Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [approximation]

Approximations to distributions, functions, or other mathematical objects. To approximate something means to find some representation of it which is simpler in some respect, but not exact.

Wikipedia has an article and another directed at more mathematical uses with further references.

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Approximate order statistics for normal random variables

Are there well known formulas for the order statistics of certain random distributions? Particularly the first and last order statistics of a normal random variable, but a more general answer would also be appreciated. Edit: To clarify, I am…
Chris Taylor
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What are the factors that cause the posterior distributions to be intractable?

In Bayesian statistics, it is often mentioned that the posterior distribution is intractable and thus approximate inference must be applied. What are the factors that cause this intractability?
Nick
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Difference of two i.i.d. lognormal random variables

Let $X_1$ and $X_2$ be 2 i.i.d. r.v.'s where $\log(X_1),\log(X_2) \sim N(\mu,\sigma)$. I'd like to know the distribution for $X_1 - X_2$. The best I can do is to take the Taylor series of both and get that the difference is the sum of the difference…
frayedchef
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Are machine learning techniques "approximation algorithms"?

Recently there was a ML-like question over on cstheory stackexchange, and I posted an answer recommending Powell's method, gradient descent, genetic algorithms, or other "approximation algorithms". In a comment someone told me these methods were…
vzn
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Evaluate definite interval of normal distribution

I know that an easy to handle formula for the CDF of a normal distribution is somewhat missing, due to the complicated error function in it. However, I wonder if there is a a nice formula for $N(c_{-} \leq x < c_{+}| \mu, \sigma^2)$. Or what the…
bayerj
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Why bother with low rank approximations?

If you have a matrix with n rows and m columns, you can use SVD or other methods to calculate a low-rank approximation of the given matrix. However, the low rank approximation will still have n rows and m columns. How can low-rank-approximations be…
Zach
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How does a random kitchen sink work?

Last year at NIPS 2017 Ali Rahimi and Ben Recht won the test of time award for their paper "Random Features for Large-Scale Kernel Machines" where they introduced random features, later codified as the random kitchen sinks algorithm. As part of…
MachineEpsilon
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Error in normal approximation to a uniform sum distribution

One naive method for approximating a normal distribution is to add together perhaps $100$ IID random variables uniformly distributed on $[0,1]$, then recenter and rescale, relying on the Central Limit Theorem. (Side note: There are more accurate…
Douglas Zare
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Root finding for stochastic function

Suppose we have a function $f(x)$ that we can only observe through some noise. We can not compute $f(x)$ directly, only $f(x) + \eta$ where $\eta$ is some random noise. (In practice: I compute $f(x)$ using some Monte Carlo method.) What methods…
Szabolcs
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Universal approximation theorem for convolutional networks

The universal approximation theorem is a quite famous result for neural networks, basically stating that under some assumptions, a function can be uniformly approximated by a neural network within any accuracy. Is there some analogous result that…
Jonas Adler
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What is the normal approximation of the multinomial distribution?

If there are multiple possible approximations, I'm looking for the most basic one.
ericstalbot
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Do Gaussian process (regression) have the universal approximation property?

Can any continuous function on [a, b], where a and b are real numbers, be approximated or arbitrarily close to the function (in some norm) by Gaussian Processes (Regression)?
Michael D
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Approximation error of confidence interval for the mean when $n \geq 30$

Let $\{X_i\}_{i=1}^n$ be a family of i.i.d. random variables taking values in $[0,1]$, having a mean $\mu$ and variance $\sigma^2$. A simple confidence interval for the mean, using $\sigma$ whenever it is known, is given by $$ P( | \bar X - \mu| >…
Olivier
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Normal approximation to the Poisson distribution

Here in Wikipedia it says: For sufficiently large values of $λ$, (say $λ>1000$), the normal distribution with mean $λ$ and variance $λ$ (standard deviation $\sqrt{\lambda}$), is an excellent approximation to the Poisson distribution. If $λ$ is…
phg
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How to compute the probability associated with absurdly large Z-scores?

Software packages for network motif detection can return enormously high Z-scores (the highest I've seen is 600,000+, but Z-scores of more than 100 are quite common). I plan to show that these Z-scores are bogus. Huge Z-scores correspond to…
Douglas S. Stones
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