Questions tagged [sampling]
Creating samples from a well-specified population using a probabilistic method and/or producing random numbers from a specified distribution. As this tag is ambiguous, please consider [survey-sampling] for the former and [monte-carlo] or [simulation] for the latter. For questions regarding creating random samples from known distributions, please consider using the [random-generation] tag.
3,146
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Gibbs sampler, how to generate samples based on odds?
I am reading a paper that contains a Gibbs sampler for a regression model with parameters $\beta$ and design matrix $X$. One of the steps in the Gibbs sampler requires simulating from a binary random ...
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blue noise error distribution in (MC)MC estimation
In computer graphics, you have an (MC)MC estimate $Q_i$ of the color value of the $i$th pixel and a true value $I_i$. Now you take $\epsilon_i:=Q_i-I_i$, which can be thought of as an "error ...
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Interpreting the Concept of 'Single Sample Normality' in the Context of the Central Limit Theorem
In the context of the Central Limit Theorem (CLT), which postulates that the distribution of sample means will approximate a normal distribution given a sufficiently large number of samples and sample ...
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General strategies for choosing priors and samplers to estimate parameters of nonlinear ODE system?
I'm new to MCMC methods, and as I learn, it seems there is a lot of art in choosing the proper priors especially when there are many parameters (which is why we use MCMC in the first place).
Are there ...
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Is there a z transformation for the correlation of non-normal distributions?
I'm writing code to calculate if the correlation between two random variables is significant.
I've recently come across Fisher's z transformation as a method for finding significance. But from reading ...
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Implementing sampling from GEV distribution from scratch
I am trying to implement sampling from GEV distribution without using external libraries (except numpy) and this is what I came up with:
...
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Drawing samples from a joint distribution defined by limits?
Assume that I want to efficiently draw samples from a (for simplicity bivariate) joint distribution $p(x,y)$, with $x \in \mathbb{R}$ and $y \in \mathbb{R}$. I don't have a closed-form expression for $...
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Can I decrease the sampling interval and still have accurate results?
A company has been collecting water chemistry data annually for 20+ years to monitor water quality. Now they're wondering if they can decrease their sampling interval to once every 2 or 3 years and ...
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What do I do when a false negative is far more expensive than a false positive?
I'm not sure how to 'responsibly' balance my model to account for this. I could predict a probability and give that to the business ('predict_proba' in SKlearn) but experience in the past has thought ...
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Statistical implications of quota sampling
This source says the difference between quota sampling and stratified sampling is that the units in each group are drawn in a non-random manner. What are the statistical implications of the fact that ...
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Population Estimation And Conditional Probability
Let's say that I have a data set comprised of age data for a large number of individuals, as well as a unique identifier for each individual. For terminology sake let's call this my base population. ...
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How can you draw a random sample from an RV with density $ \exp(x - \exp(x))$?
How can you draw a random sample from a random variable whose density is given by $\exp(x - \exp(x))$?
I am trying to work through the blog at https://staffblogs.le.ac.uk/bayeswithstata/2015/03/27/...
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How can I model the multivariate probability distribution of a dataset with both continuous and discrete variables for sampling?
This might seem like a duplicate of the following link, but I think that one is asking how to create a completely new dataset with specific distributions, rather than how to model an existing dataset ...
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Computing sum squared distances without computing center
Given an even number of sample points in a plane, I want to compute the sum of squared distances from the sample center as part of estimating the Rayleigh parameter. One way of doing it is to compute ...
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Null hypothesis significance testing when values are known
I'm looking at the association between two categorical variables in a genus of birds. The variables are 'Conservation Concern' (Yes/No) and another binary variable (Yes/No) and I have these for every ...
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How are power and statistical significance related for a one-sample hypothesis test of means?
Power, in a two-sample test, is partially determined by the narrowness of the confidence interval for the test statistic the alternative hypothesis is tested over.
This is captured in this photo
via ...
