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

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3
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39 views

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

Suppose you want to draw samples from an (unnormalized) pdf $f(x)$, $x \in \mathbb{R}^d$, $1 \le d \le 20$, which might be expensive to compute, and you have a (normalized) pdf, $g(x)$, which is an ...
0
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1answer
17 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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26 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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18 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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5 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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2answers
30 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
10 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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0answers
11 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.
0
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1answer
22 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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10 views

how to deal non response in simple random sampling if sample saize is about 380? [on hold]

How to deal non-response in simple random sampling when sample size is 380 from about 20000 population
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26 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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7 views

Doubts about Chao sampling procedure

I'm trying to implement Chao sampling, as far I understood that the procedure is as follows: [Step 1] Constitute the initial sample by selecting the first $n$ units in the population. Inclusion ...
4
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1answer
38 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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0answers
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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0answers
28 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 ...
0
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0answers
7 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 ...
0
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1answer
81 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 ...
0
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1answer
24 views

Weight values by sample size in a LOESS regression in R

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
43 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 $T$ ...
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0answers
16 views

Treating X as non-random under random sampling

Random sampling allows us to treat values of independent variables that have been sampled as non-random (for the purpose of proving the unbiasedness of OLS estimators). How is this possible? My ...
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0answers
58 views

Sampling from posterior

Assume that the likelihood is available in closed form $p(Y|X)$. And also the prior is available in close form $p(X)$ and it is easy to sample from. Then the posterior $p(X|Y) = c p(Y|X)p(X)$ ...
2
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1answer
40 views

Is the margin of error for a survey a “fake” statistic?

When I conduct a survey for a client, they are often very concerned about the margin of error for the survey, and that’s totally reasonable. Oftentimes however, when they say, “We want a margin of ...
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1answer
46 views

Inverse Sampling according to Haldane (1945)

According to the inverse-sampling method (Haldane 1945) you continue sampling until m of the rare items have been found. Let p be the frequency of the rare item ...
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0answers
38 views

Resulting distribution when repeatedly sampling without replacement from weighted elements

I have a model where I need to sample from $m$ elements without replacement, where each element exists exactly once. The element have different weights and the probability of an element being drawn is ...
5
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1answer
142 views

Why does the central limit theorem work with a single sample?

I have always been taught that the CLT works when you have repeated sampling, with each sample being large enough. For example, imagine I have a country of 1,000,000 citizens. My understanding of CLT ...
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0answers
11 views

How to exact prediction from over sampled data(Undoing oversampling)?

We are oversampling the data to use in logistic regression. Aim is to predict CTR(click probability) which is rare event scenario. I have predicted the probabilities of click but CTR results are ...
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1answer
25 views

Second order inclusion probabilities in With-Replacement Sampling

I'm reading the book "Model Assisted Survey Sampling" from Särndal et al. In chapter 2, there's a section about Sampling with replacement. I'll put this into context: We have $m$ independent draws, ...
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0answers
44 views

How to calculate probability of a random sampling of a population

Let's say that I have a city for which I know the size in square miles and I want to know the probability of a random sample of individuals from that population living within a certain threshold of ...
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27 views

Determine significance of an observed continuous distribution given many randomly generated continuous distributions

Suppose there is a vector, v, that contains the body height of every person over 30 years old on earth. It looks something like this: ...
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0answers
13 views

main advantages of cluster analysis and when is it used?

