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3
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0answers
193 views

Relationship between DFT and FFT/DTFT

Question 1: Assume we already know $x(t):[0,2\pi]\to\mathbb{R}$'s Fourier series $x[n]_{n=-\infty}^\infty$. Perform DFT on $x[n]_{n=0}^N$. How is the result connected to $x(t)$? WHY? Question 2: ...
3
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0answers
112 views

Problems sampling from a $pdf$ over $SO\left(3\right)$

I have a probability density function over $SO\left(3\right)$, which I am trying to sample from. The $pdf$ is given as a generalized fourier series: $$ f\left(\omega,\theta,\phi\right)=\sum ...
3
votes
0answers
472 views

Notation for sampling random variate

Is there standard notation for sampling a value from a probability distribution? Like, if I had a random variable $X$, setting $x$ to whatever value I happened to sample from $X$ on this occasion? I ...
2
votes
0answers
21 views

Reconstructing a signal at twice the bit-rate

I have a discrete-time signal as: $\alpha_l = \sum_k a_k g(lT/2 -k(T+\Delta T))$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {sin(2\pi t/T)}{2\pi t/T}$, $T$ is the bit period, and $\Delta T$ is ...
2
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0answers
27 views

Stratified Sampling: Total and mean estimate of population

Question: In a sample survey designed to estimate the total number of cattle, the universe of 2072 farms was stratified into 5 strata on the basis of the total acreage of farms. In the hth stratum (h ...
2
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0answers
13 views

Is a discrete random process issued from a sampled continuous ergodic WSS process also ergodic?

I have a continuous time process $\{X_t,t\in\mathbb{R}\}$ that is WSS and ergodic for the 1st and 2nd moments. I create a random discrete process $\{Y_n,n\in\mathbb{N}\}=\{X_t,t=nT\}$ by discretizing ...
2
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0answers
14 views

Sampling with an “oversampling” factor, in K-Means||

I'm trying to understand K-Means||, a scalable version of K-Means++, which itself is an "improved" version of the clustering algorithm K-Means. Please find here the link to K-Means|| paper ...
2
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0answers
15 views

Sampling from a graph

Suppose you have a graph $G=(V,E)$ that is unobservable globally and you wish to take a sample from the vertices of that graph to infer something about its global properties from local properties. ...
2
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0answers
26 views

Variance of a Population of Two Indpendent Random Variables

I have a question regarding a problem I'm looking at out of personal curiosity. Here is the basic setup of the problem: There is a population that contains half of type A, and half of type B. The ...
2
votes
0answers
142 views

Notation for sampling a random variable

my question is pretty much the same as the one asked here: Notation for sampling random variate (I did not find a satisfying answer there...): I have a random variable $X \sim U(1, 10)$. I want to ...
2
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0answers
69 views

Sampling probability

I have a pool of 36 samples (each is a pool itself). If I take a subset of eight samples at random from this pool, how do I calculate the probability of obtaining two of the same type of sample from ...
2
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0answers
100 views

How to sample from a product-of-sums distribution?

$A$ is a $M$x$N$ matrix whose entries are positive. $x$ is a $N$ dimensional binary (i.e. consisting of $0$s and $1$s) vector and the number of $1$s in $x$ is constant. Let $y = Ax$. The distribution ...
2
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0answers
93 views

Approximability of continuous sampling by discrete sampling - definitions?

Are there standard definitions that express the notion that sampling from a given continuous random variable can be approximated "to any desired degree of accuracy" by sampling from an appropriately ...
1
vote
0answers
12 views

Simulate from a distribution using Metropolis-Hastings and Rejection Sampling?

We have covered the basics behind rejection sampling as well as Metropolis-Hastings from class, but I am not sure how to use the two in conjunction to solve the following problem: Given $\pi(x) = ...
1
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0answers
20 views

Sampling Distribution of the Mean

I want to know if my reasoning is correct. Let's say I got two normal distributed variables: Variable "X": 5.4 (mean), 2.856 (variance) Variable "Y": 5.4 (mean), 5.062 (variance) Let's pick 16 ...
1
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0answers
17 views

recovering bits from distorted signal

I have a signal: $r(t) = \sum_k a_k g( lT/2 -k(T+\Delta T) )$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {\sin(2\pi t/T)}{2\pi t/T}$, $T/2$ is the sampling period, and $\Delta T$ is a ...
1
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0answers
9 views

