, e.g. to argue that a sample size of 500 ...
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2
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Size of bootstrap samples
I'm learning about bootstrapping as a means of estimating the variance of a sample statistic. I have one basic doubt.
Quoting from http://web.stanford.edu/class/psych252/tutorials/doBootstrapPrimer....
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3
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Generating data with a given sample covariance matrix
Given a covariance matrix $\boldsymbol \Sigma_s$, how to generate data such that it would have the sample covariance matrix $\hat{\boldsymbol \Sigma} = \boldsymbol \Sigma_s$?
More generally: we are ...
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1
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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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3
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Determine if a heavy tailed distributed process has improved significantly
I observe processing times of a process before and after a change in order to find out, if the process has improved by the change. The process has improved, if the processing time is reduced.
The ...
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Computation of the marginal likelihood from MCMC samples
This is a recurring question (see this post, this post and this post), but I have a different spin.
Suppose I have a bunch of samples from a generic MCMC sampler. For each sample $\theta$, I know the ...
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1
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Why is it that if you undersample or oversample you have to calibrate your output probabilities?
There are a number of stackexchange posts saying that you have to calibrate your probabilities if you oversample and undersample like 1,2. But my question is why?
Lets use an example of detecting spam ...
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Is a sample covariance matrix always symmetric and positive definite?
When computing the covariance matrix of a sample, is one then guaranteed to get a symmetric and positive-definite matrix?
Currently my problem has a sample of 4600 observation vectors and 24 ...
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1
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MCMC on a bounded parameter space?
I am trying to apply MCMC on a problem, but my priors(in my case they are $\alpha\in[0,1],\beta\in[0,1]$)) are restricted to an area? Can I use normal MCMC and ignore the samples that fall outside of ...
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2
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Best suggested textbooks on Bootstrap resampling?
I just wanted to ask which are in your opinion the best available books on bootstrap out there. By this I don't necessarily only mean the one written by its developers.
Could you please indicate ...
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4
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Are "random sample" and "iid random variable" synonyms?
I have been facing hard time understanding meaning of "random sample" as well as "iid random variable". I tried to find out the meaning from several sources, but just got more and more confused. I am ...
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Sampling from marginal distribution using conditional distribution?
I want to sample from a univariate density $f_X$ but I only know the relationship:
$$f_X(x) = \int f_{X\vert Y}(x\vert y)f_Y(y) dy.$$
I want to avoid the use of MCMC (directly on the integral ...
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1
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Intuitive examples of importance sampling
My background is computer science. I am fairly new to monte carlo sampling methods and, although I understand the math, I have hard time coming up with intuitive examples for importance sampling. More ...
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7
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How to prevent collinearity?
Ieno & Zuur 2015 describe a number of causes of collinearity among explanatory variables entered into a linear regression. One of these causes is what they call a 'data collection' cause.
They ...
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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:
\begin{align}
...
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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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Why do political polls have such large sample sizes?
When I watch the news I've noticed that the Gallup polls for things like presidential elections have [I assume random] sample sizes of well over 1,000. From what I remember from college statistics ...
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Strategies for teaching the sampling distribution
The tl;dr version
What successful strategies do you employ to teach the sampling distribution (of a sample mean, for example) at an introductory undergraduate level?
The background
In September I'll ...
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What are some techniques for sampling two correlated random variables?
What are some techniques for sampling two correlated random variables:
if their probability
distributions are parameterized
(e.g., log-normal)
if they have non-parametric
distributions.
The data are ...
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2
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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 $c(\vec{\beta}...
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1
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Sampling distribution of sample variance of non-normal iid r.v.s
In a first course in statistics we are taught that when we do not know the true variance, we can still perform certain basic tests on the sample mean using the sample variance, $S^2$, instead -- ...
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3
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How to Understand the Relationships Among Random Variables, Samples, and Populations?
I am trying to understand the relationship of a Random Variable to a population and random samples. I understand that a Random Variable is a function that maps each event in a sample space to a number....
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Sample size for categorical data
I have a population of phone calls - 200,000.
There are different reasons for each call, but lets assume the number of reasons is known.
i.e. 7 different call reasons:
1) Check on order
2) Cancel ...
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Is sampling relevant in the time of 'big data'?
Or more so "will it be"? Big Data makes statistics and relevant knowledge all the more important but seems to underplay Sampling Theory.
I've seen this hype around 'Big Data' and can't help wonder ...