I've gone through the theoretical definition of cluster analysis and have learnt the basics of it.But i want to know the advantages of the cluster analysis process and a real time example as to where ...
0
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1answer
30 views

How many replications to eliminate Noise

Marbles marked 1-100 in a bag. You continuously draw 1 marble and then put it back. You only care about marbles 1-10 and want to keep track of how many times you pick those. I'm interested in seeing ...
0
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1answer
30 views

Sample from a Normal-Inverse-Chi-Squared distribution

Is there a way to draw samples from the following distribution in Python? Unfortunately I wasn't able to find helpful information in the scipy help.
10
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1answer
178 views

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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10 views

How to deal with heterogeneous data set

Problem I have a dataset that contains three types of objects: simple objects, object groups and meta-groups. Meta-groups contain simple objects and groups. Each simple object correspond to an ...
0
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1answer
59 views

Random sampling distribution question

I have been reading this article on the random sampling distribution (RSD) and non-normal distributions. Basically, if I understand it correctly, the article proposes that the RSD of the mean of a ...
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0answers
5 views

Class by class undersampling for imbalanced classes

In multiclass training for Neural Networks it can be a problem when the number of classes is big and the number of training examples is unbalanced between classes. I know of many cost-sensitve modes ...
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0answers
19 views

Sampling size question [closed]

I wanted to know the sampling size of a population where size is low and moreover it doesn't follow a normal curve. Moreover I wanted to roll out quality numbers at monthly level as the weekly level ...
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0answers
14 views

Order of input data gives different results

The background I am predicting binary target, class 1 is undersampled in ratio 5% to 95%. I have about 120 dimensions. So first I took all samples of class 1 and then roughly same number of class 0 ...
3
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2answers
124 views

Confusing confidence interval question from old textbook

Lets say an investigator reports a 95 percent confidence interval of 1 to 23 dollars per month in reduced utility bills for a randomly selected group of 50 customers who underwent training in ...
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0answers
49 views

What are examples where only a single sample is needed?

Consider the following setup: Let $\Omega$ be a finite (but humongous) state space and $\pi:\Omega\to[0,1]$ be a probability mass function. It seems to me that when people want to "sample" in this ...
4
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1answer
60 views

Sampling of a Gaussian posterior

Sorry for my simple doubt, but I'm quite newbie and don't clearly get how to sample the posterior Bayesian distribution. My likelihood and prior are normal and I know how to calculate the posterior. ...
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0answers
31 views

Modeling the joint distribution of stream statistics

I have a question regarding computing the joint discrete probability distribution of statistics in a number stream. I posted this problem in the Mathematics section as well but I'm hoping the ...
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0answers
9 views

Regression and in- and out-of-sample testing for forecasting applications?

Suppose I have a dependent variable, Y, three predictors: X1, X2, and ...
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0answers
8 views

How to determine and use the sampling lag in the collapsed Gibbs sampler?

I am implementing a collapsed Gibbs sampler for LDA model. According to this technical note's word, average a number of samples, and often it is desirable to leave an interval of L iteration ...
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0answers
7 views

How to evaluate the quality of Bayesian network sampling?

I have generated a sample from a Bayesian network by applying Forward Sampling. I learn the parameters of the network (the same structure) from this sample so as to evaluate the quality of the sample ...
3
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1answer
65 views

Proposal distribution - Metropolis Hastings MCMC

In Metropolis-Hastings Markov chain Monte Carlo, the proposal distribution can be anything including the Gaussian (according to the Wikipedia). Q: What's the motivation for using anything other than ...
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0answers
6 views

Sampling with Replacement and Excessively Sampling a Few Observations

If I am trying to construct a matched control sample and I am sampling with replacement, there is the possibility that I may select the same observation many many times. What bias could this induce as ...
0
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0answers
28 views

Adaptive sampling strategy

This question (I am sure) was discussed a lot of times, but I could not find an answer (can not make an appropriate google request). It is pretty important: in experimental sciences people spend big ...
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1answer
18 views

How many random samples of a set of N values are needed for a 95% confidence in what N is?

Given I have a set of values N, where N is unknown to me. I can make requests for one sample at a time, which is selected randomly for me. As I request more samples, I see more and more values which I ...
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0answers
16 views

Bias and precision in estimating species richness?

I would like to estimate the total number of unique species within a community (=richness, for instance two species: cat and dog) from a randomly drawn sample. I am wondering what is the sampling ...