[R] (no subject)

[Berton Gunter]

> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Nadja Riedwyl
> Sent: Tuesday, September 06, 2005 10:22 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] (no subject)
> 
> my problem actually arised with fitting the data to the 
> weibulldistribution, 
> where it is hard to see, if the proposed parameterestimates 
> make sense.
> 
> data1:2743;4678;21427;6194;10286;1505;12811;2161;6853;2625;145
> 42;694;11491;
>           
> 14924;28640;17097;2136;5308;3477;91301;11488;3860;64114;14334
> 
> how am I supposed to know what starting values i have to take?
> i get different parameterestimates depending on the starting 
> values i choose, 
> this shouldn't be, no? how am i supposed to know, which the 
> "right" estimates 
> should be?
> 

This is a general issue with all (gradient-based) optimization methods when
the response to be optimized has many local optima and/or is poorly
conditioned. As Doug Bates and others have often remarked, finding good
starting values is an "art" that is often problem-specific. Ditto for "good"
parameterizations. There is no universal "magic" answer.

In many respects, this is the monster hiding in the closet of many of the
complex modeling methods being proposed in statistics and other disciplines:
when the response function to be optimized is a nonlinear function of "many"
parameters, convergence may be difficult to achieve. Presumably stochastic
optimization methods like simulated annealing and mcmc are less susceptible
to such problems, but they pay a large efficiency price to be so.

Cheers,

-- Bert Gunter
Genentech Non-Clinical Statistics
South San Francisco, CA