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.

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1answer
38 views

Do both Bootstrap with and without replacement create a distribution?

I'm having a "noisy debate" with colleagues about whether sampling without replacement can still create a distribution. Methodology: A bootstrap (iterative process where I calculate Somers' D for new ...
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21 views

Devising an acceptance sampling plan for False Negative Rate

I need to evaluate a binary classifier that classifies inputs in positives and negatives. Since all predicted positives (PP) are assessed, I have complete data on the true positives (TP) and the false ...
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29 views

Integration by sampling from truncated distribution

I'm reading the book Ben Lambert's Bayesian Statistics: problems and answers, which by the way I like. There is a group of problems in "Integration by Sampling" chapter 12. The first integral is $$...
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29 views

Bayesian imputation for reject inference?

I'm analyzing a dataset to predict whether a customer defaults on a loan. The problem is, the dataset only contains observations on customers who were offered a loan and accepted (ie. there is no data ...
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1answer
39 views

How to bootstrap samples from data that has more than dependent variable?

I understand bootstrap sampling with replacement. But what i still not sure about is that how to apply this approach to sample from data that has more than one dependent variables. For example, ...
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57 views

How to choose sample size from probability density for computing mutual information based on continuous variables

I need to compute mutual information gain based two continuous variables $X$ and $Y$ $I(X|Y) = \int_X\int_Y p_{x.y}(x,y) \log(\frac{p_{x.y}(x,y)}{p_{x}(x)p_{y}(y)})$. I have used Kernel Density ...
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28 views

Estimating population variance considering both population sample variance AND sampling method variance

I want to estimate the variance of a normally distributed population. I can take N samples and calculate the sample mean and sample variance, which would normally suffice; however, the sampling method ...
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1answer
58 views

What methods are available for forecasting with a sample of the data

In predictive analytics, specifically forecasting, what methods are available for getting the same predictive accuracy with $n$ (a sample of the data) which would be achievable with $N$ (all of the ...
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3 views

Sampling method to represent a larger demographic

I have a set of Google search queries for a particular user. Every query has its frequency, that is the number of times the person searched it for. Now I have to infer some information about this ...
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31 views

Posterior predictive distribution example

Assume there's some normally distributed population ($X$) whose parameters ($\mu$, $\sigma$) are not known. A sample ($x_1$) of size $n$ is drawn from $X$, and statistics are calculated: $\bar{x}_1$ ...
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22 views

How the conditional probability is being calculated in Rejection sampling

In a class lecture, the "Acceptance-rejection algorithm" was presented as follows: To generate $𝑋 \sim 𝑓(𝑥)$, Find density $g$ satisfying $\frac{f(t)}{g(t)}<=c$ for some constant $c$ for ...
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24 views

Sampling bias in multinomial logistic regression

I am interested in estimating a set of coefficients in a multinomial logistic model. However, I only observe a subsample of the true sample in which base category $A$ was chosen. I have no way of ...
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1answer
108 views

The relative size of the SE for ratios compared to the SE for means

Pardon a relative novice's question. I'm seeking a reference that describes, compares, and gives formulas for the standard error for ratios and the standard error for differences between means when ...
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12 views

rate of convergence acceptance-rejection vs inverse transform sampling

Does the acceptance-rejection method or inverse transform sampling converge to the mean quicker say for beta distribution, assuming acceptance-rejection has suitable envelope function? is there a way ...
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14 views

When to use a certain sampling technique

I'm taking a class where we learn about different sampling techniques. For the most part it has come down to SRS, Ratio/Regression/Difference estimation, Stratified random sampling, Systematic ...
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57 views

How can I estimate the optimal number of experiments? [closed]

I have a list of 20 experiments, each have a certain numerical value as a result. I would like to run many more experiments of this type (for different conditions, and so on), but 20 experiments are ...
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2answers
99 views

Sampling from sample (and not from population, and not from distribution)

[Edit: I include a specific example for clarity] Say I have two models: Model 1) fuel_consumption_model, which calculates the fuel consumption of barges. It has about a dozen input parameters that ...
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52 views

How to adjust confidence-interval based on model accuracy?

