Sunday: Warning signals edits continue

  • Marissa edits – Nearly done

  • Single-figure layout – DONE

  • equations in appendix – DONE

  • convergence / likelihood agreement between constOU and constLSN (Done, see below; consider using for a better initial-condition guessing routine for better convergence)

  • Reformulate transcritical bifurcation?

  • Rewrite cover letter

load("5598226674.Rdat")
require(warningsignals)
OU <- deterior_mc$null 
LSN <- deterior_mc$test
LSN_OU <- updateGauss(const_LSN, OU$pars, OU$X)

c(OU$loglik, LSN$loglik, LSN_OU$loglik)
[1] -1038.510 -1142.539 -1162.826
list(OU$pars, LSN_OU$pars, LSN$pars)

[[1]]
          Ro        theta        sigma 
  0.03372706 605.86310520  21.13186326 

[[2]]
       Ro     theta     sigma 
 83.49120 603.49469  14.00135 

[[3]]
          Ro            m        theta        sigma 
 93.89113902  -0.09374192 631.17624969   9.91779631 


# guess LSN parameters from OU parameterization
guess_Ro <- as.numeric(OU$pars['Ro']^2)
guess_theta <- as.numeric( OU$pars['theta']+OU$pars['Ro'] )
guess_sigma<- as.numeric(OU$pars['sigma']/sqrt(2*OU$pars['Ro']+OU$pars['theta']))

## see if the likelihood of the transformed parameters as LSN resembles the OU likelihood 
const_pars<- c(Ro=guess_Ro, theta=guess_theta, sigma=guess_sigma)

## Yay they almost agree:
-lik.gauss(OU$X, const_pars, const_LSN)
[1] -1044.504
OU$loglik
[1] -1038.510

## starting from here, they agree after optimization
new_LSN_OU <- updateGauss(const_LSN, const_pars, OU$X)
c(new_LSN_OU$loglik, OU$loglik)
[1] -1038.779 -1038.510