Population density estimation in line transect sampling requires fitting a probability density function denoted by f(y|Ѳ), where y represents the perpendicular distance from a detected animal (or object) to a transect line, and Ѳ represents the vector parameter indexing this family of probability density functions. Currently, the most popular approach to estimate f(·), is based on a semi-parametric methodology proposed by [1]. The main idea is to find the maximum likelihood estimator for Ѳ using a parametric functional form combined with a series expansion.  We present an alternative approach based on the Minimum Description Length principle (MDL) [2], and its application to estimate a density function through a histogram [3]. This methodology no longer need to assume an a priori parametric function to fit our data and variable class intervals are also allowed, optimizing the number of class intervals and compressing the available information at most.

Keywords: detectability function, distance sampling, normalized likelihood, stochastic complexity.

[1] Buckland, S. T. (1992). Maximum likelihood fitting of the Hermite and simple polynomials densities. Applied Statistics, 41, 241-266.

[2] Rissanen, J. (1978). Modeling by shortest data description.  Automatica 14, 465-471.

[3] Kontkanen, P. & Myllymäki, P. (2006). Information-Theoretically Optimal Histogram Density Estimation. Helsinki Institute for Information Technology.  10 p.