reasonable initial values recalculated to impossible values in distance sampling model

[SimonGE]

Hello nimble users,

I have been struggling with a distance sampling model for a couple of weeks and am out of ideas. The model is meant to estimate abundances (N) among species and sites (see the attached sample data).

I took care to initialize this model with what I think are reasonable starting values for every parameter in this model but am getting the familiar "NaN values in logProb of model variable y".

y is drawn from a binomial distribution of size N with probability pcap. Note that initial values for N are reasonable (I think) and so are those for pcap. After building the model, I confirm whether the model object is holding the correct values for pcap and it is not.

All the values for pcap are replaced with 1's. I also noticed that if I were to skip the summation step on line 44 `pcap[s,j] <- sum( fc[s,j, 1:n.bins] ) ` and replaced it with, say, ` pcap[s,j] <- fc[s,j, 1] ` or any number from 1 to n.bins in the 3rd index, then this doesn't happen. I don't know why that is considering that the initial values for fc along that 3rd index sum to 0.75.

I think this must be the problem but I a) don't understand why this is happening, and b) don't know what to do about it.

Any guidance would be much appreciated. Thanks in advance!

[Perry de Valpine]

Dear Simon,

Thanks for the question.

nimbleModel by default does a model$calculate() as one of its last steps. (You can skip this by calculate=FALSE, but that's not your problem.)

model$calculate() does the following: In topologically sorted order (i.e. parent nodes before descendent nodes), calculate deterministic values for deterministic nodes ("<-") or calculate log probabilities for stochastic nodes ("~"). 

Therefore, it is typically not very useful to provide initial values for deterministic nodes, as you have done. They will be overwritten by values calculated in the model as soon as model$calculate() runs. (In your case, if you use calculate=FALSE in nimbleModel, you will see your initial values for fc, which addresses part of your question but not really the underlying problem.) 

For your model, when model$calculate() operates within nimbleModel (or you can run it yourself), it appears that the deterministic calculations really do result in values of pcap that are all 1s. Roughly what I see from the code is that pcap scalars depend on fc vectors, which depend on f vectors, which depend on f_0 scalars and p vectors, which depend on up and low vectors, which depend on sigma scalars, which depend on p_sp scalars, which are the stochastic parents to that entire chain of calculations. One could follow all the calculations directly in R as well. I can't be sure but I'm thinking that there could be a mistake in your math. I am not checking the details, but roughly it looks like you have discretized a half-normal distribution into a set of bins, adjusted those bins for two dimensions, and summed the total probability, resulting (correctly?) in values of 1? I am wondering if there is a missing component to the modeling ideas.

In fact, the situation is slightly worse than having all pcap values be exactly 1. That would result in -Inf log probabilities because for y~dbin(p, N) with p==1, the probability is 0 if y is not equal to N (as you have). In your case, however, the numerical imprecisions on the calculations resulting in pcap are such that all the values are slightly > 1, which results in NaN log probabilities, which is what is happening.

If you want to gain more insight into model$calculate(), you can do:

for(node in model$getNodeNames()) model$calculate(node)

Your model as >73000 nodes you might prefer to use more of a toy example for exploration.

Finally, I note that Michael Scroggie has some tools for distance sampling models in nimble here. I don't know its state of development (I hope it's ok to point it out!).

HTH

Perry

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[SimonGE]

Amazing! Thank you so much for such a quick and thorough reply.

I am disappointed that it was exactly the problem that I spent so much time trying (and failing!) to avoid (i.e. providing good initial values). You're correct that I was wasting my time with the inits for the deterministic nodes and you correctly identified p_sp as the stochastic parent that was causing the problem. The topological sorting explains a lot. The initial values for that parameter were too large, hence pcap > 1. For posterity, this model is based on Sollmann et al. 2015. I had also looked at Michael Scroggie's GitHub but had the same question about the state of development.

Anyhow, you've solved my problem and made my day. Thanks again, Perry.