马尔科夫链蒙特卡洛方法(Markov Chain Monte Carlo),简称MCMC,产生于19世纪50年代早期,是在贝叶斯理论框架下,通过计算机进行模拟的蒙特卡洛方法(Monte Carlo)。该方法将马尔科夫(Markov)过程引入到Monte Carlo模拟中,实现抽样分布随模拟的进行而改变的动态模拟,弥补了传统的蒙特卡罗积分只能静态模拟的缺陷。MCMC是一种简单有效的计算方法,在很多领域到广泛的应用,如统计物、贝叶斯(Bayes)问题、计算机问题等。

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书名

部分观测动态系统的贝叶斯学习:Bayesian Learning for partially observed dynamical systems

书简介

本书主要整理了最近关于动态系统中贝叶斯学习的著名讲座,这里包含了关于该方面的最新知识讲解,方便机器学习从事者及时快捷了解相关最新技术与研究。

目录

  • 马尔可夫链:核,不变测度。包括观察驱动模型的示例
  • 贝叶斯推论,马尔可夫链极大似然估计的渐近性质
  • 马尔可夫链蒙特卡罗算法
  • MCMC算法的一些性质
  • 伪边缘MCMC及其应用
  • 哈密顿蒙特卡罗算法
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最新论文

Value-at-Risk (VaR) and Expected Shortfall (ES) are widely used in the financial sector to measure the market risk and manage the extreme market movement. The recent link between the quantile score function and the Asymmetric Laplace density has led to a flexible likelihood-based framework for joint modelling of VaR and ES. It is of high interest in financial applications to be able to capture the underlying joint dynamics of these two quantities. We address this problem by developing a hybrid model that is based on the Asymmetric Laplace quasi-likelihood and employs the Long Short-Term Memory (LSTM) time series modelling technique from Machine Learning to capture efficiently the underlying dynamics of VaR and ES. We refer to this model as LSTM-AL. We adopt the adaptive Markov chain Monte Carlo (MCMC) algorithm for Bayesian inference in the LSTM-AL model. Empirical results show that the proposed LSTM-AL model can improve the VaR and ES forecasting accuracy over a range of well-established competing models.

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