Turkey Hunting Survey Project Dongchu Sun University of Missouri-Columbia

April 26, 2002

Jointly with

Chong He (UMC) Roger Woodard, Ohio State U. Steven L. Sheriff, MDC John Molitor, U of S. California Jacob Oleson, UMC Larry Vangilder, MDC

Where……

Where we were?

Where we are?

Where we go?

Where we were?

Preparation: 1995--1997 He, Sun, Sheriff…….

Pilot Study: 1997--1998 Woodard

Phase 1: 1998—2000 Woodard, Molitor……

Where we are?

Ph.D Dissertations R. Woodard , 1999 Bayesian Hierarchical Models for Hunting

Success Rates

J. Molitor, 2000, Bayesian Analysis for various order

restricted problems

Articles in Refereed Journals

He & Sun (1998). EES, 223-236.

Woodard, Sun, He & Sheriff (1999). JABES, 456-472.

He & Sun (2000). Biometrics, 360-367.

Data 1988, 1990, 1992, 1994, 1996 ,

1998 Spring Turkey Hunting Survey

Hunting success rates during the entired spring season in 1994 ---- He and Sun (1998).

Here we use 1996 data for illustration.

1996 Turkey Hunting Survey

Regulations in spring of 1996: Two weeks Buy license anywhere in Missouri May hunt anywhere in Missouri May kill one turkey per trip per week

A simple random survey collected # of trips in each county each week Birds taken in each county each week

Goals Estimates:

--- Hunting success rates per trip --- hunting pressure --- harvest

Accurate for State: --- permit buyers: 95,800 --- large sample sizes: 7,000 --- returned: 5005 (71.5%)

Likelihood (model the data)

#ijy

Naïve frequency estimate of p_ij

y_ij / n_ij

Problems

Post-stratification --- cann’t draw samples at count level

Small samples for some counties

--- county 72 (4 trips in week 1)

--- county 73 (3 trips in week 1)

--- county 35 (0 trips in both weeks)

Method 1: A beta-gamma prior

Remarks on the Binomial- beta-gamma model

Good properties --- better than the naïve frequency

estimators --- quite robust in terms of choices of

(a_i, b_i) and (c_i,d_i).

Problems

--- contiguity between regions ? --- hard to include covariates

Method 2: Hierarchical linear mixed model

Stage 2 prior for Method 2

Stage 3 prior for Method 2

Method 2

Computation via MCMC

Calculation of posterior via integration is infeasible

Iterative method Produce random sample from

joint posterior distribution

Model Fitting

Hyperparameters:

Estimates

Robustness in changing hyperparameters

Model Comparison

Want to examine if Method 2 can be simplified.

AR or CAR

He and Sun (2000), AR and CAR are equally good for estimating p_ij

Improving estimates by adding covariates?

Woodard, Sun, He, and Sherif (1999) considered

Ramdom Trips n_ij Currently we have checkstation data k_ij : # killed turkeys in week I and county j Woodard (1999) modeled random trips

Unde the same prior for p_ij, the estimates of p_ij does not seem ``spatially’’ correlated as these when n_ij are treated as fixed.

Estimating k_ij

If we can estimate k_ij, could remove check stations.

Woodard, He and Sun (2001) assumed random trips n_ij,

Where we go?

Can we simultaneously estimate total # of trips, harvest, hunting success rates at county level?

How about pre-stratification? Properties of hiecarchical lines

mixed models?

--- Molitor, Sun and He (2000)……

Comments

Hierarchical Bayes models are superior to simple frequency estimates.

Normal linear mixed priors are superior to beta-gamma priors.

Spatial correlation among counties does exist.

More Comments

Include covariates such as forest coverage may not be helpful.

Assuming random trips will improve the estimates?

It can be used in a general small area estimation context.