Some Methods to Predict Risks Earlier


H. Hirose


Ishigaki International Conference on Modern Statistics Theories, Practices, and Education in the 21st Century, page 7, November 9 - 10, 2013, Okinawa, Japan. abstract invited


In observing the widely spread of patients caused by infectious diseases or the increase of the number of failures of equipments, it is crucial to predict the final number of infected patients or failures at earlier stages. Prediction methods for infectious disease spread have been dealt with from a variety of mathematical approaches. Among them are 1) the SIR/SEIR model, 2) ordinary/stochastic differential equations (ODE/SDE), 3) statistical model (likelihood approach with conditional probability), 4) time series analysis like ARIMA), 5) agent-based model, the internet-used model (twitter), and 6) matrix decomposition method. These methods are also applicable to predict the increase of the number of failures.

We, first, applied each method to predict the infectious disease spread to real data cases, such as infectious gastroenteritis caused by Norovirus in Japan, streptococcal pharingitis cases, influenza, and etc. By comparing the root mean squared error (RMSE) between the predicted and observed data, we found that some method is superior to others at very earlier stage (e.g., ODE), and some shows superiority over others at later stage (e.g., truncated model). However, such a model selection depends on data, and we cannot determine the best model in advance. Thus, we propose a new approach to use all the methods simultaneously. The predicted value for the final number of patients using data until time T becomes a function (trend) of T. We here consider the use of this trend again to predict the final number of patients. It seems that the prediction accuracy will not be increased by this method because we use the same data. However, we may expect the better predicted values if we apply the multiple methodologies, like the ensemble method, to the same data. We show the result of this approach by applying the SARS case.

To predict the risk of rainfall, traditional methods are used such as ARIMA and artificial neural networks (ANN). Here, we have tried to use the matrix decomposition method using the cylinder-type matrix, and applied the method to the case of Indian rainfall data. Using the newly introduced accuracy evaluation criterion, risky, we can see that the matrix decomposition method provides a good accuracy comparing to the ANN result and the ARIMA result.

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