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

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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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6 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
47 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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14 views

Sampling from the posterior of a bivariate exponential distribution [closed]

I have $X\sim Exponential(\alpha)$ and $Y\sim Exponential(\beta)$, $\alpha>0$, $\beta>0$, $x>0$, $y>0$. $X$ and $Y$ are independent, which makes the likelihood $\alpha \exp(-\alpha x)\beta ...
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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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1answer
48 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
84 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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50 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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17 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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1answer
17 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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2answers
41 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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1answer
9 views

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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35 views

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 ...
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17 views

Make two distributions equal

Question in short: How can I make two histograms equal by explicitly downsampling the buckets? More detailed version: I have realizations of sequences of two discrete random variables both giving ...
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1answer
30 views

Gibbs sampling and Conjugate Priors

Are conjugate priors required when performing Gibbs sampling?
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16 views

Gibbs Sampling for LDA example

Can someone provide an example of 1 (or more) iteration(s) of Gibbs sampling for LDA using real values? I have been searching for a while and I can't seem to find any good examples. Thank you.
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9 views

Blocking and representative samples

I am trying to measure the Net Promoter Score of a segment of customers for an online product. There is an attribute of these customers that I believe might affect their Net Promoter Score. So I want ...
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13 views

Random sampling as a Gauss-Markov assumption [duplicate]

In Wooldridge's Introductory Econometrics it is stated that random sampling is a Gauss-Markov assumption. As such it is a necessary condition for the unbiasedness of OLS estimators. While this can ...
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21 views

Algorithm to maximize variance within classes in two dimensions under constraint

I am working on a problem that has two dimensions, A and B. Within the two dimensions, there are 6,140 unique points. Each point has a cost associated with it. I have a total cost that I cannot ...
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1answer
41 views

Sampling distribution of unbiased estimator

Is the sampling distribution of an unbiased estimator symmetrically centered around the true value of the parameter? Why? Why not? Intuitively I think the question above is true (since I can use the ...
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1answer
9 views

number of sample I can select smaller than number of strata

I ran into a practical sampling question. I have 24 strata but I can only select 20 stores due to budget/practical constraints. What's the best way to select these 20 stores and how to correct it in ...
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30 views

Bayesian Data Analysis: Section 3.4 Sampling from the joint posterior distribution Example

For reference: $$ p(\sigma^{2}|y) \propto \tau_n N(\mu_n | \mu_0, \tau_0^{2}) \text{Inv}-\chi^{2}(\nu_0, \sigma^{2}_0) \prod_{i=1}^{n} N(y_i|\mu_n,\sigma^{2}) \tag{3.14} $$ The book states: As ...
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1answer
20 views

Bayes Rule for Random Samples?

Suppose I have $M$ samples from unknown distributions $F(X)$ and $F(Z|X)$. Is there a way from these two vectors to get samples of $F(X|Z)$? I understand Bayes rule, but I only know how to apply it ...
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68 views

Sample size for multinomial distribution

Suppose we have multinomial distribution with $k$ outcomes having the same probability $1/k$. What sample size do we need to guarantee with the probability $95\%$ that $m$ of the oucomes occur at ...
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2answers
57 views

Why would I use any MC technique other than basic sampling

I'm trying to learn sampling techniques. Lots of tutorials say that they are useful when "you can't sample directly from the pdf...." q1) If I have the algebraic form of the pdf can't I always sample ...
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1answer
32 views

How to include prior information about target pdf in MCMC

Is there a somewhat principled way to include prior information about a target density $f(x)$ in a sampling (MCMC) algorithm? [This is a much better formulated version of this question, which I am ...
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3 views

Can we do use convenience and purposive sampling at the same time?

Easy accessibility as the reason for choosing the participants but at the same time samples that have been purposely selected
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81 views

Sampling from $f(x)$ given approximation $g(x)$

(After some pondering, what I really wanted to ask is how to incorporate prior information about $f$ into a sampling method - see this question.) Suppose you want to draw samples from an (...
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1answer
23 views

Does picking randomly from an imbalanced group balance the group?

If I had a bag of marbles with 75% blue and 25% red (ratio is what matters not raw number, so this applies to 100 marbles, 1000 marbles, 100000 marbles) So if I had this imbalance of 75% blue and 25% ...
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32 views

How to determine if sampling is representative/similiar to my population

Let say for whatever reason I have obtained a sample of an initial population. (ie. we have paired case:controls on a set of confounders). I wish to compare how representative my sampled (or let me ...
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29 views

Markov chain Monte Carlo sampling using CDFs instead of PDFs

I wonder if there is any MCMC sampling method which uses the definition of the target CDF instead of the target PDF; however, I may use a proposal PDF. I would like to use Metropolis-Hastings but it ...
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6 views

Splitting an i.i.d. sample in two by criterion - what survives of independence and population representation?

Assume that I have available a $k$-dimensional i.i.d. sample of size $n$, collected in the $n \times k$ matrix $\mathbf X$. Each column represents a series of realizations from a random variable. ...
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3answers
62 views

Simulating random variables from a discrete distribution

I have the following discrete distribution where $p$ is a known constant: $p(x,p)= \frac{(1-p)^3}{p(1+p)}x^2p^x , (0<p<1), x=0, 1, 2, \ldots$ . How can I sample from this distribution?
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1answer
14 views

Chi squared test sample size

I'm trying to figure out if there's a difference across the main capitals in Europe and the voting preference of their inhabitants for extreme right political parties. So far I have categorized all ...
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15 views

Latin Hypercube/Orthogonal sampling

With some many R packages, which ones would you advise for doing LHS or Orthogonal Sampling? Also, could you give some introductory references on sampling design? Any help would be appreciated.
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1answer
28 views

Any good working method for sampling from estimated distribution in R

Suppose I have a number of points $\{x_i\}_{i=1}^N$ and I want to estimate the smooth distribution and sample from it. I have tried at the moment a lot of things, and all of them show poor ...
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29 views

R: estimate joint density and sample from conditional densities

I'm trying to implement an algorithm that estimates time-homogeneous Markov chain with continuous state space. The probability of transition from state $i$ to state $i+1$ has continuous conditional ...
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1answer
46 views

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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24 views

How to draw samples from a multivariate Gaussian distribution without having access to a function that does the job? [duplicate]

I am using the programming language Lua which does not have any built-in function for drawing samples from a multivariate Gaussian distribution. So I wonder, how can one implement a function that does ...
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34 views

Is controlling for cluster good enough in an analysis with a clustered sample?

I'm trying to understand how sampling design affects analyses and I'm a little confused about how to adjust for clustering. From what I've read, when you have a clustered sample you are supposed to ...
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8 views

What are some offline metrics for sparse data set

I have a real world machine learning problem: Predicting whether user will buy a item on our website. The model we used is point wise logistic regression and the offline metric is AUC. With about ...
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1answer
84 views

Distribution of posterior mean from different datasets

This question has originated from this question. Suppose we have the following simple setup, for $i = 1, \dots, n$ $$y_i \mid \mu \sim N( \mu, 1) \text{ and } \mu \sim N(0,1). $$ Then due to the ...
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1answer
46 views

Weight values by sample size in a LOESS regression in R [closed]

Is there a function to weight values by sample size in a LOESS regression in R? I have been told that this function is included in SAS, and I was hoping a similar function existed in R. I am working ...
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2answers
51 views

How does Gibbs sampling produce values for a variable using the univariate conditional probability?

I have a question about Gibbs sampling for generating samples. The Gibbs sampling algorithm is often stated. $x^0 = (x_1^0, x_2^0, \ldots, x_n^0)$ //initialize random values for $t=1$ in $T$ //...