The Iterated Auxiliary Particle Filter

Streaming Variational Monte Carlo

Nonlinear state-space models are powerful tools to describe dynamical structures in complex time series. In a streaming setting where data are processed one sample at a time, simultaneous inference of the state and its nonlinear dynamics has posed significant challenges in practice. We develop a novel online learning framework, leveraging variational inference and sequential Monte Carlo, which enables flexible and accurate Bayesian joint filtering. Our method provides an approximation of the filtering posterior which can be made arbitrarily close to the true filtering distribution for a wide class of dynamics models and observation models. Specifically, the proposed framework can efficiently approximate a posterior over the dynamics using sparse Gaussian processes, allowing for an interpretable model of the latent dynamics. Constant time complexity per sample makes our approach amenable to online learning scenarios and suitable for real-time applications.

Multivariate Count Data Models for Time Series Forecasting

Count data appears in many research fields and exhibits certain features that make modeling difficult. Most popular approaches to modeling count data can be classified into observation and parameter-driven models. In this paper, we review two models from these classes: the log-linear multivariate conditional intensity model (also referred to as an integer-valued generalized autoregressive conditional heteroskedastic model) and the non-linear state-space model for count data. We compare these models in terms of forecasting performance on simulated data and two real datasets. In simulations, we consider the case of model misspecification. We find that both models have advantages in different situations, and we discuss the pros and cons of inference for both models in detail.

"Exact" and Approximate Methods for Bayesian Inference: Stochastic Volatility Case Study

We conduct a case study in which we empirically illustrate the performance of different classes of Bayesian inference methods to estimate stochastic volatility models. In particular, we consider how different particle filtering methods affect the variance of the estimated likelihood. We review and compare particle Markov Chain Monte Carlo (MCMC), RMHMC, fixed-form variational Bayes, and integrated nested Laplace approximation to estimate the posterior distribution of the parameters. Additionally, we conduct the review from the point of view of whether these methods are (1) easily adaptable to different model specifications; (2) adaptable to higher dimensions of the model in a straightforward way; (3) feasible in the multivariate case. We show that when using the stochastic volatility model for methods comparison, various data-generating processes have to be considered to make a fair assessment of the methods. Finally, we present a challenging specification of the multivariate stochastic volatility model, which is rarely used to illustrate the methods but constitutes an important practical application.

Conditional particle filters with diffuse initial distributions

Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random walk type transitions which are reversible with respect to a uniform initial distribution (on some domain), and autoregressive kernels for Gaussian initial distributions. We propose to use online adaptations within the methods. In the case of random walk transition, our adaptations use the estimated covariance and acceptance rate adaptation, and we detail their theoretical validity. We tested our methods with a linear Gaussian random walk model, a stochastic volatility model, and a stochastic epidemic compartment model with time-varying transmission rate. The experimental findings demonstrate that our method works reliably with little user specification and can be substantially better mixing than a direct particle Gibbs algorithm that treats initial states as parameters.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11222-020-09975-1.

A Comprehensive Review of Micro-Inertial Measurement Unit Based Intelligent PIG Multi-Sensor Fusion Technologies for Small-Diameter Pipeline Surveying

It is of great importance for pipeline systems to be is efficient, cost-effective and safe during the transportation of the liquids and gases. However, underground pipelines often experience leaks due to corrosion, human destruction or theft, long-term Earth movement, natural disasters and so on. Leakage or explosion of the operating pipeline usually cause great economical loss, environmental pollution or even a threat to citizens, especially when these accidents occur in human-concentrated urban areas. Therefore, the surveying of the routed pipeline is of vital importance for the Pipeline Integrated Management (PIM). In this paper, a comprehensive review of the Micro-Inertial Measurement Unit (MIMU)-based intelligent Pipeline Inspection Gauge (PIG) multi-sensor fusion technologies for the transport of liquids and gases purposed for small-diameter pipeline (D < 30 cm) surveying is demonstrated. Firstly, four types of typical small-diameter intelligent PIGs and their corresponding pipeline-defects inspection technologies and defects-positioning technologies are investigated according to the various pipeline defects inspection and localization principles. Secondly, the multi-sensor fused pipeline surveying technologies are classified into two main categories, the non-inertial-based and the MIMU-based intelligent PIG surveying technology. Moreover, five schematic diagrams of the MIMU fused intelligent PIG fusion technology is also surveyed and analyzed with details. Thirdly, the potential research directions and challenges of the popular intelligent PIG surveying techniques by multi-sensor fusion system are further presented with details. Finally, the review is comprehensively concluded and demonstrated.

Inference on high-dimensional implicit dynamic models using a guided intermediate resampling filter

We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition densities arise in models defined implicitly by simulation algorithms. Widely used particle filter methods are applicable to nonlinear, non-Gaussian models but suffer from the curse of dimensionality. Improved scalability is provided by ensemble Kalman filter methods, but these are inappropriate for highly nonlinear and non-Gaussian models. We propose a particle filter method having improved practical and theoretical scalability with respect to the model dimension. This method is applicable to implicitly defined models having analytically intractable transition densities. Our method is developed based on the assumption that the latent process is defined in continuous time and that a simulator of this latent process is available. In this method, particles are propagated at intermediate time intervals between observations and are resampled based on a forecast likelihood of future observations. We combine this particle filter with parameter estimation methodology to enable likelihood-based inference for highly nonlinear spatiotemporal systems. We demonstrate our methodology on a stochastic Lorenz 96 model and a model for the population dynamics of infectious diseases in a network of linked regions.

Tracking by Risky Particle Filtering over Sensor Networks

The system of wireless sensor networks is high of interest due to a large number of demanded applications, such as the Internet of Things (IoT). The positioning of targets is one of crucial problems in wireless sensor networks. Particularly, in this paper, we propose minimax particle filtering (PF) for tracking a target in wireless sensor networks where multiple-RSS-measurements of received signal strength (RSS) are available at networked-sensors. The minimax PF adopts the maximum risk when computing the weights of particles, which results in the decreased variance of the weights and the immunity against the degeneracy problem of generic PF. Via the proposed approach, we can obtain improved tracking performance beyond the asymptotic-optimal performance of PF from a probabilistic perspective. We show the validity of the employed strategy in the applications of various PF variants, such as auxiliary-PF (APF), regularized-PF (RPF), Kullback–Leibler divergence-PF (KLDPF), and Gaussian-PF (GPF), besides the standard PF (SPF) in the problem of tracking a target in wireless sensor networks.