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

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Escobar and West Sampler for Dirichlet Process Parameters

I am reading Escobar&West paper and in particular am interested in their Gibbs sampler for the concentration parameter of Dirichlet Process. The issue I have is at the end of their section 6, ...
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23 views

When is Latin Hypercube Sampling (LHS) a good idea?

In this paper: http://salserver.org.aalto.fi/vanhat_sivut/Opinnot/Mat-2.4108/pdf-files/emat08.pdf [1] equation 6 shows that if $\operatorname{ cov} \left(f\left(x_1\right),f\left(x_2\right)\right)$ is ...
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8 views

Sampling concentration parameter of DP via Slice sampling?

Is there a published work which shows how sampling the Dirichlet Process's concentration parameter can be done via Slice sampling?
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5 views

How do I know if LHS will reduce my sampling error?

In this paper: http://salserver.org.aalto.fi/vanhat_sivut/Opinnot/Mat-2.4108/pdf-files/emat08.pdf equation 6 shows that if $cov(f(x_1),f(x_2))$ is positive LHS does not reduce random sampling error. ...
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28 views

How does data augmentation reduce overfitting?

I'm trying to understant the benefit apported by the step of data augmentation in a classification algorithm. I have a vector of hexadecimal strings and a column vector containing the label ...
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13 views

About Sampling Technique [on hold]

What sampling techniques would be most appropriate if the researcher’s goal is to make statistical inferences from a sample to the population?
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23 views

How to Gibbs sample proportional to a probability

I am reading this tutorial on Hierarchical Chinese Restaurant Process. On pdf page 141 (slide title: MCMC Problem Specification for N-grams) it says: $$F(s_{1,k})=\frac{\alpha^{S'_1+s_{1,k}}}{(\alpha)...
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198 views

Sampling from an Inverse Gamma distribution

I am using Gibbs sampling in the MCMC estimation of a stochastic volatility model. One of the posterior distributions is an Inverse Gamma distribution.I was struggling with the sampling procedure or ...
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117 views

Gibbs sampling with constraints

I am reading tutorials on Gibbs sampling for partition sampling in Dirichlet Process (Chinese Restaurant Process), and have been struggling to understand the terminology used in the tutorials. To ...
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12 views

r SMOTE return NA even the original data set contains no NA

I am trying to use SMOTE to tackle my imbalance data set. However, I don't know why it produced NA even though my original data set contains no NA. I also noticed the result is not even balanced. What ...
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9 views

Repeated sampling via stochastic approximation to estimate noise

In stochastic approximation algorithms, one is interested in finding zeroes or extrema of functions which cannot be computed directly and that we can only observe via noisy observations. To accomplish ...
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28 views

Random Variables, Samples and Population

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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14 views

Sampling from Hierarchical Distribution

Let's say I know $$ X \mid \mu, \sigma \sim \mathcal{N}(\mu, \sigma^2), \qquad \mu \sim Unif(a, b), \quad \sigma \sim Unif(c, d), $$ and I want to sample from $X \mid \mu, \sigma$. Is there a go-to ...
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121 views

How can we get a normal distribution as $n \to \infty$ if the range of values of our random variable is bounded?

Let's say we have a random variable with a range of values bounded by $a$ and $b$, where $a$ is the minimum value and $b$ the maximum value. I was told that as $n \to \infty$, where $n$ is our sample ...
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1answer
48 views

Drawing sample size 1 from a uniform distribution - Difficulty in understanding Central Limit Theorem?

