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in Dyalog22
Numerical integration is a computer task that arises in many practical problems. It is a key step in the evaluation of forensic DNA evidence that requires integrating a function likely of two to five variables corresponding to the number of people whose DNA comprises the evidential sample. Integrating a function of one variable by computer is familiar ground. For several variables there is some deep and technical literature, based on a superficially obvious extrapolation of one-variable integration. Charles will discuss an evidently elusive though simple and natural alternative extrapolation that overcomes multiple shortcomings of the published methods.
0:00 Introduction to the problem
4:00 Initial method: Volumetric voronoi cells
8:38 Issues with the method
10:18 Detour: Riemann sums
12:46 Live demo
14:55 Adaptive integration
14:29 Generalising to more dimensions
20:50 Splitting a simplex
24:01 Integration algorithm in brief
25:45 Summary and epilogue
