deletions | additions       diff --git a/subsection_Disaggregation_of_incidence_subsubsection__.tex b/subsection_Disaggregation_of_incidence_subsubsection__.tex  index f3189ef..61c0fec 100644  --- a/subsection_Disaggregation_of_incidence_subsubsection__.tex  +++ b/subsection_Disaggregation_of_incidence_subsubsection__.tex 
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Σx=1990:2012 |I(x) - Iobs(x)|2 + λβTSβ  \begin{align*}  \sum_x = 1990:2012 | \quad|  I(x) - I_{obs} (x)|^2 + \lambda \beta^T S \beta \end{align*}  Here $|I - I_{obs}|^2$ is the sum of squared errors in estimated incidence and $S$ is a difference penalty matrix applied directly to the parameters $\beta$ to control the level of variation between adjacent coefficients of the cubic-spline, and thus control (through a choice of $\lambda$) the smoothness of the time-dependent case incidence curve. Another important purpose of the use of the smoothness penalty matrix $S$ is to regularize (by creating smoothness dependencies between adjacent parameters) the ill-conditioned inverse problem (more unknown parameters than the data can resolve) that would tend to over fit the data when left ill-conditioned.