# 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.

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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 ...
9k views

### Intractable posterior distributions

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?
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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 ...
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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 ...
3k views

### 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 ...
2k views

### 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 ...
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### Distribution of the Levenshtein distance between two random strings

The Levenshtein or edit distance between two strings is the minimum number of edits (adding a letter, removing a letter or changing a letter) required to transform one into the other. Assume that we ...
832 views

### Berry-Esseen bound for binomial distribution

From the Berry-Essen theorem I can deduce $$\sup_{x\in\mathbb R}\left|P\left(\frac{B(p,n)-np}{\sqrt{npq}} \le x\right) - \Phi(x)\right| \le \frac{C(p^2+q^2)}{\sqrt{npq}}$$ with $C \le 0.4748$. My ...
678 views

### Numbers too large for R. How to approximate probability mass function?

Social network data is frequently found in a two-mode form: people vs. events they attend, people vs. classes they attend, countries vs. treaties they sign, etc. A strategy for analyzing this data is ...
992 views

### Approximation of Cauchy distribution

I have a ratio of two random, (dependent or independent) normally distributed variables. Knowing that the resulting Cauchy-distribution does not produce any moments. May I ask: Is there an ...
373 views

### Bayes Factor approximation

A brute force method to approximate the Bayes Factor (the ratio of the denominators (normalizing constants) in the Bayes formula) is to do the following for the two models of interest: repeat ...
182 views

### How to go about selecting an algorithm for approximate Bayesian inference

I am wondering if there are any good rules of thumb for how to go about selecting an approximate inference algorithm for a problem/model (specifically when exact inference is intractable)? When you ...
325 views

### Probability for finding a double-as-likely event

Repeating an experiment with $n$ possible outcomes $t$ times independently, where all but one outcomes have probability $\frac{1}{n+1}$ and the other outcome has the double probability $\frac{2}{n+1}$,...
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### Approximating the distribution of a linear combination of beta-distributed independent random variables

This question is related with these other two questions in Cross Validated, which has been already answered: Approximate the distribution of the sum of ind. Beta r.v Central limit theorem when the ...
For some events $A$, $B$, $C$ I know the occurrence probabilities $P(A),\: P(B),\: P(C)$ I also know the pairwise co-occurance probabilities $P(A,B),\: P(A,C),\: P(B,C)$ I want to approximate the ...