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How to sample from a normal distribution with known mean and variance using a conventional programming language?
I've never had a course in statistics, so I hope I'm asking in the right place here.
Suppose I have only two data describing a normal distribution: the mean $\mu$ and variance $\sigma^2$. I want to ...
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What does "independent observations" mean?
I'm trying to understand what the assumption of independent observations means. Some definitions are:
"Two events are independent if and only if $P(a \cap b) = P(a) * P(b)$." (Statistical Terms ...
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Difference between Randomization test and Permutation test
In the literature the terms Randomization and Permutation are used interchangeably. With many authors stating "Permutation (aka randomization) tests", or vice versa.
At best I believe the difference ...
user10961
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How can I estimate unique occurrence counts from a random sampling of data?
Let's say I have a large set of $S$ values which sometimes repeat. I wish to estimate the total number of unique values in the large set.
If I take a random sample of $T$ values, and determine that ...
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Simulate 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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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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What exactly does 'representative sample' refer to?
When reading passages like the following:
Based on a representative sample of 88 recent raids, we show that the Turkana sustain costly cooperation in combat at a remarkably large scale, at ...
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How to estimate $P(x\le0)$ from $n$ samples of $x$?
Suppose, we have $n$ samples $x_i$ of a random variable:
$$x \sim \mathcal N(\mu,\sigma^2) $$
Based on the samples, we want to estimate the probability that $x$ is negative:
$$P(x\le0)$$
Intuitively, ...
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Acceptance-Rejection Method Acceptance Probability Proof
I did not fully understand the proof of the acceptance probability.
The acceptance-rejection algorithm is described as follows:
suppose you have RVs $X$ and $Y$ with densities $f$ and $g$, ...
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1
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Sampling from conditional copula
I am having trouble finding anything on sampling from conditional copulas. I am only
interested in the bivariate case. So, if $C(u,v)$ is my copula, I want to sample from
it given a specific ...
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1
answer
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Using Rule of Three to obtain confidence interval for a binomial population
I have a large population of data instances (say, 1000 instances) that are either of class1 or of class2. I would like to obtain ...
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How to interpret the margin of error in a poll?
Recently the media reported on a political poll that stated that "46% of Republican voters in Mississippi think that interracial marriage should be illegal". One example story (of many around the '...
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3
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Identifying the population and samples in a study
I apologise for the silliness of this question. I ran an e-learning experiment using a class of undergrads. Participation was voluntary, so only half of the class participated.
I know that my sample ...
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Probability of not drawing a word from a bag of letters in Scrabble
Suppose you had a bag with $n$ tiles, each with a letter on it. There are $n_A$ tiles with letter 'A', $n_B$ with 'B', and so on, and $n_*$ 'wildcard' tiles (we have $n = n_A + n_B + \ldots + n_Z + n_*...
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Did I just invent a Bayesian method for analysis of ROC curves?
Preamble
This is a long post. If you're re-reading this, please note that I've revised the question portion, though the background material remains the same. Additionally, I believe that I've devised ...
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Can someone help to explain the difference between independent and random?
In statistics, does independent and random describe the same characteristics? What's the difference between them? We often come across the description like "two independent random variables" or "...
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Generating random samples from a custom distribution
I am trying to generate random samples from a custom pdf using R. My pdf is:
$$f_{X}(x) = \frac{3}{2} (1-x^2), 0 \le x \le 1$$
I generated uniform samples and then tried to transform it to my custom ...
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4
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How to generate a non-integer amount of consecutive Bernoulli successes?
Given:
A coin with unknown bias $p$ (Head).
A strictly positive real $a > 0$.
Problem:
Generate a random Bernoulli variate with bias $p^{a}$.
Does anyone know how to do this? For instance, when ...
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How to choose the training, cross-validation, and test set sizes for small sample-size data?
Assume I have a small sample size, e.g. N=100, and two classes. How should I choose the training, cross-validation, and test set sizes for machine learning?
I would intuitively pick
Training set ...
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How can I draw a value randomly from a kernel density estimate?
I have some observations, and I want to mimick sampling based on these observations. Here I consider a non-parametric model, specifically, I use kernel smoothing to estimate a CDF from the limited ...
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simple sampling method for a Kernel Density Estimator
I have developed a simple Kernel Density Estimator in Java, based on a few dozen points (maybe up to one hundred or so) and a Gaussian kernel function. The implementation gives me the PDF and CDF of ...
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