Abstract
We propose a new method of randomized forecasting (RF-method), which operates with models described by systems of linear ordinary differential equations with random parameters. The RF-method is based on entropy-robust estimation of the probability density functions (PDFs) of model parameters and measurement noises. The entropy-optimal estimator uses a limited amount of data. The method of randomized forecasting is applied to World population prediction. Ensembles of entropy-optimal prognostic trajectories of World population and their probability characteristics are generated. We show potential preferences of the proposed method in comparison with existing methods.
Highlights
IntroductionFor a studied process, forecasting as a procedure consists of four consecutive stages: modeling (model design), learning (estimation of model characteristics), testing (of the “learned” model) and prediction of future development
For a studied process, forecasting as a procedure consists of four consecutive stages: modeling, learning, testing and prediction of future development.Forecasting is based on retrospective data analysis with its subsequent extrapolation to future periods
The presented results testify that the randomized forecasting as opposed to existent methods gives a set of probability characteristics of the World population prediction, which is calculated by using the ensemble of prognostic trajectories
Summary
For a studied process, forecasting as a procedure consists of four consecutive stages: modeling (model design), learning (estimation of model characteristics), testing (of the “learned” model) and prediction of future development. The first technique, referred to as scenario forecasting [1], proceeds from the scenario approach whose objectification is replaced by the opinion of an expert group It implements only the stages of modeling and prediction: learning and testing are eliminated owing to the opinion of experts, who choose an appropriate mathematical model of a studied process and form value sets (scenarios) of the model parameters. A major assumption is that the model possesses deterministic parameters, the values of which are defined using sets of real retrospective data The latter are treated as a stochastic object with certain properties (a sample from a universe, normal distribution, etc.). In this case, one may assign different probabilistic characteristics (variances, confidence intervals, and so on) to the derived estimates of model parameters. We perform the comparative analysis of the PF- and RF-based approaches
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