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Background

I would appreciate help in identifying / explaining this operation:

To calculate each of the $n$ values of $f(\Phi)$:

  1. sample from the distribution of each of $i$ parameters, $\phi_i$
  2. calculate the $i$ values of $g(\phi_{i})$
  3. subtract each $g_i(\phi_{i,n})$ from $g_i(\hat{\phi_i})$ (these are deviation)
  4. take the sum of these deviations
  5. 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:

  1. 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.

  2. Is there a simplified form of this computation, or expression of the equation?

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