Questions tagged [sampling]

Questions about the statistical process of sampling from a population, in order to obtain information for use in statistical learning, estimation, hypothesis testing about some population or process. Use this tag along with the tags (probability), (probability-theory) or (statistics).

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Non random sampling for logistic regression

I recently joined a lab that designed a study like the following: x number of individuals with failed hearts were randomly chosen, and so were x number of people with healthy hearts. To determine the ...
sul man's user avatar
1 vote
1 answer
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How can I estimate failure rate failure samples only? [closed]

For example, in a two-dimensional case, the data X follows a standard 2D normal distribution. If I set the criterion for failure as $x_1+x_2>2$. then the failure rate can be calculated by sampling ...
random_forest's user avatar
1 vote
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Expected number of draws to sample an element using weighted sampling without replacement

Let us have $k$ elements of weights $w_1,\ldots,w_k$ where the sum of the weights $w_1+w_2+\ldots+w_k=k$, where $w_i\geq 0$ for all $i$. We sample elements using weighted sampling (probabilities ...
Sankhya's user avatar
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-1 votes
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Inverse sampling [closed]

To prove inverse sampling one can simply use $g(r)\mathrm{d}r=f(x)\mathrm{d}x$ where $r\sim f$ and $x\sim g$ ($f,g$ are probability density functions) from where it then follows that $G(r)=F(x)$ and ...
Silas's user avatar
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1 answer
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Efficient Sampling of Points from the Unit Simplex with Convex Hull Containing a Given Set

I have a set of points $P = \{p_1, \ldots, p_k\}$, where each $p_i \in \mathbb{R}^n$ and these points reside on the unit simplex, such that for each $i$, we have $p_i > 0$ and $\sum_{j=1}^{n} p_{ij}...
Nadav Kuniev's user avatar
2 votes
0 answers
82 views

Law of large numbers for non-independent and non-identically distributed samples

Let $X \sim p_X$ be a real-valued random variable with $\mathbb{E}[X] = \mu > c$ where $c \in \mathbb{R}.$ Assume you sample from $p_X$ and only accept samples such that the current sample mean is ...
tobayes's user avatar
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Bounds on solutions to $a\alpha-b\ln{\Gamma(\alpha)}-c=0$

What would give tight upper and lower bounds to the two $\alpha$ ($\alpha\in\mathbb{R}^+$) solutions of the following equation? $$a\alpha-b\ln{\Gamma(\alpha)}-c=0$$ Background I am working with a ...
jblood94's user avatar
  • 316
2 votes
1 answer
50 views

Balanced Snowball Sampling

There is a method in qualitative research called "balanced snowball sampling", which runs as follows. Say the interviews are assessing perspectives on some issue, each interviewee is asked ...
ComptonScattering's user avatar
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24 views

Empirical Distribution Convergence, Ordering Of Samples

I am trying to formally justisty a "rearrangement" algorithm, which rearranges the samples of two random variables to reflect a certain joint distribution. Suppose that we have two pairs $(...
Nicola Zaugg's user avatar
2 votes
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Finding Probability Limit

Let $\bar{Y}_n$ denote the sample average of $n$ samples from a distrubution with mean $\mu$ and variance $\sigma^2$. Assume sampling was done indepedently. Consider an estimator of $\mu$, $W_n = \...
Harry's user avatar
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Distribution of the size of the union of repeated random draws

I have $d$ items (say numbers 1 to $d$). I would like to uniformly randomly sample $k$ items out of $d$, without replacement. Suppose I do such draws independently $n$ times. I now want to take the ...
kzliu's user avatar
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2 votes
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50 views

Variance of a sample from a bipartite graph

Consider a bipartite graph for which the two vertex sets have the same size, denoted $M=|V_1|=|V_2|$. Let $d$ denote the maximum degree of vertices in $V_1\cup V_2$. Assume that $M$ is large and ...
Kris Tapp's user avatar
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15 views

Probability of new sample belonging to one set or another

I have a stochastic event with two possible outcomes ($A$ and $B$). I also have two measurement techniques, a direct and an indirect one. The direct one can tell me exactly the outcome, but it implies ...
Franco's user avatar
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Sample variation maximization during sampling

Let's say that I am sampling $\{x_i\}$ from a distribution with CDF $F(x)$, and the samples are always non-negative. For each new sample, let's say the $n$-th sample, provided that we have sampled $n-...
Rebecca Zorichyevna's user avatar
1 vote
1 answer
32 views

Weighted sampling without replacement: if the weight of an element increases, must the probability of this element being sampled also increase?