Let's say we have a uniform distribution and we are drawing samples of size 1 so that the mean is the drawn number itself. If we perform this activity sufficiently large number of times we would get ...
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2answers
27 views

How do you mechanically draw a sample of size n from N without replacement

Say I have a physical (or virtual) jar or N marbles and I wish to draw n marbles at random without replacement where the likelihood of each n marbles being drawn is 1/N ... how do I do that? Is that ...
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11 views

Accuracy of sampling from a Gaussian distribution

I am currently sampling data points out of a Gaussian distribution with a particular mean and standard deviation. I want to compare how close the sampled Gaussian distribution is to the Gaussian ...
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11 views

Is there an R package which implements choice-based sampling? [closed]

I am planning to implement Choice-based sampling. Is there a R package implements this? Thanks
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15 views

Approximate computation of a linear function

I am not sure that this is the right stackexchange site for this, but here goes: Let $d_1,\ldots,d_n$ be known real numbers, some positive, some negative. Let $v_1,\ldots,v_n$ be non-negative numbers ...
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2answers
278 views

What does “mixing” mean in sampling?

I keep seeing this term "mixing": when people want to show their sampler works better, they say it "mixes" better. The term is a little counter-intuitive.
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8 views

how to sample “partitioning arrangement” and “parameter” in Dirichlet process?

This is rather a simple question. I know how to sample the partitioning arrangement (i.e. in Chinese restaurant process metaphor the seating arrangements), and parameter of Dirichlet Proces, but I don'...
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54 views

Expectation and variance of sample mean with random sample size

I have a question regarding sampling where the sample size itself is a random variable. Say I have two sub-populations $A$ and $B$ from which I can sample a real valued random variable with ...
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1answer
12 views

Sampling Distribution question - Probability finding

Suppose it is known that 8% of males are color blind. In a random sample of 500 males, what is the approximate probability that at least 10% of them are color blind? I am doing review for finals ...
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43 views

Why are all CLT problems using a single random sample when the CLT requires “repeatedly drawing random samples”?

In our course notes, it says: "The CLT states that if random samples of size $n$ are repeatedly drawn from any population with mean $\mu$ and variance $\sigma^2$, then when $n$ is large the ...
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1answer
33 views

How can I calculate when a text corpus is representative of a language?

I am collecting and analyzing articles and other publications for building a text corpus. I'd like to know how to calculate when my text corpus is representative of a field. That is, how many texts, ...
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7 views

Possibility of using stratification to reduce the variance of an estimator

The problem in brief There are two schools run by missionaries located in the same compound. The applicant children have to sit for a common admission test for these two schools. Those who fail are ...
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21 views

How to calculate a sample size in the case of a stratified 3 degrees sample design ?

I am trying to calculate the sample size (and the repartition between PSUs and SSUs) needed to obtain an estimation of a proportion (that I assume to de around 50%) with a 0.05 standard error in the ...
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1answer
18 views

How to design a train and test set from a labeled dataset with class imbalance?

The labeled dataset I am using is almost 80% positive examples, 20% negative examples. However, I do not know the distribution of the data fed into the classifier. In this case, does it make sense ...
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9 views

Rule of Thumb for Relative Margin of Error

I need to do some survey sampling and am approximating the sample size I need. The key statistic I want to measure is a Yes/no question and I suppose very few people will vote for yes (~1% probably). ...
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1answer
65 views

Add extra level to multilevel model that was not part of the sampling process

Consider a population of students, clustered within schools. We are interested on explaining results of a math test at the student level. Assume we use a multistage sampling process in order to ...
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29 views

Smart sampling techniques to ensure boundary/edge cases are included

In an effort to reduce the time it takes to test software against various data sets I would like to do create an application that looks at a data set and creates a "smart sample" from the it. The ...
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15 views

Evaluate “sampling error” due to lack of data

I'm working on a problem of evaluating the long term success of some investments in some companies around Europe. My problem is that I have the information, before the investment was done, of say 100 ...
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24 views

Systematic sampling and informed consent: Does the requirement for informed consent introduce sampling bias into randomly selected samples

Probability sampling methods help reduce sampling bias. In clinical research, simple random sampling methods works well for randomised control trials, and systematic sampling methods are easy to ...
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12 views

Sample size determination for estimating a count

I want to estimate a simple variable: "**how many times my website is visited in 2015?". Suppose that I cannot count all visits to my website (it is expensive!), but I can count the connections on ...
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16 views

