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# 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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### Optimization: Approximate function - Which points to evaluate next?

I am looking for a statistical method (and a link to a nice R package would be cool too!) which allows me to find which point to evaluate next for a given function. I have a non-stochastic function z ...
406 views

### Normal approximation to Poisson: With Continuity Correction the Approximation Seems Worse

This is Exercise 3 in Section 6.3 of Probability and Statistics, 4th edition, by DeGroot and Schervish: Suppose that the distribution of the number of defects on any given bolt of cloth is the ...
274 views

### Analytically solving sampling with or without replacement after Poisson/Negative binomial

Short version I am trying to analytically solve/approximate the composite likelihood that results from independent Poisson draws and further sampling with or without replacement (I don't really care ...
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### Compression of 18000 curves

I have over $18000$ curves that I need to compress to save $\geq 50\%$ of space. Each curve is described by points $f(1), f(2), ..., f(96)$, each $f(x)$ is 8-bit long. The curves in compressed form ...
203 views

### Approximating the mathematical expectation of the argmax of a Gaussian random vector

Let $X = \left( {{X_1},...,{X_n}} \right) \sim \mathcal{N}\left( {{\mathbf{\mu }},{\mathbf{\Sigma }}} \right)$ be a Gaussian random vector and $I = \mathop {\arg \max }\limits_{i = 1,n} {X_i}$. $I$ ...
141 views

### CLT for random sums: Anscombe's Theorem vs. “classical” version

Given a compound Poisson distribution $$S(t):=\sum_{k=1}^{N(t)} X_{k}$$ with $N(t)\in\mathbb{N},\,t\geq0$ a Poisson process with rate $\lambda.$ $X_{k}$ are non-negative iid random variables such ...
931 views

### Continuous approximation to binomial distribution

Consider an integer variable $k$ that follows a binomial distribution, $$\binom{N}{k}p^{k}\left(1-p\right)^{N-k}$$ with total draws $N$ and probability of success $p$. I am interested in the ...
53 views

### What's a good approximation to the count distribution of people for days of birth?

I have data on $n$ people's dates of birth and let's ignore the years and look only at the $k$ = 366 days of the year (including Feb 29). Assuming that dates of birth are uniformly and independently ...
43 views

### Difference vs log-difference: do they behave similarly?

Consider two positively-valued time series, $\{X(t),Y(t)>0|t\geq0\}$. Now consider two transformations: $$U(t) = Y(t) - \beta X(t),\\ V(t) = \ln{[Y(t)]} - \ln{[\beta X(t)]},$$ with $\beta>0$ ...
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### Estimate correlation between data and data-fit model for variance reduction in Monte Carlo estimate

Say that I want to estimate the mean of a function $f$, $\mathbb{E}[f(X)]$, given some input distribution $x\sim P(x)$. I don't know anython about the form of $f$ except that it is smooth and ...
100 views

### Estimating function with Gaussian Procceses

I do not have strong math background, but I am trying to understand Gaussian Processes by example using the lecture Machine learning - Introduction to Gaussian processes by Nando de Freitas. Here is ...
93 views

### Evaluate approximation of PCA from randomized algorithms

I have been comparing different PCA implementations (some via explicit calculation of the covariance matrix, some with randomized/truncated SVD) in terms of speed, and now wanted to compare how good ...
51 views

### Contraction or Reduction of a Neural Network

Circuit size reduction is common practice in Theoretical Computer science. It is very common to approximate a circuit with a smaller circuit (Or a polynomial and so on). Are there any such techniques ...
55 views

### Better skill checks for RPGs - Conditional probability given 2 independent parameters

I am trying to find a better way (theoretically, not practically speaking) to do a skill check for a Skill Trial in RPGs. In several RPGs, a skill check consists of a Playing Character (PC) trying to ...
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### Correcting wild deviations in polynomial interpolation/regression

When using polynomials to do spline interpolation or least-squares regression on a set of points which are not evenly spaced, there is a tendency for the polynomial to deviate wildly in those regions ...
As I understand it, the Welch–Satterthwaite equation says that if $s_i^2$ is the sample variance of group $i$ (with $n_i$ samples), then, assuming that the measurements in each group are iid's that ...