ON A CONSERVATIVE BAYESIAN METHOD OF INFERRING EXTINCTION


As mentioned, it is technically possible to compute agnostic probabilities even if there is a single sighting. Because this would be nonsense, the two-sighting cutoff is used in all the simulations reported here. By contrast, Alroy (2014) excluded species with less than three sightings, because CSD probabilities are otherwise not computable. Based on the count of species with posterior


extinction probabilities ε>0.50 (black line in Fig. 2), the agnostic estimates are accurate but usually very slightly downward biased relative to the true count (gray lines in Fig. 2). However, the gap seems unimportant, with the true tallies and ε>0.50 tallies being off by


675


about 2–6% throughout most of the time series (starting from around interval 20) when one assumes that extinction probabilities are expo- nentially distributed (Fig. 2B). Furthermore, CSD’s performance is arguably worse (see Alroy 2014: Fig. 2B). The truly striking differ- ence is that CSD very often infers ε>0.95 or even 0.99, whereas the 0.50, 0.95, and 0.99 ε lines are widely spaced in the current simulation (Fig. 2A,B). In other words, the new method is very conservative in the narrow sense of tending not to infer extinction strongly (meaning it produces few false positives) but no more or less conservative with respect to inferring survival (because the


FIGURE 2. Performance of the agnostic equation based on a simulation analysis involving a cohort of 1000 species. The per-interval extinction probability E is 0.05 and the per-interval sampling probability ps is 0.5. The dotted line indicates the number of species that have been sampled at least twice up to this point and therefore have computable extinction probabilities; gray line, number of those that are actually extinct; thick black line labeled 50, number with posterior extinction probabilities >0.5; thin lines, number with probabilities at other cutoffs (as labeled). Compare with Figure 2B in Alroy (2014). A, Results obtained by assuming a uniform distribution of extinction probabilities. B, Results obtaining by assuming an exponential distribution of extinction probabilities. C, First differences of the data shown in (A), that is, interval-by-interval rates of actual and inferred extinction. To improve visibility, the black line is based on summed posteriors instead of counts of posteriors >0.5. D, First differences of the data shown in (B). Black line is based on summed posteriors.


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