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Weighting and masking

In some historical data sets, certain data may be known to be affected by external agents such as war, or there may be some other bias or problem. This provides an incentive for weighting data sets. This is accomplished by introducing a weight vector of length m $\bold w = \{w_1,\,\ldots,w_m\}$ that contains the weight for each data point di. Weighted least squares is thus denoted

\begin{displaymath}\text{vary $\bold P$\space such that}\quad
\sum {\left(\frac{r_i}{w_i}\right)}^2 \quad \text{is minimized}
\end{displaymath}

If $\bold w_i = 1$ for all i, then we have the same model as before.

With historical time-series data, a more accurate analysis may be achieved by focusing on ``quiet'' periods and excluding unrepresentative data; for example, an analysis of nuclear testing data might be improved by excluding data from the years around the signing of the Nuclear Test Ban Treaty. Exclusion is accomplished by setting $\bold
w_i = 0$ for certain values of i. This is sometimes referred to as ``masking'' data, as we are hiding some of the points from the fitting engine.

Loglet Lab accommodates masking of the data. However, it does not allow use of user-specified weight vectors, though this functionality could be added in the future.


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Next: French Mobility: an example Up: Numerical Methods for Estimating Loglet Parameters from Time-Series Previous: Numerical Methods for Estimating Loglet Parameters from Time-Series
Perrin S Meyer
1998-07-14