Creating samples from a well-specified population using a probabilistic method and/or producing random numbers from a specified distribution.
27
votes
8answers
2k views
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 ...
19
votes
8answers
1k views
How to estimate how many people attended an event (say, a political rally)?
A student asked me today, "How do they know how many people attended a large group event, for example, the Stewart/Colbert 'Rally to Restore Sanity' in Washington D.C.?" News outlets report estimates ...
19
votes
4answers
1k views
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 + ...
19
votes
3answers
975 views
What if your random sample is clearly not representative?
What if you take a random sample and you can see it is clearly not representative, as in a recent question. For example, what if the population distribution is supposed to be symmetric around 0 and ...
17
votes
1answer
172 views
Sampling model for crowdsourced data?
I'm working on an open health survey application, planned to be used in developing country.
The basic idea is that survey interviews are crowdsourced - they are performed by unorganized volunteers ...
16
votes
2answers
305 views
Is “every blue t-shirted person” a systematic sample?
I'm teaching an intro stats class and was reviewing the types of sampling, including systematic sampling where you sample every kth individual or object.
A student asked if sampling every person ...
15
votes
3answers
358 views
How to sample from $c^a d^{a-1} / \Gamma(a)$?
I want to sample according to a density
$$
f(a) \propto \frac{c^a d^{a-1}}{\Gamma(a)} 1_{(1,\infty)}(a)
$$
where $c$ and $d$ are strictly positive.
(Motivation: This could be useful for Gibbs ...
13
votes
4answers
2k views
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 ...
13
votes
4answers
396 views
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, ...
13
votes
2answers
399 views
Managing error with GPS routes (theoretical framework?)
I'm looking for the appropriate theoretical framework or speciality to help me deal with understanding how to deal with the errors that the GPS system has - especially when dealing with routes.
...
11
votes
3answers
265 views
An unbiased estimate of the median
Suppose we have a random variable $X$ supported on $[0,1]$ from which we can draw samples. How can we come up with an unbiased estimate of the median of $X$?
We can, of course, generate some samples ...
10
votes
1answer
2k views
Can someone explain Gibbs sampling in very simple words?
I'm doing some reading on topic modeling (with Latent Dirichlet Allocation) which makes use of Gibbs sampling. As a newbie in statistics -- well, I know things like binomials, multinomials, priors etc ...
10
votes
5answers
325 views
Can I use “left eye” and “right eye” in my sample as two different subjects?
My data is as follows. I have two groups of patients. Patients in each group had a different type of eye surgery. 5 variables were measured on patients in each group. I want to compare those variables ...
10
votes
5answers
4k views
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 ...
10
votes
3answers
463 views
Estimate the size of a population being sampled by the number of repeat observations
Say I have a population of 50 million unique things, and I take 10 million samples (with replacement)... The first graph is I've attached shows how many times I sample the same "thing", which is ...
10
votes
3answers
2k views
Can non-random samples be analyzed using standard statistical tests?
Many clinical studies are based on non-random samples. However, most standard tests (e.g. t-tests, ANOVA, linear regression, logistic regression) are based on the assumption that samples contain ...
10
votes
1answer
575 views
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 ...
9
votes
3answers
269 views
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 ...
9
votes
2answers
299 views
How to quickly sample X if exp(X) ~ Gamma?
I have a simple sampling problem, where my inner loop looks like:
v = sample_gamma(k, a)
where sample_gamma samples from the ...
8
votes
3answers
2k views
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 ...
8
votes
2answers
376 views
Solving a simple integral equation by random sampling
Let $f$ be a nonnegative function. I am interested in finding $z \in [0,1]$ such that
$$ \int_0^{z} f(x)\,dx = \frac{1}{2}\int_0^1 f(x)\,dx$$ The caveat: all I can do is sample $f$ at points in ...
8
votes
1answer
204 views
Definition of quantile
Given N sampled values, what does the "p-th quantile of the sampled values" mean?
8
votes
2answers
528 views
How to calculate sample size for simulation in order to assert some level of goodness in my results?
I am a stats newbie, so apologies in advance if I'm asking a braindead question. I have searched for answers to my question, but I find that many of the topics are either too specific, or quickly go ...
8
votes
1answer
170 views
Can I estimate the frequency of an event based on random samplings of its occurrence?
Some edits made...
This question is just for fun, so if it isn't fun then please feel free to ignore it. I already get a lot of help from this site so I don't want to bite the hand that feeds me. ...
8
votes
2answers
510 views
Sampling from bivariate distribution with known density using MCMC
I tried to simulate from a bivariate density $p(x,y)$ using Metropolis algorithms in R and had no luck. The density can be expressed as $p(y|x)p(x)$, where $p(x)$ is Singh-Maddala distribution
...
7
votes
4answers
245 views
Variance of resistors in parallel
Suppose you have a set of resistors R, all of which are distributed with mean Ī¼ and variance Ļ.
Consider a section of a circuit with the following layout: (r) || (r+r) || (r+r+r). The equivalent ...
7
votes
3answers
928 views
How to resample in R without repeating permutations?
In R, if I set.seed(), and then use the sample function to randomize a list, can I guarantee I won't generate the same permutation?
ie...
...
