Probability distribution for f0

questions concerning analysis/theory using program MARK

Probability distribution for f0

Postby Granjon » Wed Mar 20, 2019 1:02 pm

Hi there,

I'm estimating the population abundance of some apes, and given I have only 2 detection occasions, I ran a null model M0 and a time-model Mt with RMark - so far so good.

Now I need the full probability distribution/likelihood profile for f0 - and eventually Nhat - not only the ML estimate with the 95% confidence interval. In other words, I need the likelihood of all potential values of f0. I've been trying to look into the Mark book for that, but I seem to have a conceptual barrier somewhere.

Any thought on how I could get there?
Thanks in advance
Granjon
 
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Re: Probability distribution for f0

Postby jlaake » Wed Mar 20, 2019 1:19 pm

In RMark, you can get profile intervals but not the entire distribution by setting the mark function argument profile.int=TRUE. See ?mark in package. This should have been posted in the RMark subforum if your question was specific to how to do this with RMark.
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Re: Probability distribution for f0

Postby egc » Wed Mar 20, 2019 6:43 pm

No 'one button way' to do this. Basically, you do it manually -- fix all the parameters to some value, except the one you want the likelihood profile for, and then manually iterate through the rest. For example, the figure on p. 41 of Chapter 10 (multi-state models) was generated that way. Similarly, figures on pp. 49-50 in Chapter 14 (closed abundance).

But, you can get there ferom here using MCMC in MARK (Appendix E). The likelihood for both f0 and N can be pulled out of the MCMC object that gets created when the .BIN file MARK creates is post-processed.
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Re: Probability distribution for f0

Postby Granjon » Thu Mar 21, 2019 6:03 am

Thanks for your quick replies, this is indeed the kind of figures I need. Thanks also for the hint on Appendix E and the profile interval. I'll look into both.
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Re: Probability distribution for f0

Postby cooch » Thu Mar 21, 2019 7:40 am

Granjon wrote:Thanks for your quick replies, this is indeed the kind of figures I need. Thanks also for the hint on Appendix E and the profile interval. I'll look into both.


The MCMC approach works pretty well...and is relatively easy to implement. The MCMC appendix needs an overhaul (pers. obs.), but there is sufficient there to get you started.
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Re: Probability distribution for f0

Postby ACGranjon » Wed Apr 24, 2019 9:55 am

Hi, in the end, I guess my question was more complicated than what we really needed, so I thought I might communicate what we ended up doing:

We used the beta estimate and se for f0 to obtain its distribution in the link space (log scale), and then back-transformed it to obtain the distribution of the real parameter f0. That’s all we needed, really. :)
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