[ADMB Users] very small number math
Larry Jacobson (NOAA Federal)
larry.jacobson at noaa.gov
Mon Mar 11 11:58:04 PDT 2013
This came up recently here at NEFSC. One of the things we decided is
that VPA solutions might be hard to find in admb because the parameters
(terminal F or abundances) in the vicinity of the best solutions could
have flat gradients. The gradients might be flat because of the
convergence properties of the VPA (Chris Legault pointed this out).
That is, asmall tweak to one of these parameters (say the initial F/N
for the youngest age group or for the oldest true age) can have little
effect on the model or on the objective function. I don't know for sure
but guess this would happen whether you were solving for F internally or
as a formal parameter.
Cheers!
On 3/11/2013 2:43 PM, Richard Methot - NOAA Federal wrote:
> Mark,
>
> The approach I take for stable estimation of F rates is to use a
> well-defined starting point for the search and to search over a fixed
> number of iterations. In particular, I get the starting point from
> Pope's approximation to calculate an exploitation rate (for each fleet
> relative to the mid-year available biomass for that fleet); then
> convert these U's into an approximation for each F, then tune these
> F's over a fixed number of iterations. This converges well enough
> with just 4 iterations even with multiple fleets. The trick to rapid
> convergence is to base the updated F values based on the anticipated
> total Z after adjusting the Fs, not the current total Z. Note that
> this is in a separable model, so it is looking for the F that matches
> catch biomass conditioned on a set of selectivity parameters.
>
> This approach leads to very steep gradients for other parameters when
> F is high and the catch data is considered to be precise, so
> convergence of the overall model is slow because the model is
> constantly maintaining a good fit to the catch data. For these cases,
> I find it useful to switch over (during BETWEEN_PHASES) to treating
> the F's as ADMB model parameters, rather than as a set of scaling
> factors to match the catch. When treating the F's as parameters, the
> model tends to wait until the last iterations to get a good fit to the
> catches.
>
> Overall, I find that the variance on other model outputs (such as
> final population biomass) is rather insensitive to F as coefficient
> vs. F as parameter, but haven't tested this in high F situations.
>
> Rick
>
>
> On Mon, Mar 11, 2013 at 10:35 AM, Fowler, Mark
> <Mark.Fowler at dfo-mpo.gc.ca <mailto:Mark.Fowler at dfo-mpo.gc.ca>> wrote:
>
> Yes, and I use epsilon for proper parameters. The situation I'm
> addressing is 'non-ADMB' iterative mortality (F) estimates. These are
> just loop functions to estimate F's to create population and mortality
> matrices. Obviously candidates as parameters, but I needed to keep
> them
> as originally written. I was translating a particular type of VPA
> written in a language called ACON to R and ADMB. Only the
> reference year
> abundances are estimated with a serious optimizing function in the
> original model (to reasonably estimate catchabilities). Initially
> this
> served for truthing until I finished the translations. Hence the issue
> of dealing with extremely small values are the profusion of F
> loops. And
> I'm doing these in an equivalent manner to your suggestion, I just
> don't
> use epsilon per se because I like to restrict it to parameters.
>
> I've since been keeping the loops while comparing vulnerabilities to
> local minima across the three programs, so only the reference year
> abundances are optimized directly. Both optim and the ACON optimizer
> (NLLS) clearly work left to right on parameter sets. The optim
> function
> gets trapped in local minima with high uninformative constants for
> priors on a vector that grades high to low. Starting left-most they go
> up, which is correct relative to numbers to the right but wrong in
> absolute terms. NLLS starts out similarly (run with few iterations you
> get the same answer) but doesn't stay there, so maybe breaks the
> left-to-right rule at some point to explore the range, or has some
> threshold point at which it gives up on the first parameter. So
> far I'm
> stymied with ADMB. I'm thinking maybe the F estimations confound
> tracking of gradients?
>
>
> > Mark Fowler
> Population Ecology Division
> > Bedford Inst of Oceanography
> > Dept Fisheries & Oceans
> > Dartmouth NS Canada
> B2Y 4A2
> Tel. (902) 426-3529 <tel:%28902%29%20426-3529>
> Fax (902) 426-9710 <tel:%28902%29%20426-9710>
> Email Mark.Fowler at dfo-mpo.gc.ca
> <mailto:Mark.Fowler at dfo-mpo.gc.ca>
> Home Tel. (902) 461-0708 <tel:%28902%29%20461-0708>
> Home Email mark.fowler at ns.sympatico.ca
> <mailto:mark.fowler at ns.sympatico.ca>
>
>
> -----Original Message-----
> From: users-bounces at admb-project.org
> <mailto:users-bounces at admb-project.org>
> [mailto:users-bounces at admb-project.org
> <mailto:users-bounces at admb-project.org>] On Behalf Of dave fournier
> Sent: March 8, 2013 11:52 AM
> To: users at admb-project.org <mailto:users at admb-project.org>
> Subject: Re: [ADMB Users] very small number math
>
> This is proabably a good use of phases. In the early phase you add
> something
>
> like
>
> x/(eps+y)
>
> and let eps get smaller or 0 in a later phase.
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>
> --
> *Richard D. Methot Jr. Ph.D.
> **NOAA Fisheries - **/Science Advisor for Stock Assessments/*
> *Office: 206-860-3365**
> Mobile: 301-787-0241
> *
>
>
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--
**********************
Larry Jacobson
National Marine Fisheries Service
Northeast Fisheries Science Center
166 Water Street
Woods Hole, MA 02543-1026
Voice: 508-495-2317
Fax: 508-495-2393
E-mail: larry.jacobson at noaa.gov
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