Dirichlet Process Prior in a Catch-Effort Hierarchical Model for Animal Abundance

1. Carleton College Prasit Dhakal Jun Young Park Dirichlet Process Prior in a Catch-Effort Hierarchical Model for Animal Abundance

2. TPA (Turkey Permit Areas)

3. Previous Model (1) Assume that the population of the wild turkey in region i is Ni and the number of wild turkeys harvested in region i in period j is yij. (2)pij is the removal probability of region i in period j, then the probability that an animal is removed during, but not before period j, is equal to (3)So the pmf of yij given Ni and would be Multinomial

4. Previous Model (4) Catch-effort Model: probability model for pij (5) Abundance Model One way to model Ni would be using Poisson distribution, say Where is the mean animal abundance in region i. Where is the average density of animals per unit area in region i

5. What is Dirichlet Process Prior? • Anew estimate of a parameter either comes from previously drawn values or from a baseline distribution G0 • Given a Dirichlet process DP(G0,α) G0

6. Different alphas

7. Neal Function Update for in tthiteration of MCMC consists of 2 steps of Metropolis-Hastings algorithm. STEP 1) Updating Clustering Ex) if K=3 clusters in tth iteration After step 1,K=4 clusters in (t+1)th iteration STEP 2) Updating the unique values of From step 1, We are updating, After updating, say So in (t+1)th iteration

8. Neal Function STEP 1) Assume in tthiteration Draw a candidate for (t+1)th iteration by using the DPP Calculate the MH ratio for each i. Thus we have

9. Neal Function STEP 2) We update Draw a candidate from Calculate the MH ratio r for each i Then

10. Results Model without DPP Model with DPP