Statistics Colloquium

Department of Statistics

University of Manitoba

Winnipeg, MB, Canada

Age Groups of Fish from Length-Frequency Data Using Partially

rank Ordered set Sampling

 In fisheries studies aging the fish involves examining the otoliths (ear bones), scales or other bony parts which is time consuming and requires substantial scientific process. The age group of fish can be estimated indirectly by the use of less expensive and easily obtained length-frequency data which is often represented by a nite mixture model (FMM). In practice, it is desired to provide efficient estimates of the parameters of the underlying FMM. In this talk, we present a novel methodology based on partially rank-ordered set (PROS) sampling design to better estimate the parameters of a FMM and use it in a fishery example. A PROS sampling design first selects a simple random sample of fish and creates partially rank-ordered judgement subsets by dividing each set into subsets of a pre specified size. The final measurements are then obtained from these partially ordered judgement subsets. These observations have a unique data structure different from the simple random sample. The traditional expectation-maximization (EM) algorithm is not directly applicable for these observations. We propose a suitable EM algorithm to estimate the parameters of the FMMs based on PROS samples. We also study the problem of classification of the PROS sample into the components of the FMM. Numerical study shows that the maximum likelihood estimators based on PROS samples perform substantially better than their simple random sample counterparts even with small sample sizes. The results are used to classify a population of a sh species in the Chesapeake Bay area using the length-frequency data.

This is a joint work with Armin Hatefi (University of Toronto, CANADA) and Omer Ozturk (The Ohio State University, USA).