Sequential Bayesian inference in complex and realistic dynamical systems

该博士职位将专注于计算统计学，贝叶斯分析，统计信号处理和机器学习之间的有趣重叠，旨在改善人类生活和环境的应用。成功的申请者将由Victor Elvira博士指导。预计还将与法国和美国的科学家进行一些国际合作。不同科学领域中的许多问题都可以通过统计模型来描述，该模型通过一些未观察到的参数将顺序观测数据与隐藏过程联系起来。在贝叶斯框架中，未知数的概率估计由这些参数的后验分布表示。然而，在大多数现实模型中，后验是难以处理的，必须近似。例如，基于重要性抽样（IS）的算法是蒙特卡罗方法，它在贝叶斯推理的许多问题中显示出令人满意的性能，包括顺序设置。在本文中，我们将开发复杂系统（高维、大数据量、非线性非高斯关系、模型错误规范等）中贝叶斯推理的新方法。更具体地说，我们将提出新的有效的计算方法来处理这些复杂的模型，以便在这样一个具有挑战性的背景下克服更传统的蒙特卡罗技术的局限性。我们还将探讨这些方法在结构方程模型中的应用，这些模型最近在机器学习和统计学中引起了很大的兴趣。这些方法的发展可以使许多实际应用受益，包括气候学、生物系统或生态学等方面的问题。

This PhD position will be at the interesting overlap between computational statistics, Bayesian analysis, statistical signal processing, and machine learning, motivated by applications that aim to improve human life and environment. The successful applicant will be supervised by Dr. Victor Elvira. Several international collaborations with scientists in France and USA are also expected. Many problems in different scientific domains can be described through statistical models that relate the sequential observed data to a hidden process through some unobserved parameters. In the Bayesian framework, the probabilistic estimation of the unknowns is represented by the posterior distribution of these parameters. However in most of the realistic models, the posterior is intractable and must be approximated. For instance, Importance Sampling (IS)- based algorithms are Monte Carlo methods that have shown a satisfactory performance in many problems of Bayesian inference, including the sequential setting. In this thesis, we will develop novel methods for Bayesian inference in complexsystems (high-dimensional, large amount of data, non-linear non-Gaussian relations, with model misspecification, etc). More specifically, we will propose novel efficient computational methods to deal with these complex models in order to overcome current limitations of more traditional Monte Carlo techniques in such a challenging context. We will also explorethe application of these methods to structural equation models which have recently gained a lot of interest in machine learning and statistics. Many practical applications can be benefited from the development of these methodologies, including problems in climatology, biological systems, or ecology, among many others.