Number of samples with replacement to reach expected coverage of population under non-uniform sampling

I am interested in finding the number of times $n$ I need to draw with replacement from a population of size $N$ such that the expected proportion of the population seen is at least $P$. From this ...
1
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0answers
20 views

Convergence of sampling from Brownian motion

For a standard linear Brownian motion $\{B(t)\mid\ 0\le t\le 1\}$, for natural $n\ge 0$ and natural $1\le k\le 2^n$, let $d(n,k)=B\left(k2^{-n}\right)-B\left((k-1)2^{-n}\right)$ be the differences of ...
1
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0answers
40 views

problem on standard error in sample data

From a population of 20,000 observations, a sample of 500 observations is selected. how to Calculate the standard error of sample mean if the population standard deviation equals 20.
1
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0answers
26 views

Mean & SD of Sampling Distribution

A population consists of 4 numbers {0, 2, 4, 6}. Consider drawing a random sample of size n = 2 with replacement. (a) What is the sampling distribution of $\bar x$? Is this a normal distribution ? ...
1
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0answers
26 views

What are incoherent matrices

What does incoherence means in terms of matrices? I am brushing on some compressive sampling theory and I did not find any easy to understand or straight forward answer about what does the word ...
1
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0answers
70 views

Statistics - Uniform sample vs. Representative sample

I have a question concerning two different samples, with the first being more uniform that the second. a) Chance errors are likely to be smaller... using the first set of subjects using the second ...
1
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0answers
18 views

Correct sampling methods for this data set / requirements

I am just looking for a push in the right direction as to what kind of sampling methods I can use to fulfill this set of sampling criteria. I had thought stratified sampling, but I'm not sure if ...
1
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0answers
14 views

Design effect due to survey weights

I have a quick question on design effects due to survey weights. I would like to ask help since I am stuck in some particular parts though. Here it is: Show that the following expressions for design ...
1
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0answers
18 views

Gibbs sampler for local linear trend model

Question: Consider the local linear trend model given by: \begin{align*} y_t = \mu_t + \tau \varepsilon_t \ \cdots \ \text{Observation equation} \\ \mu_{t+1} = \phi \mu_t + \eta_t \ \cdots \ ...
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0answers
36 views

Relation with $F$ distribution and $t$ distribution

If $X\sim F_{n,n}$ , then show that $$\frac{\sqrt n(\sqrt X-\frac{1}{\sqrt X})}{2}\sim t_n$$
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0answers
136 views

Interpreting the meaning of sampling distribution

I have asked a couple of questions related to statistics recently as I just started to study the topic again (I ignored my university course on statistics and I now eat my fingers in anger). I asked ...
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0answers
260 views

Shannon vs dirichlet kernel interpolation method for signal reconstruction

I am currently studying fourier transform, and especially the way that the signal could be reconstructed from its spectrum. In many lectures, I have seen the shannon interpolation method to ...
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0answers
51 views

Gibbs / MCMC sampling for sum of parameters - how to improve slow mixing?

Suppose I have a hierarchical Bayesian model, where my observational prediction, $y'$, is calculated as the sum of other parameters, ${\alpha_i}$. My observation equation (the likelihood) is: $P(y | ...
1
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0answers
22 views

Population size and accuracy of expected value

If I have a series of populations, and a set of outcomes for these populations, how can I be certain that the observed proportions are, in fact, credible? I have investigated certain sampling methods ...
1
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0answers
77 views

Problem generating random vectors with a randomized linear programming with equality constraints (weird clustering)

Summary For simulation problems, I need to be able to generate large numbers of random lists of numbers, say $x_1, x_2, \dots, x_n$ (where $n \approx 1000$), subject constraints similar to what one ...
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0answers
163 views

Discrete approximation to a continuous probability density function

I want to approximate a continuous, finite probability density function, with a specified number $N$ of points, in the following way: If the pdf is 1-dimensional, defined over the section [0,1], then ...
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0answers
34 views

Suitable change of measure with importance sampling

I'm working on a project on Importance Sampling. When one tries to estimate the small probability $\alpha:=\mathbb{P}(X \in A)$, one can do a change of measure. There is change of measure which ...
1
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0answers
57 views

Continuous random sampling with replacement.

