Nested Sampling: A Case Study in Parameter Estimation

Author:

Keskin Fesih

Abstract

Nested Sampling (NS) is a powerful Bayesian inference algorithm that can be used to estimate parameter posteriors and marginal likelihoods for complex models. It is a sequential algorithm that works by iteratively removing low-likelihood regions of the parameter space while keeping track of the weights of the remaining points. This allows NS to efficiently sample the posterior distribution, even for models with complex and multimodal posteriors. NS has been used to estimate parameters in a wide range of applications, including cosmology, astrophysics, biology, and machine learning. It is particularly well-suited for problems where the posterior distribution is difficult to sample directly or where it is important to obtain accurate estimates of the marginal likelihood. This study explores the potential of NS as an alternative to these traditional methods for Direction of Arrival (DoA) estimation. Capitalizing on its strengths in handling multimodal distributions and dimensionality, we explore its applicability, practical application, and comparative performance. Through a simulated case study, we demonstrate the potential superiority of NS in certain challenging conditions. However, it also exposes computational intensity and forced antecedent selection as challenges. In navigating this exploration, we provide insights that advocate for the continued investigation and development of NS in broader signal-processing settings.

Publisher

IntechOpen

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