2019/10/28 by Christian Soize, Soize, Christian, Roger Ghanem +1 · 1 citation
Computer Science · Mathematics · #60J20 #62F15 #68F15 #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1910.12717
openalex publication_date 2019/10/28 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
This paper tackles the challenge presented by small-data to the task of\nBayesian inference. A novel methodology, based on manifold learning and\nmanifold sampling, is proposed for solving this computational statistics\nproblem under the following assumptions: 1) neither the prior model nor the\nlikelihood function are Gaussian and neither can be approximated by a Gaussian\nmeasure; 2) the number of functional input (system parameters) and functional\noutput (quantity of interest) can be large; 3) the number of available\nrealizations of the prior model is small, leading to the small-data challenge\ntypically associated with expensive numerical simulations; the number of\nexperimental realizations is also small; 4) the number of the posterior\nrealizations required for decision is much larger than the available initial\ndataset. The method and its mathematical aspects are detailed. Three\napplications are presented for validation: The first two involve mathematical\nconstructions aimed to develop intuition around the method and to explore its\nperformance. The third example aims to demonstrate the operational value of the\nmethod using a more complex application related to the statistical inverse\nidentification of the non-Gaussian matrix-valued random elasticity field of a\ndamaged biological tissue (osteoporosis in a cortical bone) using ultrasonic\nwaves.\n