We develop a mixture model for transition density approximation, together with soft model selection, in the presence of noisy and heterogeneous nonlinear dynamics. Our model builds on the Gaussian mixture transition distribution (MTD) model for continuous state spaces, extending component means with nonlinear functions that are modeled using Gaussian process (GP) priors. The resulting model flexibly captures nonlinear and heterogeneous lag dependence when several mixture components are active, identifies low-order nonlinear dependence while inferring relevant lags when few components are active, and averages over multiple and competing single-lag models to quantify/propagate uncertainty. Sparsity-inducing priors on the mixture weights aid in selecting a subset of active lags. The hierarchical model specification follows conventions for both GP regression and MTD models, admitting a convenient Gibbs sampling scheme for posterior inference. We demonstrate properties of the proposed model with two simulated and two real time series, emphasizing approximation of lag-dependent transition densities and model selection. In most cases, the model decisively recovers important features. The proposed model provides a simple, yet flexible framework that preserves useful and distinguishing characteristics of the MTD model class.

中文翻译：

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具有高斯过程混合过渡分布的自回归密度建模

在存在噪声和异构非线性动力学的情况下，我们开发了一个用于过渡密度近似的混合模型，以及软模型选择。我们的模型建立在连续状态空间的高斯混合转移分布 (MTD) 模型之上，扩展了具有非线性函数的分量均值，这些函数使用高斯过程 (GP) 先验建模。当多个混合组件处于活动状态时，生成的模型可以灵活地捕获非线性和异质滞后依赖性，识别低阶非线性依赖性，同时在少数组件处于活动状态时推断相关滞后，并在多个和竞争的单滞后模型上进行平均以量化/传播不确定性。混合权重上的稀疏诱导先验有助于选择活动滞后的子集。分层模型规范遵循 GP 回归和 MTD 模型的约定，采用方便的 Gibbs 抽样方案进行后验推理。我们用两个模拟和两个实时序列展示了所提出模型的特性，强调了滞后相关过渡密度的近似和模型选择。在大多数情况下，模型会果断地恢复重要特征。所提出的模型提供了一个简单而灵活的框架，该框架保留了 MTD 模型类的有用和显着特征。该模型果断地恢复了重要特征。所提出的模型提供了一个简单而灵活的框架，该框架保留了 MTD 模型类的有用和显着特征。该模型果断地恢复了重要特征。所提出的模型提供了一个简单而灵活的框架，该框架保留了 MTD 模型类的有用和显着特征。