How to deal with a non representative sample [duplicate]

Say we want to know whether age can explain the probability of a particular response (which is binary 0 = negative and 1 = positive). Plotting the data and applying a logistic regression we get the ...
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22 views

Variance of an unbiased estimator is 0 when the sample size goes to infinity

So I would like a proof for the following but I can't seem to do it myself. I have a random variable $X$ and I draw $n$ samples($\{X_1, \ldots, X_n\}$) from it and I have $$ Z_n = \frac{\sum_{i = ...
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14 views

Picking tuples from a list with low discrepancy

Given a list of m items, I am looking for a way to repeatedly pick a tuple of n distinct items from this list with low discrepancy. For example, suppose I have a list of 3d points, and I want to ...
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8 views

Can two stage cluster sampling have clusters of size zero?

Can a cluster size be zero in cluster sampling? Say in a two stage cluster sampling, one has unequal cluster sizes with some zero-sized clusters, which means no items will be sampled from the zero-...
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1answer
50 views

Bootstrapping a sample from a finite population

Can someone point me to some reference for theory on bootstrapping a sample took from a population of known size? I am used to use Bootstrap to calculate confidence intervals of a sample when the ...
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9 views

Citation of a particular paper discussing the phrase “representative” sample

Some time ago (like decades?) I read a paper that gently explained why the phrase "representative sample" is an unfortunate and misleading usage, and why one should speak of random samples, perhaps in ...
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49 views

sampling from a distribution: other ways than Markov Chain Monte Carlo

I have this density $f(y|z) = \kappa*\exp(-\kappa y) / (1 - \exp(-\kappa z))$, where $\kappa$ is some known value and $0 < y < \kappa$. I get the distribution by integrating with respect to $y$. ...
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3answers
95 views

Sampling without Replacement and Non-uniform Distribution

There are $N$ items, numbered $1 \ldots N$. The probability of selecting item $i$ in one draw is $p_i$. Items are drawn without replacement, so after each draw we need to do a re-normalization. Now, ...
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1answer
43 views

Sample From a 'Constrained' Distribution

Consider identically distributed random variables $X_1, \dots, X_n$ and a constant $k \in [0,n]$. How would I sample from the distribution $$ f_{X_1,\dots,X_n}(x_1, \dots, x_n) = c \cdot I[(\sum_{i=...
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1answer
59 views

Statistical test for random sample of data

I'm trying to determine if some particular measurements - in this case taken from a subset of genes of interest (50 genes) - show a significant difference to the rest of the population (15000 genes), ...
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37 views

How to sample from a variational autoencoder when KLD is not small?

I am training a variational autoencoder on samples of large size (4-D images of size 224 x 224). I have tried training with many different hyper parameter settings and the average KLD term is not ...
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9 views

Case control study - possible options

Lets assume that I have a two populations ${A, B}$ and they are different in terms of some features such as country. Both samples have fairly large number of ...
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19 views

How to choose the test set size when the training set size is given?

I have data on 64 subjects collected in a medical setting. With the help of ROC curve analysis and bootstrapping, I have identificed two predictors for illness(present or not present) in the group. ...
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42 views

Calculating power of a sample (need a layman's/beginner's definition)?

We have a bi-annual survey and an intended sample size of 1,300. This sample size was determined using Krejcie's means formula for finite populations, and we drew the sample using 2-stage clustering. ...
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Estimating minimum sample size for item ranking based on frequencies

Assume that we observe some objects (e.g. people, car models, etc.). Our task is to sort objects based on their frequency of observation. For example, Here is the top 5 best-selling cars in America: ...
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Generating samples from high-dimensional multivariate Gaussian with few training samples

Say I have a $n\times d$ dataset $D$ where $n\ll d$ ($n$ number of observations, $d$ number of dimensions). Currently, if I want $m$ samples from $D$ assuming it is multivariate Gaussian, I can do ...