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