Uncertain predictions

In this work, we study the difficulty of predicting the time evolution of a phenomenon, as a pandemic or an epidemic, when the data are affected by statistical fluctuation, even if we know the function governing the evolution of that phenomenon. The initial fluctuations in the process imply great uncertainties of the fitted parameters and in the extrapolated function and, consequently, in the quantitative forecast of the evolution of the pandemic. Besides the statistical fluctuations, covariances of the adjusted parameters contribute to the uncertainties and doubts about the evolution of the studied phenomenon. The discussed problem is introduced using a phenomenon familiar to physics students.

Keywords
Statistical treatment of data; parameter fitting; variances and covariances; pandemic and epidemic evolution