Sequential Bayesian inference in complex and realistic dynamical systems

这个博士职位将在计算统计学、贝叶斯分析、统计信号处理和机器学习之间有趣地重叠，其动机是旨在改善人类生活和环境的应用程序。成功的申请者将由维克多·埃尔维拉博士监督。预计还将与法国和美国的科学家进行几次国际合作。不同科学领域的许多问题都可以通过统计模型来描述，这些模型通过一些未观测的参数将连续的观测数据与隐藏的过程联系起来。在贝叶斯框架中，未知数的概率估计用这些参数的后验分布来表示。然而，在大多数真实感模型中，后验是难以处理的，必须进行近似。例如，基于重要性抽样(IS)的算法是蒙特卡罗方法，在贝叶斯推理的许多问题上都表现出了令人满意的性能，包括序列设置。在本论文中，我们将为复杂系统(高维、大数据量、非线性非高斯关系、模型误指定等)开发新的贝叶斯推理方法。更具体地说，我们将提出新的高效的计算方法来处理这些复杂的模型，以克服目前更传统的蒙特卡罗技术在这样一个具有挑战性的背景下的局限性。我们还将探索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获得了很大的兴趣。许多实际应用可以从这些方法的发展中受益，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.