Construct a set $s\subseteq[0,1]$ by sampling points in $[0,1]$ with uniform probability density $x\leq1$ so that $|s|=x$. Interpret this as a sampling frame during which data is captured. Now, ...
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0answers
38 views

Sphere on a grid

So, this is a little tricky kind of a question and I'm not totally sure if it's a mathematic question or a more programming one, but I nevertheless hope to find answers. I want to find out the error ...
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0answers
98 views

Is it possible to calculate/impute the sample size “N” from a given mean and standard deviation?

Can anyone provide with some advice? - thank you I am required to calculate the sample size for two groups, given the following data: Total sample N (group1+group2)=583 group 1: mean=8.35, SD1.07, ...
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0answers
135 views

generating a binomial distribution

I'm trying to sample from a data set using a binomial distribution with parameters p and n. Implementation-wise, I follow these steps I generate an array containing the values of the cumulative ...
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0answers
74 views

Estimating the number of observations from a set of samples

I repeatedly measure a value $S_n$ which is the sum of a set of $n$ hidden inputs. The goal is to identify the number of hidden inputs. All of the hidden inputs are driven by an experimenter ...
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0answers
39 views

Sample estimated normal distribution - what will be the expected effect of another sample?

Assume I already have n samples of a 2D variable. I can compute the sample mean and variance. If I assume that the samples are taken from a normal distribution, then using the mean and variance I get ...
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0answers
46 views

How to sample the walk which visits each vertex of a graph specific number of times?

Is there any MCMC mathod that allow me to uniformly sample from all feasible walks where the following restrictions apply: ...
1
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0answers
49 views

Sampling a distribution with restrictions: eliminating the correlation between two variables

I have a collection of 400.000+ word-pairs. Each word-pair has an association strength, which is a measure of how related the two words are to each other (as in cow-milk). Each word-pair also has a ...
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0answers
48 views

Bias in Resampling

I'm currently doing some work with Particle Filters, a sampling-based method for computing expectations of functions with respect to dynamic (ie: time-variant) random variables. For example, consider ...
0
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0answers
20 views

Statistics, measuring unknown mean with standard deviation and probability

So I am stuck on this question and wondering if anyone can give me any hints towards it Estimate the mean pH of rainfalls in an area. Previous studies showed that the standard deviation in the area ...
0
votes
0answers
15 views

Sampling combinations (from a binomial coefficient) without replacement

The total number of combinations of $k$ items out of $n$ total is $n \choose k$, or a binomial coefficient. This can be a very large number even for pretty small $n$. The binomial coefficient ...
0
votes
0answers
16 views

Oversampling and trees

I want to create a model to predict the propensity to buy a certain product. As my proportion of 1's is very low, I decided to apply oversampling (to get a 10% of 1's and a 90% of 0's). Now, I want to ...
0
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0answers
8 views

Reconstructing symbols from another set of symbols

I have a discrete-time signal as: $r_l = r(lT/2) = \sum_m h_m \alpha_{l-m}$ where $\alpha_l = \sum_k a_k g(lT/2 -k(T+\Delta T))$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {\sin(2\pi t/T)}{2\pi ...
0
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0answers
6 views

Sensitivity analysis of paramaters and input variables

I am trying to perform a sensitivity analysis of an optimization problem $f(x,\alpha)= \min_{ Q} {g(x,\alpha , Q)}$ where $x$ is an input variable for our function, and $\alpha $ is a parameter. ...
0
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0answers
5 views

Expected number of distinct nodes visited in a directed bipartite graph

Let $G = (V,E)$ be a directed bipartite graph with $V = \{I \cup O\}$ where $\left\vert{I}\right\vert = n$ and $\left\vert{O}\right\vert = m$. All the edges start from a vertex in $I$ and end on a ...
0
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0answers
14 views

Sampling Question about Sample Size

A random sample of $16$ has a sample mean of $400$ and a sample standard deviation of $15kg$. Assume normality. A $90\%$ confidence interval for the mean is? I got $(393.43,$ $406.57)$. ...
0
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0answers
17 views

Outcome of multiple samples on continuous probablity function

I'm timing a signal from it's generation to return, and trying to figure out the error due to the difference between when the signal is actually sent out / received and when the clock starts/stops, ...