Suppose we have $n$ elements with weights $w_i$'s for $i \in [n]$ with $\sum_i w_i = 1$ and we want to sample $k < n$ elements using sampling without replacement. When we use sampling with ...
Vezen BU's user avatar
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State how inverse-transform sampling produces one random sample of $X$.

Let $0 < p < 1$. Let $X$ be a random one of two objects, coded as $1$ and $2$ , where $\mathbb{P}(x=1)= p$ and $\mathbb{P}(x=2)=1-p$. State how inverse-transform sampling produces one random ...
user1052623's user avatar
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30 views

Sufficiency in sampling theory

Introduction We have a finite population $U$ with $N$ individuals, namely $U:=\{1,\dots,N\}$. Each individual stores a secret fixed value, so let's write $y_i$ for the value corresponding to the $i$-...
Álvaro G. Tenorio's user avatar
2 votes
1 answer
49 views

Sampling with order and with/out replacement as random variable

A random sample of size $n$ is drawn from a lot of $N$ items, of which a fraction $p$ are defective. Let $X = $ number of defective items in the sample. Determine $f_X (x) = P(X = x)$ if $\cdot$ The ...
daniel's user avatar
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Suppose X1, X2,..., X9 are i.i.d N(u, 1) and Xbar = 1/9(X1 + X2 +...+ X9)

I have deduced this from the question: We have $9$ independent and identically distributed (i.i.d.) random variables $X_1, X_2, ..., X_9$, each following a normal distribution with mean $μ$ and ...
Gadin Naidu's user avatar
1 vote
0 answers
14 views

Statistical Sampling for Tasks With Different Complexities

We have contractors submitting tasks of different complexities (High/Medium/Low) and we would like to audit them. Considering the auditing resource availability, we have to sample the submitted tasks ...
Math Lover's user avatar
1 vote
0 answers
62 views

An one dimensional sampling version of Penrose tiles in 2D

I was initially interested in aperiodic sampling for signals to address the problem of aliasing in the frequency domain. A design like Penrose tiling in 2D (which is non-repeating) can be very ...
CfourPiO's user avatar
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29 views

Sampling problem: why being able to sample from $P(s)$ and being able to compute $P(a|s)$ implies being able to sample from $P(a)$

I call $P(s)$ a probability distribution for some variable $s$. I call $P(a)$ the probability distribution for some variable $a$. I have: $$P(a)=\sum_s P(a|s) P(s)$$ Imagine that I have a computer ...
EasyMan's user avatar
0 votes
1 answer
53 views

Independent sampling with at least two elements, without re-sampling

Suppose we have a sequence of numbers (WLOG, $[n]$) and we want to sample elements from it into a set $S$, where each element is sampled independently at random with $p_i := \Pr[i \in S] \in (0, 1), \...
Vezen BU's user avatar
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1 vote
0 answers
44 views

Why is sampling in high dimensions generally intractable (in the context of monte-carlo sampling?

It's unclear to me why sampling from product measures is tractable while generally randomized sampling is not. This is in the context of MC rejection sampling. Suppose we want to sample from a ...
amy's user avatar
  • 23
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0 answers
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Sampling in scattering; how to keep track of the coordinates

I'm working on a monte carlo simulation involving scattering. The challenge is that I'd like the initial direction of the particle to be isotropic. But collisions after are no longer isotropic, but ...
Stefan de WIt's user avatar
1 vote
1 answer
120 views

Computing Posterior Distribution of Hyperparameter in a Multivariate Normal Model

I need guidance on computing the posterior distribution of a hyperparameter in a specific multivariate normal model. Here's a brief description of my problem: I have a dataset where the observed ...
Dalek's user avatar
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What is the maximum noise value along a line segment in a simplex noise function?

