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add log_Phi_approx function and its complement #1025

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@bob-carpenter

Description

@bob-carpenter

Description

For arithmetic stability in CDF calculations, we should have an approximate Phi and its complement on the log scale.

Note

  • Ideally this will be done with custom derivatives
  • Ideally this will be properly vectorized

If not, there's a log_inv_logit that could be called.

A naming convention for complements needs to be established. logc_Phi_approx seems a bit too cryptic despite our having lcdf and lccdf functions.

Current Math Version

v2.18.0

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