Jonathan Olmsted

Transformations

Useful Transformations in Optimization

Below are several useful transformations used to express bounded parameters in terms of unbounded parameters. This is helpful when working with un-constrained optimization algorithms but the problem is more naturally viewed as a constrained optimization problem.

Correlation Parameters
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## Correlation Transformation
## 'rho' must be in [-1,1]
## 'x' must be in Reals
rho <- (exp(2 * x) - 1) / (exp(2 * x) + 1)
Variance Parameters
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## Variance Parameter Transformation
## 'sigmasq' must be in (0, Inf)
## 'x' must be in Reals
sigmasq <- exp(x)