# Tagged Questions

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

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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 ...
293 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 ...
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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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### 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, ...
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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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### 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 ...
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### How can I simulate census microdata for small areas using a 1% microdata sample at a large scale and aggregate statistics at the small area scale?

I would like to perform an individual-level multivariate analysis at small levels of geographic aggregation (Australian census collection districts). Clearly, the census isn't available at these ...
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### Explanation of finite 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 a correction on the sample's mean and standard error using this formula: ...
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### 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 ...
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### Sample size for a variable number of answers

I have N different possible results (ex. red, yellow, or blue). I go to a population of infinite size and ask a bunch of people a question the answer to which is one of the N options.... How large ...
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### 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 ...
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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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### Derive househould weights from a uniformly distributed person sample

The Swiss Public-Use Sample of the national census is a 5% sample drawn from the entire census survey. According to the documentation, the persons are sampled uniformly without replacement. Persons ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Random permutation of a vector with a fixed expected sample correlation to the original?

Suppose you have an $n$-vector $X$. For a fixed real number, $r$ between $-1$ and $1$, can one generate a random permutation of the integers $1,2,\ldots,n$, call it $i_1,i_2,\ldots,i_n$ such that the ...
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### What is a representative sample?

I understand the rationale that underpins representative sampling (i.e. to avoid bias so that the sample 'broadly' represents the target population). Suppose the size of the target population is 600 ...
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### Definition of quantile

Given N sampled values, what does the "p-th quantile of the sampled values" mean?
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### Variance of resistors in parallel

Suppose you have a set of resistors R, all of which are distributed with mean μ and variance σ. Consider a section of a circuit with the following layout: (r) || (r+r) || (r+r+r). The equivalent ...
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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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### Sampling from a fixed population

Here's a real basic question. I'm trying to teach myself a bit of stats with Verzani's Using R for Introductory Statistics. In question 5.13 he asks: A sample of 100 people is drawn from a population ...
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### Posterior distribution for multinomial parameter

(topic moved from maths.stackexchange.com) I'm currently developing an application integrating a probabilistic inference engine for Bayesian Networks. The Bayesian Network integrates some form of ...
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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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### What alternatives are there for dataset reduction beside the random sampling?

I have 3 millions instances with 30 features each and I am trying to reduce it in a sensible size for my computer for a classification problem. What are possible methods I can use to reduce the data ...
512 views

### Statistical significance of a survey/poll?

Let's pretend I'm conducting a poll/survey. It's a simple yes/no poll (i.e. everyone only gives 1 of 2 answers). I have asked N people so far, and X of them have said "yes". I would like to stop ...
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### Random sampling (Real data) is so important, why?

How it is understandable for computer (or software) that a sampling method is Random? In fact, it is possible to data sampling by random method in N cases but one of the N cases been like as ...
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### Is it necessary for a sample to broadly reflect the target population distribution?

Following the question here, the target population is made up of 600 units which are distributed as follows: while units (17%) black units (42%) green units (8%) yellow units (33%) A ...
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### 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. ...
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### 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 ...
564 views

### Do confidence intervals apply to quota sampling?

French polling institutes are currently facing a major crisis after they recently published what can only be called the most ridiculous poll so far on the 2012 presidential election horse race. The ...
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### 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 ...
414 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 ...
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### Who first developed the idea of “sampling distributions”?

Who created sampling distributions? I have looked everywhere and I'm writing a paper, but, so far, all I've been able to come up with is the theory and the definition. Please help me find the who, ...
339 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 ...
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### 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 ...
291 views

### Assessing the representativeness of population sampling

I am looking for some suggestions about assessing the representativeness of a particular dataset I am analyzing. In this dataset I am looking at the relationship between two variables (e.g., X and ...
143 views

### Can one force randomness in a sample?

I recently spoke to a large qualitative analysis company who were working on in-depth analysis of the potential customers of train company. I asked them how they chose the people to include in their ...
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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 correct uneven sampling distribution when calculating the mean?

Suppose I have a function f, and I want to sample it at 100 points in the interval [0, 100]. For some reason (that seemed smart ...
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### With simple random sampling, how to approximate variance of R=avg(Y)/avg(X)?

Recenly I am reading "Mathematical statistics and data analysis" written by Rice myself. At page 207, theorem A said: With simple random sampling, approimxate variance of ...
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### Optimal importance sampling with ratio estimator

This is probably a stupid question, but here goes: so we want to approximate the following expectation: $$\mathbb{E}[h(x)] = \int h(x)\pi(x) dx$$ Where $h(x)$ is an arbitrary function and $\pi(x)$ is ...
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### Inference to the population when the survey response rate is only 30%

I have conducted a survey in which the questionnaires were sent out to 450 individuals, but only 30% of them answered the questionnaires. Is it still valid to interpret the usual inference analysis ...
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### Sampling from marginal using integrated conditional

I would like to sample from: $$p(\theta_2|x)=\int p(\theta_2|\theta_1,x) . p(\theta_1|x) . d\theta_1$$ knowing that I can easily sample from $p(\theta_1|x)$ and (less easily) from ...
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### Most efficient way of sampling a product of distributions $k \cdot f(x) \cdot g(x)$, given that PDFs $f(x)$ and $g(x)$ can easily sampled?

Is there an efficient approach tailored to sampling from a PDF $k \cdot f(x) \cdot g(x)$ (where $k$ is a normalizing constant) that would perform better than naive Metropolis, slice sampling, etc.? ...
Low-discrepancy sequences in a real space ($[0,1]^n$) seem like a really excellent tool for evenly sampling a sample space. As far as I can tell, they generalise well to any real space, if you use an ...