An expectation maximization and smoothing approach for indirect acoustic estimation of fish size and density

The smoothed expectation and maximization (EMS) method is shown to be super ior to deconvolution, the most commonly used indirect method for estimating fish acoustic size. This is primarily because EMS avoids artifactual modes in estimates of acoustic size. The expectation, maximization and smoothing method starts with the iterative statistical technique called expectation and maximization and adds smoothing between iterations. Application of the EMS method assumes that the acoustic observations in the voltage domain are realizations of a non-homogeneous Poisson process of rate lambda(i). The E -step estimates expected values of lambda(i) using the conditional distribu tion of the "complete" data, which is binomial, given the Poisson distribut ed acoustic observations. The M-step uses the log likelihood function of th e Poisson distributed "complete" data to find maximum likelihood estimates of lambda(i). The S-step smoothes the lambda(i) estimates, with a Gaussian convolution filter. The method is demonstrated using a simulated data set o f known statistical properties and a data set from the acoustics literature . (C) 1999 International Council for the Exploration of the Sea.