Background Informatiom
I would appreciate help in identifying or explaining this operation:
To calculate each of the $n$ values of $f(\Phi)$:
- Sample from the distribution of each of $i$ parameters, $\phi_i$
- Calculate the $i$ values of $g(\phi_{i})$
- Subtract each $g_i(\phi_{i,n})$ from $g_i(\hat{\phi_i})$ (these are deviation)
- Take the sum of these deviations
- Add the sum of these deviations to the median
in summary, this is the calculation:
$f(\Phi_n)=g(\hat{\phi}) + \sum_i(g_i(\phi_{i,n})-g_i(\hat{\phi_i}))$
- $\phi_i$ is the distribution of each of $i$ parameters
- $\hat{\phi}$ is a vector of the parameter medians
- $g$ is a vector of $i$ univariate splines, one for each parameter estimated by evaluating a multivariate model across the range of $\phi_i$ while all $\phi_{\text{not}i}$ held at their medians (a univariate sensitivity analysis of a computationally intensive prognostic model)
- $g_i(\hat{\phi_i})$ is the $i^{th}$ spline evaluated at the median of $\phi_i$
Questions:
Is there a name or simple way to describe this calculation?
My first attempt to describe the above operation:
The spline ensemble is calculated as the sum of deviations from the median for for each parameter added to the median.
An alternative suggestion:
The spline ensemble is calculated based on the univariate anomalies for each parameter.
Is there a simplified form of this computation, or expression of the equation?