The sampling tag has no wiki summary.
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Sample $x$ from $g(x)$
I got confused with all this randomness and probability functions. I was trying to implement the rejection sampling method which (apparently) is really simple. I was reading from Rejection Sampling in ...
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1answer
12 views
Optimal sampling for an arbitratry area
I have a closed area (2D) of arbitrary shape and some number of sample points to take from the area.
Now I would like to find optimal distribution of the sample points, so that distances from sample ...
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1answer
17 views
please prove the following proof related to F distribution.
Suppose $S_1^2$ and $S_2^2$ are two independent unbiased estimate of the common population variance $\sigma^2$ from two random sample of sizes $n_1$ and $n_2$ respectively.
Then show that
...
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0answers
21 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 ...
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21 views
Discrete Fourier Transform calculating elements
Consider a sound signal sampled at 20,000 samples per second. Suppose that the discrete Fourier transform (DFT) of a segment of 0.05 seconds of the sound is computed.
...
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9 views
How can the distribution characteristics in different random sample sizes be known?
Here is my logic:
A sample from a random pool (algorithm or natural) is known to have a certain distribution (normal, uniform, etc.) assuming both the sample and the pool (population?) are big ...
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12 views
How to work out the t statistic with 2 different samples?
So the question is whether a placebo works -
2 samples, Group A (n=100) takes the drug and 75 get better. Group B (n=100) take a placebo and 65 get better.
I started with the Hypothesis that the ...
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0answers
27 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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68 views
Simulate random sampling with replacement
Any ideas on how to approach this problem?
(Due to Karp)
Consider a bin containing d balls chosen at random (without replacement) from a collection of n distinct balls. Without being able to see or ...
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1answer
29 views
Monte Carlo Rejection Sampling Method
I have the following passage from a set of lecture notes I am working on that I would like to understand a little better.
$\underline{\text{Algorithm for Rejection Sampling}}$:
Given two densities ...
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0answers
21 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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25 views
optimum weights for minimum variance
If $X_i$ is an estimator for $x_i$, and an estimate of the sum i.e. $ Y = x_1 + x_2 + ... + x_n $ is made by the ration $X_i / p_i$ where $p_i$ is the probability that $X_i$ is chosen , then what are ...
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1answer
61 views
How to sample from joint Bernoulli distribution?
I have done searches on google.com and here but haven't found a related one. I apologize if this is a re-post.
Here is my question:
I have a set $n$ of Bernoulli random numbers, and I know the ...
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17 views
selection for variance reduction in monte-carlo
I need to prove that the following variance reduction operations lead to the optimum value. A related question i asked here about variance reduction gives the optimal proportions are according to ...
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0answers
21 views
Sampling Problem with Sets
$|X|$ contains $|Y|$ and $|Z|$, but $|Y|$ and $|Z|$ are disjoint. We have $|X|=20$, $|Y|=10$, and $|Z|=5$.
If we are considering $f:X\to X$, how many of these sets map $Y\to Y$, how many map $Z\to ...
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1answer
33 views
variance reduction
Say i have $n$ variables with variances $V_1,V_2,...V_n$. The sum of the variables will have a variance of $V=V_1+V_2+..V_n$ .Now if i am given N total simulations to reduce the variance V, how do i ...
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2answers
61 views
Simple random sampling without replacement of huge dataset
For an application I'm working on, I need to sample a small set of values from a very large data set, on the order of few hundred taken from about 60 million(and growing).
Usually I use the technique ...
2
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1answer
108 views
Sampling from discrete probability distribution from first principles
I have a set $S=\{a_1,a_2,\dots,a_n\}$. The probability with which each of the element is selected is $\{p_1,p_2,\dots,p_n\}$ respectively (where of course $p_1+p_2+\cdots+p_n=1$).
I want to ...
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2answers
36 views
Sampling problem with and without replacement
Find the probability of the event that number $1$ and number $7$ were chosen first and third, respectively at the experiment of choosing five numbers from this set of numbers $\{1,2,3,4,5,6,7,8,9\}$ ...
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25 views
Power spectral Density after Sampling
I'm working in a project where I need to identify the noise features in a signal coming from a sensor. Suppose to call the noisy signal as $y(t)$, we define its components as
$y(t) = y_{true}(t) + ...
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24 views
Generating unbiased sample with given simple property
Suppose we can generate independent samples of random variable $X$ but the distribution of $X$ in unknown.
How can we generate unbiased samples of random variable $Y$ for which $E[Y]E[X]=1$, and ...
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1answer
37 views
Sample size requirements in survey
If am doing some market research and want to answer the question "What percentage of the users of a service, searched for the given service online?". Lets say I go out and get people to take a survey. ...
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1answer
85 views
Probability to choose specific item in a “weighted sampling without replacement” experiment
Given $n$ items with weight $w_n$ each -- what is the probability that item $i$ is chosen in a $k$-out-of-$n$ "weighted random sampling without replacement" experiment? Can a closed-form solution that ...
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30 views
sampling functions and effect on DFT
I'm looking for help on pointing me to the right literature....
My question is as follows...
Let's assume I have a discrete function (sinusoidal in nature) sampled at N equi-spaced points. However ...
