A Simple Approach to Parameter Inference in State-Space Models

状态空间模型中参数推断的简单方法

• 批准号: 2610815
• 金额: --
• 依托单位: University of Bristol
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2610815
• 关键词: Simple; Approach; Parameter; Inference; State

Abstract(no more than 4,000 characters including spaces, clearly explain which EPSRC research area the project relates to - for more info see overleaf) State-space models are popular tools in many areas of science, including economics, biology or ecology, and are mainly used to predict an unobserved (or latent) time series of interest from the available data. For instance, in economics we are often interested in inferring the risk of an asset from its price, while in ecology one may want to use some observations to estimate the evolution of the population size of a given group of animals. As in any statistical models, state-space models depend on parameters that need to be learnt from the data. Parameter inference in this class of models is however known to be challenging, because computing the associated log-likelihood function, or its gradient, requires to integrate out the latent variables, a task which is usually intractable. Particle filter algorithms have proven to be powerful Monte Carlo techniques for estimating expectations with respect to the unobserved variables, and state-of the art methods for parameter inference in state-space models amount to using these Monte Carlo estimates within "standard" algorithms (such as the Metropolis-Hastings algorithm for Bayesian inference, or the gradient ascent algorithm for maximum likelihood estimation). Despite the undeniable usefulness of these approaches, they are typically difficult to implement and to tune for non-experts in Monte Carlo methods, in addition to be computationally expensive even for moderate sample sizes. Consequently, in practice, simpler but theoretically unjustified algorithms are often preferred to learn the model parameter from the data. The most popular of these simpler approaches is probably the one proposed 20 years ago by Liu and West (2001), in which the unknown model parameter is simply treated as an additional latent variable. If this strategy has the merit to be simple to implement it however has the drawback of not being supported by any theoretical results. Following the idea of Liu and West (2001), the objective of this research is to propose a theoretically justified way of treating the parameter of a state-space model as a latent variable in order to learn its value. To achieve this goal this research will build on the approach developed by Gerber and Douc (2021) for parameter estimation in static models, and leverage results on the concentration properties of the Bayesian posterior distributions that arise in partially observed Markov models (see Douc et al., 2020). By providing an easy to implement but theoretically justified approach to parameter inference in the widely used class of state-space models, the research will benefit to a broad range of researchers and practitioners whose scientific conclusions and predictions rely on these models. This project falls within the EPSRC Statistics and Applied Probability research area.

摘要（包括空间在内的不超过4,000个字符，清楚地说明该项目相关的EPSRC研究领域 - 有关更多信息，请参见Overleaf）州空间模型是许多科学领域的流行工具，包括经济学，生物学或生态学，主要用于预测可用数据中未观察到的（或潜在的）时间序列。例如，在经济学中，我们通常有兴趣从其价格中推断出资产的风险，而在生态学中，人们可能希望使用一些观察结果来估计给定动物群体的种群规模的演变。与任何统计模型一样，状态空间模型取决于需要从数据中学到的参数。然而，该类别模型中的参数推断是具有挑战性的，因为计算相关的对数可能性函数或其梯度需要集成潜在变量，这是一个通常是棘手的任务。 Particle filter algorithms have proven to be powerful Monte Carlo techniques for estimating expectations with respect to the unobserved variables, and state-of the art methods for parameter inference in state-space models amount to using these Monte Carlo estimates within "standard" algorithms (such as the Metropolis-Hastings algorithm for Bayesian inference, or the gradient ascent algorithm for maximum likelihood estimation).尽管这些方法具有不可否认的有用性，但它们通常很难实现，并且对于蒙特卡洛方法中的非专家来说，除了计算中，即使对于中等样本量，它们也很昂贵。因此，在实践中，通常首选简单但理论上不合理的算法从数据中学习模型参数。这些简单的方法中最流行的方法可能是20年前Liu and West（2001）提出的一种方法，其中未知的模型参数只是将其视为附加的潜在变量。如果此策略的优点是易于实施的，但是没有任何理论结果支持的缺点。遵循Liu and West（2001）的想法，这项研究的目的是提出一种理论上合理的方式，将状态空间模型的参数视为潜在变量，以了解其价值。为了实现这一目标，这项研究将基于Gerber和Douc（2021）在静态模型中开发的方法，并利用部分观察到的Markov模型中出现的贝叶斯后分布的浓度属性的结果（参见Douc等，2020）。通过在广泛使用的一类国家空间模型中提供易于实施但理论上有理的参数推断方法，该研究将受益于广泛的研究人员和从业人员，他们的科学结论和预测依赖于这些模型。 该项目属于EPSRC统计数据和应用概率研究领域。