Is it possible to find the highest "noise" value along a line segment defined by two endpoints within a Simplex (or Perlin) function by using an equation? The reason I ask is to avoid ...
ddxm's user avatar
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1 vote
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Riemannian metric on fixed rank manifold

I know that one can define metrics on the manifold of SPD matrices $$ \mathcal{S}^n = \{ A \in \mathbb{R}^{n\times n} \ | \ \text{A positive semi-definite} \} $$ like the Log-Euclidean metric or the ...
Nomeal's user avatar
  • 11
1 vote
1 answer
71 views

Uniformly sampling with a constraint on a linear combination of logarithms

Suppose we have $N$ fixed reals $p_1, p_2, \dots, p_N$ satisfying $p_i\in [0, 0.5]$ and $N$ variables $q_1, q_2, \dots, q_N$ in the range $[0, 0.5]$ such that $$\sum_{i=1}^{N}p_i\log (q_i) + (1-p_i)\...
Benjamin Wu's user avatar
-2 votes
1 answer
30 views

Sampling a cosine [closed]

If you sample a cosine of fundamental period 0.1 milliseconds with a sampling rate of 10^5 samples per second, how much phase difference is there between two consecutive samples? I can't solve this ...
zedyjy's user avatar
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1 vote
1 answer
31 views

Unbiased estimate of log-likelihood of Markov bridge

Note: Cross-post from CrossValidated. I have the following problem I am trying to solve. I have a parametric family of "transition" distributions $p_\theta(x_{i+1}\mid x_i)$ and I am given a ...
Daniel Robert-Nicoud's user avatar
1 vote
2 answers
66 views

Uniform Sampling points on a line using 2 Uniform distributions

I have been struggling with this problem for quite some time but I am not sure how to proceed. So I am given a sampling algorithm : We would like to uniformly sample points on a line between A and B. ...
kuuhaku's user avatar
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0 votes
0 answers
13 views

Is sample average deterministic if I condition on the whole sample?

I'm a little bit confused with the deterministic of sample average, so I have sample X and Y, where X is composed of $x_1,x_2,...x_n$, $\bar{X}$ is the sample average. Can I say: $E[\frac{Y}{\bar{X}}|...
Eileen's user avatar
  • 87
0 votes
0 answers
10 views

Dependent sampling preserving individual probabilities

I am considering the following way of dependent sampling which preserves individual probabilities: Input: Given $N$ items $[N]$, each associated with a probability $p_i$, $\forall i \in [N]$ Output: ...
Vezen BU's user avatar
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0 votes
0 answers
19 views

which sampling strategy is better?

Assume we have a variable $x \in [x_{min},x_{max}]$, and an increasing function $f(x)$. And we want to estimate $x$ according to the sampling of $y=f(x)+n$, where $n$ is the Guassian $N(0,1)$. Assume ...
Harry's user avatar
  • 699
0 votes
0 answers
22 views

Estimate standard error of population proportion based on one sample

There is a basket with unknown number of red balls ($N_r$) and green balls ($N_g$). I draw a random sample of $k$ balls without replacement and see that $P_r$ of the balls are red and $P_g$ of the ...
Mikhail's user avatar
  • 101
0 votes
0 answers
13 views

Should I have discrepancies in the mean of a discrete distribution when estimating it's PDF using Inversion sampling?

