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Provided the data are strictly positive, a better measure of relative accuracy can be obtained based on the log of the accuracy ratio: log(F t / A t) This measure is easier to analyze statistically and has valuable symmetry and unbiasedness properties.
In fisheries terms, maximum sustainable yield (MSY) is the largest average catch that can be captured from a stock under existing environmental conditions. [21] MSY aims at a balance between too much and too little harvest to keep the population at some intermediate abundance with a maximum replacement rate.
The maximum sustainable yield (MSY) is the largest amount of biomass that can be collected annually for indefinite periods. MSY assesses the productive capacity of the fishery, rather than demand or economic costs. MSY output may be greater or less than monopolistic or competitive output.
The concept of maximum sustainable yield (MSY) has been used in fisheries science and fisheries management for more than a century. Originally developed and popularized by Fedor Baranov early in the 1900s as the "theory of fishing," it is often credited with laying the foundation for the modern understanding of the population dynamics of fisheries. [1]
The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
Standard method like Gauss elimination can be used to solve the matrix equation for .A more numerically stable method is provided by QR decomposition method. Since the matrix is a symmetric positive definite matrix, can be solved twice as fast with the Cholesky decomposition, while for large sparse systems conjugate gradient method is more effective.
The use of the MAPE as a loss function for regression analysis is feasible both on a practical point of view and on a theoretical one, since the existence of an optimal model and the consistency of the empirical risk minimization can be proved. [1]
First, with a data sample of length n, the data analyst may run the regression over only q of the data points (with q < n), holding back the other n – q data points with the specific purpose of using them to compute the estimated model’s MSPE out of sample (i.e., not using data that were used in the model estimation process).