[Rd] Numerical optimisation and "non-feasible" regions

[Mathieu Ribatet]

Dear Patrick (and other),

Well I used the Sylvester's criteria (which is equivalent) to test for 
this. But unfortunately, this is not the only issue!
Well, to sum up quickly, it's more or less like geostatistics. 
Consequently, I have several unfeasible regions (covariance, margins and 
others).
The problem seems that the unfeasible regions may be large and sometimes 
lead to optimization issues - even when the starting values are well 
defined.
This is the reason why I wonder if setting by myself a $-\infty$ in the 
composite likelihood function is appropriate here.

However, you might be right in setting a tolerance value 'eps' instead 
of the theoretical bound eigen values > 0.
Thanks for your tips,
Best,
Mathieu


Patrick Burns a écrit :
> If the positive definiteness of the covariance
> is the only issue, then you could base a penalty on:
>
> eps - smallest.eigen.value
>
> if the smallest eigen value is smaller than eps.
>
> Patrick Burns
> patrick at burns-stat.com
> +44 (0)20 8525 0696
> http://www.burns-stat.com
> (home of S Poetry and "A Guide for the Unwilling S User")
>
> Mathieu Ribatet wrote:
>   
>> Thanks Ben for your tips.
>> I'm not sure it'll be so easy to do (as the non-feasible regions
>> depend on the model parameters), but I'm sure it's worth giving a try.
>> Thanks !!!
>> Best,
>>
>> Mathieu
>>
>> Ben Bolker a écrit :
>>     
>>> Mathieu Ribatet <mathieu.ribatet <at> epfl.ch> writes:
>>>
>>>
>>>       
>>>> Dear list,
>>>>
>>>> I'm currently writing a C code to compute the (composite) likelihood -
>>>> well this is done but not really robust. The C code is wrapped in an R
>>>> one which call the optimizer routine - optim or nlm. However, the
>>>> fitting procedure is far from being robust as the parameter space
>>>> depends on the parameter - I have a covariance matrix that should be a
>>>> valid one for example.
>>>>
>>>>         
>>>   One reasonably straightforward hack to deal with this is
>>> to add a penalty that is (e.g.) a quadratic function of the
>>> distance from the feasible region, if that is reasonably
>>> straightforward to compute -- that way your function will
>>> get gently pushed back toward the feasible region.
>>>
>>>   Ben Bolker
>>>
>>> ______________________________________________
>>> R-devel at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-devel
>>>
>>>       

-- 
Institute of Mathematics
Ecole Polytechnique Fédérale de Lausanne
STAT-IMA-FSB-EPFL, Station 8
CH-1015 Lausanne   Switzerland
http://stat.epfl.ch/
Tel: + 41 (0)21 693 7907