标题： 非同步观测扩散的贝叶斯推断 显示英文标题

标题： Bayesian Inference for Non-Synchronously Observed Diffusions

摘要： 我们研究了双变量数据的贝叶斯推断问题，这些数据在时间上被观测到，但观测时间是非同步的。 特别是在金融领域中的许多应用中都会出现这种情况，例如高频交易或原油期货交易。 我们采用扩散模型来描述数据，并构建了一个带有未知参数先验以及隐变量表示的贝叶斯模型，用于所谓的缺失数据。 然后，我们考虑使用马尔可夫链蒙特卡洛（MCMC）方法拟合该模型的计算方法。 由于完整数据似然函数难以处理，我们必须求助于时间离散化方法，这可能导致当数据以低频观测时MCMC面临显著问题。 在高频观测情况下，我们提出了一种基于欧拉-丸山（Euler--Maruyama）时间离散化的简单粒子MCMC方法，可以通过多层蒙特卡洛（MLMC）进行增强。 在低频观测情况下，我们引入了一种后验连续时间的新桥接表示法，以解决此情况下的MCMC问题。 这种表示法通过MCMC和MLMC进行离散化和拟合。 我们将我们的方法应用于真实数据和模拟数据，以验证其有效性。 显示英文摘要

摘要： We consider the problem of Bayesian inference for bi-variate data observed in time but with observation times which occur non-synchronously. In particular, this occurs in a wide variety of applications in finance, such as high-frequency trading or crude oil futures trading. We adopt a diffusion model for the data and formulate a Bayesian model with priors on unknown parameters along with a latent representation for the the so-called missing data. We then consider computational methodology to fit the model using Markov chain Monte Carlo (MCMC). We have to resort to time-discretization methods as the complete data likelihood is intractable and this can cause considerable issues for MCMC when the data are observed in low frequencies. In a high frequency observation frequencies we present a simple particle MCMC method based on an Euler--Maruyama time discretization, which can be enhanced using multilevel Monte Carlo (MLMC). In the low frequency observation regime we introduce a novel bridging representation of the posterior in continuous time to deal with the issues of MCMC in this case. This representation is discretized and fitted using MCMC and MLMC. We apply our methodology to real and simulated data to establish the efficacy of our methodology.