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Uniform sampling from intersection of hypercube and simplex
Background
Discussion from http://blog.geomblog.org/2005/10/sampling-from-simplex.html and https://cs.stackexchange.com/questions/3227/uniform-sampling-from-a-simplex have shown algorithms of sampling ...
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Design Effect ZERO
Is Design Effect (DEFF) possible to be zero?
Note: Design Effect (DEFF) is defined as the ratio of the variance of an estimator
under a certain survey design (non SRS) to the variance of the estimator ...
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Need help to interpret sampling numbers
This question was flagged as offtopic, but I am sorry, this is NOT a question which "focuses on programming, debugging, or performing routine operations, or it asks about obtaining datasets"....
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How to be explicit about negative sampling for Link prediction using GNN?
Regarding recommendation systems of bi-partite graphs with PyTorch geometric, most of the tutorials I found about Link prediction using GNNs suggest using negative sampling in an (I guess) random way.
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What could lead to this misbehavior for the expected sample size (ESS)?
I am using Hamiltonian Monte Carlo (HMC) to sample the posterior of a continuous-time Markov Chain (CTMC).
However, after running 10 parallel chains with 100 draws each, the effective sample size (ESS)...
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Understanding the ridge leverage scores sampling from an arXiv paper
I give a try to read the arXiv paper Distributed Adaptive Sampling for Kernel Matrix Approximation, Calandriello et al. 2017. I got a code implementation where they compute ridge leverage scores ...
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How do sample size and measurement accuracy affect the measurement of the parameters of a log-normal distribution?
Assume that we have objects (e.g. particles) whose properties (e.g. diameter) follow a log-normal distribution that can be described by a geometric mean $\mu_g$ and a geometric standard deviation $\...
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Critical Region and level of a test
A concept I'm struggling with is the type 1 error and the level of a test, for me the type 1 error is P(Wn|H0)
where Wn
is the rejection zone. Is it not a way to measure Wn
given that H0
is true ? So ...
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What is the general procedure to come up with different estimator with smaller MSE?
PDF of a random variable $X$ is,
$$
\begin{equation}
f\left(x|\gamma\right)=
\begin{cases}
\frac{1}{\gamma} \exp(-\frac{x}{\gamma}) & x > 0 \\
0 & \text{otherwise.}
\end{cases}
\end{...
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Sample until a desired condition is met
Suppose I have a population of N elements. For the sake of example, imagine these elements take either a value of 1 or a value of 0. My goal is to estimate the sum of the N elements.
To do so, I wish ...
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Unbalanced cross-sectional data
My research endeavors to explore the relationship between conflict exposure and attitudes towards international institutions. Specifically, my hypothesis posits that individuals who have experienced ...
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Maximum likelihood of sample mean
It is an easy computation to show that given some data sampled from the binomial, gaussian, Poisson, or exponential distribution, the MLE of the mean of the distribution is the sample mean. However, ...
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Post-stratification with missing subpopulations in the survey
I have some survey data on a population described by age, gender, and weight. It’s quite skewed so I want to reweight it to a known target population (a larger ...
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What should be the sample size in a stratified random sample to get the same precision of a simple random sample?
I was reading example 3.2 on stratified sampling in Sampling: Design and Analysis by Lohr where a stratified random sampling design is proposed and compared with a simple random sample one.
The point ...
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Gibbs sampler: Conditional distribution with nested latent variable distributions
I have the following model (simplified here for the description). The obsvered variable is $y_i$ which is a linear function of some random variable $\eta_i$ and a random error term $\epsilon_i$:
$y_{i}...
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How many samples to be reasonably sure? [duplicate]
I am new to probability, and I am struggling with the right language to ask or google this question.
I have a population of size $n$ and everyone is say some color. I want to verify that at least half ...
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Should I use null hypothesis significance testing when I have the full population? [duplicate]
I have data on every species in a genus, and am interested in how two factors relate to each other specifically within that genus. Should I use a statistical test to do this or does it not make sense? ...
