Computing Ordinary Least-Squares Paramerter Estimates for the National Descriptive Model of Mercury in Fish.

摘要

A specialized technique is used to compute weighted ordinary least-squares (OLS) estimates of the parameters of the National Descriptive Model of Mercury in Fish (NDMMF) in less time using less computer memory than general methods. The characteristics of the NDMMF allow the two products X'X and X'y in the normal equations to be filled out in a second or two of computer time during a single pass through the N data observations. As a result, the matrix X does not have to be stored in computer memory and the computationally expensive matrix multiplications generally required to produce X'X and X'y do not have to be carried out. The normal equations may then be solved to determine the best-fit parameters in the OLS sense. The computational solution based on this specialized technique requires O(8p2+16p) bytes of computer memory for p parameters on a machine with 8-byte double-precision numbers. This publication includes a reference implementation of this technique and a Gaussian-elimination solver in preliminary custom software. The National Descriptive Model of Mercury in Fish (NDMMF) is a statistical model used to predict the concentration of methylmercury in fish tissue. This model is of interest in current research at the U.S. Geological Survey (USGS) because of its ability to explain much of the variation in fish-tissue methylmercury concentrations as variation by geographic location, variation over time, and variation by fish species and length.