Last year we took a look at basis function interpolation which fits a weighted sum of

It is quite tempting, therefore, to use weighted sums of PDFs to construct new PDFs and in this post we shall see how we can use a simple probabilistic argument to do so.

*n*independent functions, known as basis functions, through observations of an arbitrary function's values at a set of*n*points in order to approximate it at unobserved points. In particular, we saw that symmetric probability density functions, or PDFs, make reasonable basis functions for approximating both univariate and multivariate functions.It is quite tempting, therefore, to use weighted sums of PDFs to construct new PDFs and in this post we shall see how we can use a simple probabilistic argument to do so.

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