7
votes
1answer
163 views
Given that one can sample $X \sim f(x)$, is there an easy way to sample $Y \sim k \cdot f(g(y))$ (such as $k \cdot f(e^y)$)?
Say I'm able to sample an RV $X$ from a PDF $f(x)$, can I exploit this to efficiently sample another RV $Y \sim k \cdot f(g(y))$ (where $k$ is a normalizing constant)?
I'm interested in something ...
7
votes
1answer
106 views
How do you call this dynamic sample-size selection strategy?
Imagine that you want to assess the compressibility of a large document very fast. You could randomly pick a subsequence, try to compress it. This can serve as a prediction for the overall ...
7
votes
2answers
495 views
Using MCMC to evaluate the expected value of a high-dimensional function
I am working on a research project that is related to optimization and recently had an idea to use MCMC in this setting. Unfortunately, I am fairly new to MCMC methods so I had several questions. I'll ...
7
votes
1answer
671 views
How to calculate sample size for comparing the area under the curve of two models?
Because I would like to calculate the sample size for comparing the area under the curve (AUC) of 2 models (cross-sectional study, predictor = continuous variable). Can you point me which function in ...
6
votes
4answers
210 views
How can I sample from a distribution with incomputable CDF?
Semi-computer science simulation related problem here.
I have a distribution where
P(x) = $\frac{(e^b-1) e^{b (n-x)}}{e^{b n+b}-1}$
for some constants b and n, and x is an integer such that $0\leq ...
6
votes
2answers
541 views
Acceptance rates for Metropolis-Hastings with uniform candidate distribution
When running the Metropolis-Hastings algorithm with uniform candidate distributions, what is the rationale of having acceptance rates around 20%?
My thinking is: once the true (or close to true) ...
6
votes
2answers
321 views
Why is random assignment important in stratified sampling?
Background
I raised this question because of an argument I am having with a question from user697473 here. The title of his question is "Formal definiton of random assignment." In the post he ...
6
votes
1answer
81 views
Does it make sense to apply a chi-squared test on a contingency table when the whole population has been surveyed?
As I understand it, one of the main goal of the chi-squared test on a contingency table is to determine if the link between lines and columns of the table is "more" than the sampling bias and the ...
6
votes
1answer
131 views
Suggested books on spatial statistics
What are some of the best books for studying
i) variability of univariate and multivariate variables (real, count data) across a spatial domain.
ii) sampling a univariate or multivariate variable ...
6
votes
3answers
240 views
With a small sample from a normal distribution, do you simulate using a t distribution?
I want to simulate temperature data for some "what-if" calculations. The problem is, I only have a time series of 10 actual temperature data values. I want to use temperature as an input to the ...
6
votes
2answers
281 views
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 ...
6
votes
1answer
141 views
Capture-recapture sampling valid in literary analysis?
So I've been compiling a list of fictional (anime/manga) characters which meet a certain criteria (http://www.gwern.net/hafu#list) from a universe of all anime/manga characters since 1963 (which is of ...
6
votes
1answer
221 views
How to generate a Bernoulli variate with bias $a/\mathbb{E}[X]$ given a sampler of $X$ and uniform variates?
Given:
A loaded "die" with unknown probabilities generating a discrete, positive random variable $X$ taking on values in $\mathcal{X}$.
A real number $a$, such that $0 \leq a \leq \mathbb{E}[X]$.
...
6
votes
2answers
330 views
Subsample of a random sample: random sample?
Let's say you have a large random sample of soccer players in Europe but you are only interested in what happens in Spain. Could you reduce your sample to players in Spain and still call it a random ...
6
votes
3answers
427 views
6
votes
1answer
228 views
Estimating the variance of poker win rates
Suppose you have a casino with n poker players. Each player has a win rate - the amount of money he wins or loses per hand. We assume that these win rates are normally distributed with a mean of 0. ...
6
votes
0answers
167 views
Gaussian Like distribution with higher order moments
For the Gaussian distribution with unknown mean and variance, the sufficient statistics in the standard exponential family form is $T(x)=(x,x^2)$. I have a distribution that has ...
5
votes
4answers
2k views
Why is it claimed that a sample is often more accurate than a census?
When learning the course of sampling, I meet the following two statements:
1) Sampling error leads to mostly variability, nonsampling errors lead to bias.
2) Because of nonsampling error, a sample ...
5
votes
3answers
254 views
Why are samples within a cluster less informative than randomly chosen ones from entire population?
Please give me mathematical explanation if possible. And also in the book Kothari 2004, it says:
There is also not as much information in ānā observations within a cluster as there happens to be ...
5
votes
4answers
866 views
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 ...
5
votes
3answers
214 views
Sampling with non-uniform costs
Suppose that I have a population, each represented by a bit $b_i$ for $i \in \{1,\ldots, n\}$. I would like to compute an estimate $\hat{B}$ of the parameter $B = \sum_{i=1}^nb_i$ so that with high ...
5
votes
1answer
201 views
How do I determine how well a dataset approximates a distribution?
Quite simple, I have some probability distribution p(x), how can I measure whether one empirical density (set of delta masses) is a better approximation than another. I know that KL-divergence is a ...
5
votes
2answers
401 views
Recommend references on survey sample weighting
Let's aim for some at an introductory level, some articles and some textbooks. Applied is more helpful, including R code is great. Thanks!
