Prior and posterior probabilistic models of uncertainties in a model for producing voice

Abstract

The aim of this paper is to use Bayesian statistics to update a probability density function related to the tension parameter, which is one of the main parameters responsible for the changing of the fundamental frequency of a voice signal, generated by a mechanical/mathematical model for producing voiced sounds. We follow a parametric approach for stochastic modeling, which requires the adoption of random variables to represent the uncertain parameters present in the cited model. For each random variable, a probability density function is constructed using the Maximum Entropy Principle and the Monte Carlo method is used to generate voice signals as the output of the model. Then, a probability density function of the voice fundamental frequency is constructed. The random variables are fit to experimental data so that the probability density function of the fundamental frequency obtained by the model can be as near as possible of a probability density function obtained from experimental data. New values are obtained experimentally for the fundamental frequency and they are used to update the probability density function of the tension parameter, via Bayes's Theorem.