Better parameter estimates for tropical forests

[dfalster]

• intercept of LMA-turnover function ( k_l0)
• theta for tropical forests
• scaling of H-A (from baad)
• ks ??
• reproductive allocation function

[dfalster]

in 98491c54c1abc57bda278f006b95c470204e0705 I reduced k_l0 so that better aligns with tropical data.

More generally, aligning model output with empirical estimates of dbh growth in figure 1 seems like an ideal candidate for model-data fusion

[dfalster]

More generally, want to fit model to data.

Spoke with @dsteinberg about possible techniques. Here's suggested way forward

1. Initially setup using non-linear least squares solver, optimises fit over parameters
   • Could use Levenberg Marquardt algorithm (one of several possible). Typically needs derivatives, but for few dimensions (tens) can do these numerically.
   • probably do in R - gives us full control
   • generates single best fit parameter value. Many drawbacks to this, but good starting point.
2. Then proceed into Bayesian framework to get full posterior distributions
   • possible use methods from Steinberg & Bonilla 2014 - uses variational Bayes to speed up parameter estimation, by assuming posterior is Guassian
3. Then move into data fusion - constrain parameters using multiple sources of data

[dfalster]

@jscamac suggests using minpack.lm. According to this blog, the standard nls routine in R does not use the Levenberg-Marquardt approach, which "is more robust, i.e. finds a solution even if it starts very far off the final minimum. This is because its switching between Gauss-Newton and gradient descent.

[jscamac]

I've been using it to provide initials parameter values for the JAGS models. Still is highly susceptible to starting conditions though... but less so than nls() .

[jscamac]

This might also be more useful. http://cran.r-project.org/web/packages/gnm/index.html.

More details on custom equations here: http://stackoverflow.com/questions/26344429/fitting-generalized-nonlinear-model-in-r/26407073#26407073