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Steps in estimating $K$

1. (Command-line version) Set COMPUTEPROBS and INFERALPHA to 1 in the file extraparams. (Front End version) Make sure that $\alpha$ is allowed to vary.
2. Run the MCMC scheme for different values of MAXPOPS ($K$). At the end it will output a line "Estimated Ln Prob of Data''. This is the estimate of $\ln{\rm Pr}(X\vert K)$. You should run several independent runs for each $K$, in order to verify that the estimates are consistent across runs. If the variability across runs for a given $K$ is substantial compared to the variability of estimates obtained for different $K$, you may need to use longer runs or a longer burnin period. If $\ln{\rm Pr}(X\vert K)$ appears to be bimodal or multimodal, the MCMC scheme may be finding different solutions. You can check for this by comparing the $Q$ for different runs at a single K. (cf Data Set 2A in Pritchard et al. 2000a, and see the section on Multimodality, below).
3. Compute posterior probabilities of $K$. For example, for Data Set 2A in the paper (where $K$ was 2), we got cm $K$ $\ln{\rm Pr}(X\vert K)$ cm 1 cm 2 cm 3 cm 4 cm 5 We can start by assuming a uniform prior on $K=\{1,...,5\}$. Then from Bayes' Rule, ${\rm Pr}(K=2)$ is given by

$${{e^{-3983}}\over{e^{-4356}+e^{-3983}+e^{-3982}+e^{-3983}+e^{-4006}}}$$ (3)


It's easier to compute this if we simplify the expression to

$${{e^{-1}}\over{e^{-374}+e^{-1}+e^0+e^{-1}+e^{-24}}} = 0.21$$ (4)