N.I.M.R.O.D.  
Functions/Subroutines

penalization.f90 File Reference

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Functions/Subroutines

subroutine logLikelihood_penalization (bparam, pena)
 Penalization for log-likelihood.
subroutine gradients_penalization (bparam, pena)
 Penalization for gradients used in scores.
subroutine hessian_penalization (bparam, pena)
 Penalization for diagonal of the hessian terms.

Function Documentation

subroutine gradients_penalization ( double precision,dimension(npm),intent(in)  bparam,
double precision,dimension(npm),intent(out)  pena 
)

Penalization for gradients used in scores.

AUTHOR : Melanie Prague Daniel Commenges Julia Drylewicz Jeremy guedj Rodolphe Thiebaut

DESCRIPTION :

We assume normal independent priors for the fixed effects, half-Cauchy priors for the variances of the random effects with median parameter ${s^{j}}^2$ and conventional one-dimension Jeffreys-type improper priors for the variances of the measurement errors, then the penalization function $\frac{\partial J(\theta)}{\partial \theta}$ where $J$ is:

\[ J(\theta)=\sum _{j=1}^p \frac{[\phi_j- E (\phi_j)]^2}{2{V (\phi_j)}} + \sum _{j=1}^{n_{e}} \frac{[\beta_j- E (\beta_j)]^2}{2{V (\beta_j)}} \nonumber \ + \sum _{j=1}^q \log({\sigma^{j}}^2+{s^{j}}^2) + \sum _{j=1}^m \log(\sigma_{m}), \]

where $E$ and $V$ are the expectation and the variance under the prior.This must correspond to the first derivative of penalization defined in logLikelihood_penalization.

MODIFICATION:

01/09/2012 - Prague - Refactoring

INFORMATIONS:

Parameters:
[in]bparamparameter vector
[out]penaPenalization value

Definition at line 114 of file penalization.f90.

References WorkingSharedValues::esp_prior, WorkingSharedValues::penalisationAll, WorkingSharedValues::penalisationBiologique, and WorkingSharedValues::std_prior.

Referenced by derivMARC(), and derivRVS().

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subroutine hessian_penalization ( double precision,dimension(npm),intent(in)  bparam,
double precision,dimension(npm),intent(out)  pena 
)

Penalization for diagonal of the hessian terms.

AUTHOR : Melanie Prague Daniel Commenges Julia Drylewicz Jeremy guedj Rodolphe Thiebaut

DESCRIPTION :

We assume normal independent priors for the fixed effects, half-Cauchy priors for the variances of the random effects with median parameter ${s^{j}}^2$ and conventional one-dimension Jeffreys-type improper priors for the variances of the measurement errors, then the penalization function $\frac{\partial J(\theta)^2}{\partial^2 \theta}$ where $J$ is:

\[ J(\theta)=\sum _{j=1}^p \frac{[\phi_j- E (\phi_j)]^2}{2{V (\phi_j)}} + \sum _{j=1}^{n_{e}} \frac{[\beta_j- E (\beta_j)]^2}{2{V (\beta_j)}} \nonumber \ + \sum _{j=1}^q \log({\sigma^{j}}^2+{s^{j}}^2) + \sum _{j=1}^m \log(\sigma_{m}), \]

where $E$ and $V$ are the expectation and the variance under the prior. This must correspond to the second derivative of penalization defined in logLikelihood_penalization.

MODIFICATION:

01/09/2012 - Prague - Refactoring

INFORMATIONS:

Parameters:
[in]bparamparameter vector
[out]penaPenalization value

Definition at line 190 of file penalization.f90.

References WorkingSharedValues::penalisationAll, WorkingSharedValues::penalisationBiologique, and WorkingSharedValues::std_prior.

Referenced by derivMARC(), and derivRVS().

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subroutine logLikelihood_penalization ( double precision,dimension(npm),intent(in)  bparam,
double precision,intent(out)  pena 
)

Penalization for log-likelihood.

AUTHOR : Melanie Prague Daniel Commenges Julia Drylewicz Jeremy guedj Rodolphe Thiebaut

DESCRIPTION :

We assume normal independent priors for the fixed effects, half-Cauchy priors for the variances of the random effects with median parameter ${s^{j}}^2$ and conventional one-dimension Jeffreys-type improper priors for the variances of the measurement errors, then the penalization function $J(\theta)$ can be written:

\[ J(\theta)=\sum _{j=1}^p \frac{[\phi_j- E (\phi_j)]^2}{2{V (\phi_j)}} + \sum _{j=1}^{n_{e}} \frac{[\beta_j- E (\beta_j)]^2}{2{V (\beta_j)}} \nonumber \ + \sum _{j=1}^q \log({\sigma^{j}}^2+{s^{j}}^2) + \sum _{j=1}^m \log(\sigma_{m}), \]

where $E$ and $V$ are the expectation and the variance under the prior.

CAUTION : Normally, these subroutines must not be modified in routine by users.

MODIFICATION:

01/09/2012 - Prague - Refactoring

INFORMATIONS:

Parameters:
[in]bparamparameter vector
[out]penaPenalization value

Definition at line 39 of file penalization.f90.

References WorkingSharedValues::esp_prior, WorkingSharedValues::penalisationAll, WorkingSharedValues::penalisationBiologique, and WorkingSharedValues::std_prior.

Referenced by funcpa().

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