Tagged Questions

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0answers
35 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 ...
0
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2answers
46 views

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 ...
0
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0answers
69 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 ...
0
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0answers
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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0answers
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 ...
1
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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 ...
1
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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 $\{1,2,3,4,5,6,7,8,9\}$ ...
0
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0answers
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 ...
2
votes
1answer
92 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 ...
2
votes
1answer
227 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 ...
0
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0answers
131 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 ...
1
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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
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 ...
1
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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
votes
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 ...
1
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0answers
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 ...
1
vote
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 ...
0
votes
1answer
184 views

Hypothesis testing by random sampling

I'm sure this has been asked before, if so please point me to the relevant answers. Anyway, I have about 26000 phone subscription entries in a database. A number of these might contain wrong ...
2
votes
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 ...
3
votes
1answer
66 views

Samples in the convex body vs. samples on the convex surface

Let $K$ be a bounded convex body in $\mathbb{R}^n$. Suppose we have a sampler $\mathcal{S}_1$ that can generate points uniformly distributed in $\mathrm{int}K$, and another sampler $\mathcal{S}_2$ ...
2
votes
1answer
76 views

Uniform sampling of multicolored balls

If I uniformly sample-without-replacement a small bunch of multicolored balls (say, five colors) from one urn into a "smaller" urn, will the distribution of ball colors in the smaller urn be the same ...
4
votes
3answers
287 views

What is “sampling from a distribution”?

Exercise 4.11.3 of Grimmett and Stirzaker's Probability and Random Processes reads "Use the rejection method to sample from the gamma density $\Gamma(\lambda,t)$ where $t (\geq 1)$ may not be assumed ...
11
votes
2answers
391 views

What is the distribution of gaps?

Randomly select $n$ numbers from the universe $\{1,2\dots,m\}$ with or without replacement, and sort the numbers in ascending order. We can get a list of number $\{a_1,a_2,\dots,a_n\}$, and then we ...
4
votes
4answers
154 views

Sample: don't confuse measurements with actual values?

In Wikipedia's article on Sample there is the following remark: ''Note that a sample of random variables (i.e. a set of measurable functions) must not be confused with the realizations of these ...
2
votes
2answers
121 views

Generate a Monte Carlo sample from a PDF defined by a Fourier Series

I have a probability distribution (PDF) defined by a Fourier series.. actually it's a purely cosine series over a known range. The PDF quite smooth, so most of the power is in the low 5 or so ...
5
votes
2answers
240 views

Collisions in a sample of uniform distribution

Asked at a Microsoft interview: Assume you have a uniform distribution (can be discrete or continuous) of size X and you randomly select a sample of size Y. 1) What is the probability in terms of X ...
5
votes
1answer
233 views

How is a Halton sequence related to a Latin hypercube?

I currently use a Halton sequence to choose parameter sets for a prognostic model (e.g. using metabolic rate and protein content parameters to predict growth rate). From my understanding, both a ...