utility of MCMC results

[andrew_thompson]

Hello,

We are analyzing data from a study we conducted last summer to evaluate abundances of the Coachella Valley Fringe-toed lizard.

Our data set consists of capture-recapture information from four sites with one or two plots per site. We had yearlings and adults at 3 sites and adults only at 1 site. In total, we partitioned the data set into eight groups (e.g., plot 1 adults, plot 1 juveniles, plot 2 adults, plot 2 juv, etc...). Our goal is to obtain abundance estimates for each group.

We compared 8 closed population models that evaluated effects on det probability of site, initial and subsequent capture, and individual heterogeneity. The best supported model was one that included all factors: pi(.)p(c+site)N(plot,age). However, total captures were low at some sites resulting in high CI around estimates of N for some groups or even failure to produce an estimate in one case.

I also ran a MCMC analysis for the best supported model. Here, real estimates of N for each group produced much tighter CIs. My question is what is the utility of the estimates for abundance estimates from the MCMC analysis. Can I justify using these values for our abundance estimates?

Also, if anyone has any other suggestions for how to analyze this data to obtain better estimates of N for each group, I would appreciate it.

Thank you,
Andrew

[dhewitt]

Since no one else piped up, I'll throw in a few thoughts.

First, we don't have nearly enough information about the density of your capture-recapture data (occasions, number marked and recapped) to provide guidance. What are estimates of p like in your output? Given your comment about total recaps being low sometimes, you're probably not going to be able to estimate abundance, especially in all those strata. Just a fact of life that abundance is tough to estimate. That said, I guess I'm surprised that model selection pointed toward a model with substantial structure. Are you sure you don't have estimation problems ("failure to produce an estimate")?

Second, the MCMC routine is a Bayesian implementation with a weak beta prior on the parameters like Phi and p. I'm sure Gary chose a prior that is "uninformative" in the face of good data, but with sparse data the prior matters. Things can look rosier than perhaps the data support. (Of course, this depends on whether you're a Bayesian.)

As an example, we've had CJS models for which we get boundary estimates of Phi (1.0) with nonsense SEs (0) with direct likelihood optimization. With a MCMC run we get non-boundary estimates (say, 0.95) with decent confidence intervals. It's obviously a personal choice as to whether the MCMC results are "justifiable" in such cases, but to me it doesn't pass the straight-face test.

What you'd like to know is the degree to which the prior is contributing to the estimates. I'm not sure if it's possible to easily calculate the relative influence of the prior from these models (i.e., something along the lines of "how many data points is the prior equivalent to?").

[murray.efford]

Andrew
I'd echo the need for more detail, going right back to the actual sampling methods (visual search vs pitfall trap etc.). You mention plots, but I imagine these are open and allow animals move in and out, so you would probably be better to use spatially explicit capture-recapture to estimate density rather than focussing on N.
Murray