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1answer
216 views
unbiased estimator of sample variance using two samples
I have a couple questions, I'm hoping someone can help!
Let $X_1...X_n$ is a random i.i.d. sample from a $N(\mu,\sigma^2)$ distribution, and $Y_1...Y_m$ is a random i.i.d. sample from a ...
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0answers
72 views
tolerance intervals, solving for probability
Given a small sample from a normally-distributed population, how do I calculate the probability that a specified percentage of the population that is within some bounds [A,B]?
I'm trying to do some ...
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4answers
107 views
Sampling from a $2$d normal with a given covariance matrix
How would one sample from the $2$-dimensional normal distribution with mean $0$ and covariance matrix $$\begin{bmatrix} a & b\\b & c \end{bmatrix}$$ given the ability to sample from the ...
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0answers
13 views
For a process made up of subprocesses, how to sample each subprocess' distributions to meet certain conditions?
I have a process made up of, on average, about 10 independant subprocesses that follow approximately a normal distribution. I know the individual distributions of the subprocesses, but not the ...
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1answer
63 views
How to sample from a Gamma distribution with shape not integer
I'm looking for an effective method to sample from a Gamma distribution that has the shape parameter not integer.
However, I found everywhere the method to sample from a Gamma with an integer shape ...
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1answer
49 views
Sample-based median calculation
Is there any technique to find the median of a large data set using sampling (or maybe randomized algorithms)?
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42 views
Sampling + Bandpass
A one dimensional function $f(x)=2\cos \pi \xi_0 x$ is sampled at a rate $\xi_s$, which is just above $\xi_0$. Commom reconstrucion filter such as the zero-or-first order-hold circuits have a passband ...
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1answer
44 views
Determining Sample Size - Design Problem
I have a hypothetical problem were say I have a sample size of about 5000 people. I then will collect data on them say, how man calories of food they eat per day for a month. Now I can't obviously run ...
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1answer
26 views
Generating statistics from data samples, that are of snapshots.
My question is part math part computers but I need more of the math answer then a computer answer. I am going to be grabing snapshots of a moment of time on how a computer is performing. Because of ...
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0answers
56 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
128 views
Use importance sampling to estimate the quantity [Matlab]
So I've been doing some importance sampling by hand for much easier problems but im troubled with this task and thus running it through MATLAB would be much easier I think. Use importance sampling to ...
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1answer
64 views
Should I ignore $0$ when do inverse transform sampling?
Generic method
Generate $U \sim \mathrm{Uniform}(0,1)$.
Return $F^{-1}(U)$.
So, in step 1, $U$ has domain/support as $[0,1]$, so it is possible that $U=0$ or $U=1$,
but $F^{-1}(0)=-\infty$. ...
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72 views
Bootstrap sampling
The usual way to create bootstraps is by sampling with replacement from the original data set.
The resulting resampled bootstraps have the same length (N records/data points) as the original data ...
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53 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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34 views
How do I find the frequency response of an ideally sampled-in-time signal?
Please consider the image below. It contains the problem and the work I have done. I am off by a minus sign and I'm not sure how to get rid of it. Consider what I have and what the book has. ...
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1answer
42 views
Statistics and clarification of Central Limit Theorm
If I have 1,000 participants ranking on a scale of 1 to 10 regarding some object how do I interpret the confidence level and margin of error of the resulting rank? I am used to of seeing 99% ...
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1answer
18 views
What is the name of (1-a)*current + a*sample
Say we take a sample every time unit, we have a calibrated value which needs tracking for drift, however every sample has a given variance causing jumping if we were to use it directly as the new ...
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87 views
Giving sampling distribution of population total estimator [Homework]
Given sampling data below,
Considering a Simple Random Sampling(SRS without replacement) of size 4, what is the sampling distribution of the estimators for total of y's? t1 and t2 where
i) t1 is ...
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48 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
Uniformly sample points over a circular patch of a sphere without rejection [duplicate]
Possible Duplicate:
Generate a random direction within a cone
A point on a unit sphere $(x,y,z)$ and an maximal angular separation $\theta$ defines a patch with an area of $\Omega = 2 \pi ...
2
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1answer
81 views
Designing an efficient sampling strategy
In a Monte Carlo simulation, my goal is to compute an estimate of the mean of a distribution via sampling.
Traditional, straightforward statistics generates samples (via simulation) and computes the ...
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0answers
97 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 ...
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63 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 ...
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1answer
169 views
uniform sampling of the sphere w.r.t. inner products other than the usual one
I will have a small (usually 2 or 3, probably no bigger than 6) positive integer $n$
and symmetric positive-definite real $n$-by-$n$ matrices $A$,
and will want to sample an ...
3
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2answers
120 views
Determining sparse frequency distribution via discrete Fourier transform
Consider the function $$f(t) = 2 \sin(t)+\sin(2t)+25 \sin(400t)$$
(for example).
In this case, how many samples of this function would I have to take, and at what sampling frequency, to determine the ...
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2answers
106 views
Sampling a combination randomly
I want to sample a combination of $N$ elements (without replacement) from a list of $M$ elements where $M\gg N$. There are algorithms to do this when each element is picked with uniform probability. I ...
