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That the sum of two Gaussians is a Gaussian an be found in any basic text on statistics. That combining distributions, calculating them in parallel or online is
by absherwin 14y ago
That the sum of two Gaussians is a Gaussian an be found in any basic text on statistics. That combining distributions, calculating them in parallel or online is possible isn't new either. The Kalman filter which was published in 1961 is an example of an online algorithm for fitting a Gaussian.
This is a interesting exposition and places specific results in a more general algebraic framework; however, the title suggests this is a revolutionary discovery which it isn't
- montecarl 14y agoI think you mean product. The sum of two Gaussians isn't a Gaussian.
- yummyfajitas 14y agoI think he meant the sum of two gaussian random variables is a gaussian. I.e., if X and Y are both drawn from a gaussian distribution, then X+Y is too.
- mturmon 14y agoRight. (You also need X and Y to be independent, or at least multivariate Gaussian -- i.e., X and Y can both be Gaussian but (X,Y) can fail to be Gaussian as a pair.) The product of Gaussian random variables is certainly not Gaussian.
- Evbn 14y agoWhen thinking about monoids, the word sum and product aren't distinguishable unless you specific the precise operation, as neither one is a canonical analogy to integer sum/product. Pointwise combination is an unattractive definition, as it ignores a lot of interesting structure in a connected space like real numbers. Indeed, convolution, the common way of combining functions, is defined as a sum of products at each point.