I've been trying to create the Inversion sampling method in R for the distribution $Y \sim X_1 + X_2$, where $X_1 \sim Bin(100, 0.3)$ and $X_2 \sim Bin(100, 0.7)$. I haven't used ...
Rowan Harley's user avatar
0 votes
1 answer
89 views

Intuition of understanding the independence of $\overline{X}$ and $X_i - \overline{X}$

Let $X_1, X_2, \dots, X_n$ be i.i.d with $E[X_i]=\mu$, Var$(X_i)= \sigma^2$. random variables. Define the sample mean as $\overline{X} = \frac{1}{n} \sum_{i=1}^{n} X_i$. My question is how to ...
MTH's user avatar
  • 37
1 vote
0 answers
18 views

Sampling procedure to obtain groups with same categorical distribution

Imagine that we have $n$ (mutually-exclusive) sets of different sizes, $X_1, X_2, ..., X_n$. The total number of elements is $N = |X_1| + ... + |X_n|$. I want to partition these $N$ elements into ...
pterojacktyl's user avatar
1 vote
0 answers
15 views

Question about proving a survey sampling problem

Problem I'm confused about (iii) only, I have no idea about where to start. Please help me out;)
ZJ Q's user avatar
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1 vote
1 answer
115 views

How do I calculate the expected number of duplicates in a set based on the number of duplicates found only in a sample?

I have a set of 10,000 points of data. I know that some of those points of data are identical to other points of data (i.e. duplicates), but (for now) there are no triplicates, quadruplets, etc. This ...
Sass's user avatar
  • 11
2 votes
0 answers
31 views

Finding a mapping from the hypercube to a convex hull that conserves the uniform distribution

I am drawing points uniformly in a hypercube $x \in [-1,1]^n$ and I would like to find a map f(x) = y such that $||y||_1 \leq 1$ and that the uniform distribution is conserved. My own attempt at this ...
tbolind's user avatar
  • 45
0 votes
1 answer
41 views

Sampling Normal Distribution; Box-Muller, Inverse Transform, Rejection, Approximations?

I assume $X\sim\mathcal{N}(\mu,\sigma)$ and wish to sample values but I am confused about different approaches and concepts that seem to be relevant for this problem. It appears to me that this ...
Ronnie Marksch's user avatar
0 votes
1 answer
41 views

Please help me derive the formula for upper bound for one sided confidence interval $\bar{x} + z_{\alpha}(\frac{\sigma}{\sqrt{n}})$?

I want to derive for myself the known formula for the upper bound for one sided confidence interval $\bar{x} + z_{\alpha}(\frac{\sigma}{\sqrt{n}})$ for mean $\mu$ for a sample of size $n$ from a ...
Alex's user avatar
  • 1,550
0 votes
0 answers
10 views

Size of sample to extend regression model

I have the results of a constructed logistic regression model in which the objective function is $Y = Y(X_1, ..., X_k)$. By result I mean here the values in the interval $[0,1]$ obtained by the ...
WawMathematician's user avatar
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0 answers
31 views

Using distribution of sample mean to find expected value, variance, bias and MSE of sample mean

a) Determine the values of the population mean and the population variance. b) Suppose we use an SRSWOR of size $n=4$, list all the possible samples of size $4$. What is the probability for each ...
user985724's user avatar
0 votes
1 answer
45 views

Visual representation of accept/reject sampling

I understand how Accept/Reject sampling works, but sometimes I see graphical representations like this one: Here we have the sample distribution above the target distribution. Then at a certain x-...
Ronald's user avatar
  • 61
0 votes
0 answers
11 views

Sample size estimation for networks

0 I have $n$ data points that run in hundreds of millions. Ideally, I want to connect them with each other (based on a condition), run random walks on this interaction network, and make some ...
user2167741's user avatar
2 votes
0 answers
38 views

Sampling of independent Bernoulli variables with fixed cardinality

Suppose we have $n$ probabilities $p_1, p_2, \ldots, p_n \in [0, 1]$, and let $A_1, A_2, \ldots, A_n \in \{0, 1\}$ be corresponding independent Bernoulli events, where $A_i = 1$ with probability $p_i$....
Vezen BU's user avatar
  • 1,812
1 vote
1 answer
25 views

Standard error on subsample

Suppose that I know that $N$ samples $(x_1, x_2,...,x_N)$ are iid drawn from a distribution with known variance $\sigma^2$. I also observe the first $k<<N$ samples, and estimate the mean on ...
max1993's user avatar
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