I have a dataset on animals released at various locations and the number of them recorded in subsequent years. A simplified version of the data set could look like this:
Release_ID
Occasion
n
S1
Released
150
S1
2022
46
S2
Released
150
S2
2022
12
S3
Released
150
S3
2022
37
The real data set contains 11 Release points and counts for the years 2022, 2023, and 2024. What would be a good way to compare the resulting records statistically among each other in a Bayesian framework?
What question are you trying to answer with these data? Estimate a survival rate? If so is it assumed to be constant or variable across sites? Across years? Are the number recorded in subsequent years assumed to be an exhaustive census or is there a possibility of non-detection of surviving individuals?
I already used a continuous-time survival model on the complete detection data. Here, I would like to compare the number of detected animals per year across the different stocking locations to determine whether there is a statistically significant difference in the number of recorded individuals per year among the release site groups. I hope that makes it clearer.
Is there any difference between studying site-specific variation in the number of recorded individuals versus site-specific variation in survival rates?
I mean, the survival model is based on a couple of assumptions and interprets the decreasing detection rate as an increasing mortality rate. This is basically about the reviewer requesting a statistical test for this figure, to show how similar or dissimilar the detection patterns are.
You mean you want to compute a p-value? Is the null hypothesis that they’re all the same and you want to measure the significance of the rejection of this null hypothesis? For that, the simplest thing I can think of is a chi-squared test (though please take this advice with a grain of salt—my knowledge of hypothesis tests is more textbook driven than experience driven).
Calculating significance is not really something we do in Bayesian statistics, so if you literally want the above, then just choose a frequentist test and report the p-value. You could fit a model with a single recapture probability and a model with varying probabilities and compare them using Bayes factors, but I wouldn’t recommend that for all the reasons Gelman et al. go over in the Bayesian Data Analysis chapter on model comparison (free pdf on line at book’s home page).
If you want to do this in a Bayesian way, you have to set up what the quantity of interest is that you want to measure because point null hypothesis have zero probability when measured using probability theory.
Because you begin by releasing the same number of individuals at each site, “significant” variation in subsequent counts is conceptually the same thing as “significant” variation in the apparent survival rate. The count is precisely a constant times the apparent survival rate.
