Estimating Parameters in Complex Systems with Functional Outputs - a Wavelet-Based Approximate Bayesian Computation Approach

• Activity Number: 34 - Bayesian Functional and Data Models
• Type: Contributed
• Date/Time: Sunday, July 30, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ruijin Lu* and Hongxiao Zhu and Chen Ming and Anupam K. Gupta and Rolf Muller
• Companies: Virginia Polytechnic Institute and State University and Assistant Professor, Virginia Tech and Department of Mechanical Engineering, Virginia Tech and Department of Mechanical Engineering, Virginia Tech and Department of Mechanical Engineering, Virginia Tech
• Keywords: functional data inference ; Approximate Bayesian Computation(ABC) ; wavelet-decomposition ; Gaussian process surrogate ; Markov chain Monte Carlo ; joint distribution estimation

Abstract

We consider a family of parameter estimation problems involving functional data. In these problems, the relationship between functional data and the underlying parameters cannot be explicitly specified using a likelihood function. These often occur when functional data arises from a complex system and only numerical simulations can be used to describe the underlying data-generating mechanism. To estimate the unknown parameters under these scenarios, we introduce a wavelet-based approximate Bayesian computation (wABC) approach that is likelihood-free and computationally scalable to high-dimensional functional data. The proposed approach relies on near-lossless wavelet decomposition and compression to reduce the high-dimensional and high-correlated functional data. We adopt a Metropolis-Hastings sampler to obtain posterior samples of the parameters. To avoid expensive simulations from the simulator, a Gaussian process surrogate for the simulator is introduced. We motivate our approach and demonstrate its performance using the foliage-echo data arising from a sonar simulation system. Our inference provides the joint posterior distribution of all parameters.