A network flow approach in finding maximum likelihood estimate of high concentration regions

A maximum likelihood estimation (MLE) method of high density regions in spatial point processes is introduced. The method is motivated from a network flow approach for flexibly incorporating geometric restrictions in computing the MLEs. An easy-to-implement computational algorithm having a low order of complexity is provided. Simulation studies show that it performs very well in many difficult situations, and reaches the global optimality. Two real data sets illustrate the applicability of the proposed method.