Initial state probs for deterministic/stochastic states

questions concerning analysis/theory using programs M-SURGE, E-SURGE and U-CARE

Initial state probs for deterministic/stochastic states

Postby Morten Frederiksen » Mon Oct 22, 2012 5:54 am

I have a data set where birds are marked and observed at 2 sites, and there is resighting heterogeneity at both sites, for a total of 4 states (site A and B, high and low observability). I'm struggling a bit with how to model initial state probabilities, since the distribution of newly marked birds between sites is given by study design (thus deterministic), whereas the distribution between observability classes is unknown (thus probabilistic) and may differ between the two sites. In addition, there's a large year-to-year variation in the distribution of marking effort between the two sites.

Any thoughts on how to model this? Perhaps the initial state probs can be modelled with two steps, first the deterministic and then the probabilistic.

Incidentally, the transitions aren't simple either in a case like this!

Morten
Morten Frederiksen
 
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Re: Initial state probs for deterministic/stochastic states

Postby CHOQUET » Tue Oct 23, 2012 3:58 am

Hello Morten,

Let the states be: A high, A low, B high, B low (For the initial states, we didn't take into account the
dead state). In our case, you have to introduce two steps, one for the site and the second to model
the classes:

1. The matrix pattern is 1x2

[ pi *]

pi represent the proportion of individual in site A. It may be set time-dependant later.

2. The matrix pattern is 2x4

[ L * - -
- - L * ]

L represents the proportion of individual in site A in class Low. It may be set time-dependant and/or site dependant later.

Sincerely,

Rémi
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Re: Initial state probs for deterministic/stochastic states

Postby Morten Frederiksen » Wed Oct 24, 2012 2:47 am

Thanks Rémi,

That seems to work - although the model has great trouble converging to a stable solution. As far as I can see, your suggestion is a more interpretable reparameterisation of the one-step solutions, where all ISP's are estimated simultaneously - at least if the probabilities in step 2 are set site-dependent. So I'd expect the same deviance for the two models - this is difficult to achieve! I've used most of the suggested settings: EM(20)+Quasi-Newton,25 random sets of initial values, 500 iterations, reduced tolerance - and I'm slowly getting there.

Morten
Morten Frederiksen
 
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Joined: Thu May 29, 2003 4:53 am
Location: Roskilde, Denmark


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