I have a binary classifier with 94% accuracy on unknown test data. I use that model to classify samples from a large population in order to infer the proportion of positives within the population. I ...
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0answers
37 views

Sampling particles according to their distance

I'm trying to draw 2 particles out of $n$ particles, where the probability for drawing the particles is proportional to a Gaussian of their displacement: $$ p(\boldsymbol{x}_i,\boldsymbol{x}_j) \...
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1answer
23 views

Roulette Wheel for sampling user defined pdf

Following is the pdf from which I want to sample so, I used roulette wheel sampling Code to generate pdf ...
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0answers
14 views

Weighting community-level observations in representative survey data

I am working with survey data that contain information at the individual, household and community level. The survey is representative at the national and first-administrative level but provides ...
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1answer
26 views

Probability proportional to size

Consider the problem of drawing a sample of size $2$ from a finite population of size $20$ . The sampling is done with replacement using probability proportional to size scheme . The normed size ...
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0answers
31 views

Sampling disttibution

If $(x_1,x_2,\ldots,x_n)$ be a random sample drawn from a normal population with mean $\mu$ and standard deviation $\sigma,$ then find the sampling of $T=\sqrt{\sum_{i=1}^n (x_i-\bar{x})^2}.$ Further ...
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1answer
5 views

how posterior function is calculated in JAGS

I have a theoretical question. I understand the JAGS samples from the posterior function of a model. But I don't understand (nor I can find in the documentation) how it calculates the posterior in the ...
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11 views

How to measure “well-sampled”ness i.e. how well a distribution is sampled in a given set of data

Say we have samples $x_i$ from an unknown distribution $F(x)$. We want to know the number of samples $n$ such that we can say the distribution is "well sampled". Generally we need some sort of ...
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9 views

Power analysis for assessing performance of a binomial classification model [duplicate]

I'm looking to perform third-party assessment of the false-positive rate of a video classification algorithm. I am feeding unlabeled video through a given classification algorithm and need to assess ...
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5answers
1k views

Why we don’t make use of the t-distribution for constructing a confidence interval for a proportion?

To calculate the confidence-interval (CI) for mean with unknown population standard deviation (sd) we estimate the population standard deviation by employing the t-distribution. Notably, $CI=\bar{X} \...
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1answer
58 views

Determining sample size for ML algorithm validation

I'm looking to do a third-party assessment of the false-positive rate of a video classification algorithm. Since I have a lot of video I'm trying to do a power analysis to figure out exactly how much ...
2
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1answer
35 views

Item sampling techniques to reduce processing time for questionnaire

I have a well-crafted draft of a questionnaire, containing 240 items. The average processing time is 20 secs per item, so the entire questionnaire would take around 1 hour 20 min to complete. I want ...
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1answer
28 views

Deriving mu and sigma from the log normal distribution given the expected mean and variance?

I'm attempting to sample from the log normal distribution using numbers.js. Looking at Wikipedia it looks like I need to solve for mu and sigma. So if I want the mean of the samples to be 10 then I ...
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0answers
35 views

How to generate multiple, non-independent samples from a multivariate normal distribution?

Suppose I have a multivariate normal (MVN) distribution: $$\textbf{X} \sim MVN({\mu},\Sigma)$$ where $\Sigma \neq \sigma^2\textbf{I}$ i.e. the RVs within $\textbf{X}$ have some correlation structure....
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0answers
14 views

How to determine the proper number of samples for development/test set in machine learning

I would like to know if there is a statistical/empirical method to determine the proper number of samples for development/test set used for testing the generalized ability of a machine learning model. ...
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1answer
31 views

Sampling Methods : Pattern Recognition and Machine Learning Bishop

I am reading chapter 11 . Sampling Methods from the book : Pattern Recognition and Machine Learning by Bishop : In the introduction , in short,he evaluates expectation of some function $f(z)$ with ...
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0answers
20 views

Probability of sparse spectrum

Consider a vector $v$ such that $v \sim \mathrm{Unif}(\mathbb{S}^{d-1})$, the uniform distribution on the unit sphere in $d$ dimensions. Question: is there an upper bound on the probability that $v$ ...
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0answers
23 views

