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derivatives of Gaussian PDF’s

We showed in Chapter 6 that side information Y for the horse race X can be used to increase the growth rate by the mutual information I(X;Y). We now extend this result to the stock market. Here, I(X;Y) is an … Continue reading

[T]he point of introducing L^p spaces in the first place is … to exploit … Banach space. For instance, if one has |ƒ − g| = 0, one would like to conclude that ƒ = g. But because of the … Continue reading

Upon my return [to academia, after years of private statistical consulting], I started reading the Annals of Statistics … and was bemused. Every article started with: Assume that the data are generated by the following model… followed by mathematics exploring … Continue reading

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November 12, 2011
Tagged academia, academic jousting matches, academic trends, academic trifles, academic wars, academics getting off track, artificial intelligence, C P Snow, econometrics, image recognition, Leo Breiman, machine learning, math, mathematics, maths, psychometrics, random forests, signal processing, statistics
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Mathematical matrices are blocks of numbers. So they don’t necessarily have definite characteristics the way plain vanilla, singleton numbers do. They’re freer. For example 131 ∈ positive and −9 ∈ negative. But is positive, negative, or zero? Well, it has … Continue reading

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Tagged economics, kernel, linear algebra, math, mathematics, maths, matrices, numbers, positive semi-definite, signal processing
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Daubechies D20 Ingrid Daubechies constructed several orthogonal discrete wavelet bases. Wavelet bases span function space, which includes for example sound, video, and images. Orthogonal wavelets are independent of each other. Discrete wavelets are easy for computers to deal with.

This is the reason for aliasing in music samples, Moire vibration in digital images, and is a useful formula for interpolation of data. (Source: http://academicearth.org/lectures/main-properties-of-shah-function-)