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Importance sampling weights for NN training
Say you're training an NN and have different groups of samples, say number of groups is ngroups.
Each group has a different number of samples, say ...
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What is the sampling bias in sample Pearson correlation coefficient squared?
Suppose $r$ is the sample Pearson correlation coefficient estimator of two random variables $X$ and $Y$, while $rho$ is the population correlation coefficient. From various sources, e.g., Is the ...
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How to draw from a uniform distribution over a large state space via MCMC
Motivating question
I have a high-dimensional state space $\Omega \subseteq \mathbb R^n$ with an admissible subset $S\subseteq \Omega$, which is connected. I would like to draw a uniform random sample ...
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Generating uniformly distributed particles on a $n$-dimensional flat torus or periodic hypercube [closed]
I am trying to generate evenly distributed particles in an $n$-dimensional flat torus or a periodic hypercube.
I am not sure if any of this approaches suffices. Can you suggest alternative methods for ...
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How to make sampling ignorable in Bayesian model with random (unequal) sampling probabilities?
Suppose you sample N people with unequal probabilities from some superpopulation. Your sample contains W_sample the probability with which the person was sampled from the superpopulation and their ...
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How to determine effective sample size when sampling averaged samples?
I have a sampling process like the following:
Randomly select psus from one stage with equal probability
Use all ssus of each psu selected for estimation.
Each ssu is associated with a statistic from ...
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How to pool estimates from multiply-imputed datasets with complex sampling designs?
Analysts often use Rubin's rule (RR) to obtain a pooled estimate of a popular quantity from multiple (imputed) datasets. While popular statistical software (such as the R ...
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Sampling from multiple distributions with well defined sum
Let's say I have three distributions, P1, P2, and P3, which are probability distributions with domains defined between 0 and 1. Generically these are not Gaussian (more like Beta distributions). I can ...
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Does a single observation from a population have the same distribution as that population?
Suppose X1 is one observation from a population with Beta(θ,1) PDF. Would X1 also have Beta(θ,1) PDF?
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How to sample from a given accessible PDF?
I am learning Gibbs Sampling for GMMs. Particularly, given $\boldsymbol \theta$, I must sample from the latent $\boldsymbol z$ before sampling $\boldsymbol x$.
The PDF of $\boldsymbol z$ is given as$$
...
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Running Metropolis-Hastings algorithm with changing proposal kernel; each time the kernel is changing starting the algorithm afresh. Does it work?
I have a Markov kernel $Q$ from which I would like to generate proposals for the Metropolis-Hastings algorithm. The problem is: When the proposal is accepted, the "internal state" of $Q$ ...
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LDA Document Topic Distribution Prediction for Unseen Document
Popular python libraries for topic modeling like gensim or sklearn allow us to predict the topic-distribution for an unseen document, but I have a few questions on what's going on under the hood. I've ...
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Can I use the Z-Test with estimators for mean and standard deviation?
I'm trying to select feature columns in a binary classification model.
I'd like to remove near-constant columns that don't predict the target column values very well. One way of defining this is the ...
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No-U-Turn Sampler (NUTS) for handling class imbalance
I have a dataset of about 100 records and about 80% of those records belong to one class. The rest belong to another class. I'm building two Bayesian models (logistic regression and multiple linear ...
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1
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103
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Calculating the probability my observation, $Y_i$, is drawn from a random variable $X$?
If I sample a population distribution 2,000 times and get an estimator for the population mean, $\mu$, and the standard deviation, $\sigma$, how can I use these to get the probability that an ...
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Understanding Objective in OpenAI InstructGPT paper?
The following objective is taken from the paper 'Training language models to follow instructions with human feedback':which is used to fine-tune the pre-trained language model using Proximal Policy ...
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Optimizing a Laplace distribution's scale parameter for rejection sampling in R
I am using the Laplace distribution (location = 0, scale = b) to sample from a standard normal distribution. The normal distribution ranges from -1 to 2. I am using the rejection sampling method. In ...
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