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B1486
Topic: Contributed on Directional statistics Title: Approximate likelihood inference for the Bingham distribution Authors:  Marco Bee - University of Trento (Italy) [presenting]
Roberto Benedetti - University of Chieti - Pescara (Italy)
Giuseppe Espa - University of Trento (Italy)
Abstract: Likelihood inference for the Bingham distribution is difficult because the density function contains a normalization constant that depends on unknown parameters and cannot be computed in closed form. We propose to estimate the parameters by means of Approximate Maximum Likelihood Estimation (AMLE), thus bypassing the problem of evaluating the likelihood function. The method can be seen as a frequentist reinterpretation of Approximate Bayesian Computation (ABC) techniques. Instead of approximating the likelihood and then maximizing it, AMLE directly approximates the MLE by simulating observations form the distribution of interest. The restriction to uniform prior distributions is the crucial difference between AMLE and a classical ABC approach. We study the impact of the input parameters of the AMLE algorithm and suggest some heuristic approaches for choosing their numerical values and for performing statistical inference. When the dimension of the problem is small, simulation experiments and real-data applications suggest that the performance of the method is in line with MLE based on the approximation of the normalizing constant via the Holonomic Gradient Method. In large dimensional problems we find that, according to our simulation-based evidence, AMLE is more efficient in terms of RMSE.