Statistically evaluating classification accuracy of machine learning model

Let's say I'm trying to evaluate a classification algorithm and suppose there are $m$ data points in my test set. Here's my understanding so far: assuming my evaluation metric is the classification ...
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0answers
19 views

Sampling multiple non-identical categorical variables subject to a constraint

Say I have multiple (independent) categorically distributed random variables: $X_1, X_2, \ldots, X_k$, which all range from $0,1,2,\ldots,N$, and with each coming from distributions with different ...
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0answers
27 views

Literature on design of importance sampling distribution using MLE or point-estimates of highest modes

Suppose I have many distributions $p_i(\theta)$ I wish to take expectations over $$\mathbb{E}_{p_i}[\mathbf{f}_i(\theta)]$$ where the $\mathbf{f}_i$ are vector-valued. In my problem the $p_i$ share ...
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0answers
8 views

Oversampling in Uplift Modelling

I hope any of you can help me in the following matter: I am about to write my master thesis addressing the question how response and uplift modelling differ in terms of performance but also the ...
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0answers
13 views

Large population size = relatively smaller sample size?

Assuming 95% Confidence Level & 8% Margin of Error, a population frame of 37 yields a sample size of 30 (81% of pop) but a population frame of 370 yields a sample size of 107 (29% of pop) and a ...
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0answers
15 views

Can't sample all conditions for each participant — strategies to compensate?

I am attempting to design a study using Category Comparison Rating / Double Stimulus Comparison Scale to evaluate participant perception of different stimulus conditions. The original study design ...
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0answers
9 views

classify samples from two different gaussian distributions [duplicate]

Assume we have two sampling process, i.e. we can draw samples from two different gaussian distributions P and Q. At first, we draw samples from gaussian distribution P only. But after some time t, we ...
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1answer
82 views

What does it mean exactly to divide a distribution by another distribution?

In the notes I'm working through, distributions are often "divided" by other distribution, and while I sort of understand what is meant, i would rather a rigorous explanation. Let me provide an ...
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2answers
32 views

For the Average Treatment Effect (ATE) in causal inference, defined as $E(Y(1) - Y(0))$, what is $E(Y(1))$ usually referred to as?

For the Average Treatment Effect (ATE) in causal inference, is it usually defined as $$ E(Y(1) - Y(0)) $$ I am wondering what the most commonly referred to name for $E(Y(1))$ is? Is it not the ...
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0answers
41 views

Particle filter for diagnosis

I have two annual measurements taken on medical images depicting a lung cancer tumor 's condition. I have likelihood function that taken in the measurement values and estimates malignancy of the tumor....
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0answers
17 views

How does the rejection sampling method work in layman's terms?

Suppose that I have no knowledge of sampling methods and that I have some knowledge of probability theory (e.g. probability distribution and marginal distribution). How would you explain the ...
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0answers
25 views

Can you find the posterior mode of an unknown distribution without MCMC?

I was wondering if you wanted to compute the MAP estimate of an unknown posterior distribution, is there a non-sampling based method that would suffice? As in, if you don’t need to know anything more ...
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1answer
17 views

Customer time series analysis

Statistically speaking, If I have 720 0000 unique customer information, how best can I sample from this population such that it is a representative of the whole data set? Also how large should my ...
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1answer
35 views

Estabilishing an upper bound for the probability of an impossible event, by sampling [duplicate]

Lets suppose there is an event that gives a random outcome each time it happens. The set of possible events is finite, but their probabilities differ, sometimes by orders of magnitude. (imagine a ...
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41 views

How to randomly downsample from matrix [closed]

I'm trying to downsample from a matrix of numbers. Each number is the number of times we saw a particular event. By downsample I mean I want to pseudo-randomly select values from each row so they ...
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0answers
17 views

Is my Reservoir Sampling Intuition correct?

In reservoir sampling, you are taking in a stream of numbers of size i, and as i grows, sampling a number is done by swapping the current number you have with the tail of the stream with probability 1/...