Improving MCMC Using Efficient Importance Sampling

This paper develops a systematic Markov Chain Monte Carlo (MCMC) framework based upon Efficient Importance Sampling (EIS) which can be used for the analysis of a wide range of econometric models involving integrals without an analytical solution. EIS is a simple, generic and yet accurate Monte-Carlo integration procedure based on sampling densities which are chosen to be global approximations to the integrand. By embedding EIS within MCMC procedures based on Metropolis-Hastings (MH) one can significantly improve their numerical properties, essentially by providing a fully automated selection of critical MCMC components such as auxiliary sampling densities, normalizing constants and starting values. The potential of this integrated MCMC- EIS approach is illustrated with simple univariate integration problems and with the Bayesian posterior analysis of stochastic volatility models and stationary autoregressive processes. --Autoregressive models,Bayesian posterior analysis,Dynamic latent variables,Gibbs sampling,Metropolis Hastings,Stochastic volatility

A Bayesian Multivariate Functional Dynamic Linear Model

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic linear models for multivariate time series to the functional data setting. We also develop Bayesian spline theory in a more general constrained optimization framework. The proposed methods identify a time-invariant functional basis for the functional observations, which is smooth and interpretable, and can be made common across multivariate observations for additional information sharing. The Bayesian framework permits joint estimation of the model parameters, provides exact inference (up to MCMC error) on specific parameters, and allows generalized dependence structures. Sampling from the posterior distribution is accomplished with an efficient Gibbs sampling algorithm. We illustrate the proposed framework with two applications: (1) multi-economy yield curve data from the recent global recession, and (2) local field potential brain signals in rats, for which we develop a multivariate functional time series approach for multivariate time-frequency analysis. Supplementary materials, including R code and the multi-economy yield curve data, are available online

Imaging sediment structure: the emerging use of Magnetic Resonance Imaging (MRI) for 3D analysis of sediment structures and internal flow processes

Magnetic Resonance Imaging (MRI) can be used for 3D analysis of small-scale porous media structure and internal flow-related processes. It offers notable advantages over traditional sediment sampling (e.g. cores or surface-based scanning) as it is capable of high spatio-temporal resolution of the full 3D volume, including the sub-surface. Similarly, compared to X-Ray tomography, the extensive catalogue of MR pulse sequences typically provides: faster capture for imaging dynamic fluid processes; greater flexibility in resolving chemical species or tracers; and a safer radiation-free methodology. To demonstrate the relevance of this technique in geomorphological research, three exemplar applications are described: porous media structure of gravel bed rivers; measurements of fluid processes within aquifer pores and fractures; and, concentration mapping of contaminants through sand/gravel frameworks. Whilst, this emerging technique offers significant potential for visualizing many other ‘black-box’ processes important to the wider discipline, attention is afforded to discussion of the present constraints of the technique in field-based analysis

Relaxation-based importance sampling for structural reliability analysis

This study presents an importance sampling formulation based on adaptively relaxing parameters from the indicator function and/or the probability density function. The formulation embodies the prevalent mathematical concept of relaxing a complex problem into a sequence of progressively easier sub-problems. Due to the flexibility in constructing relaxation parameters, relaxation-based importance sampling provides a unified framework for various existing variance reduction techniques, such as subset simulation, sequential importance sampling, and annealed importance sampling. More crucially, the framework lays the foundation for creating new importance sampling strategies, tailoring to specific applications. To demonstrate this potential, two importance sampling strategies are proposed. The first strategy couples annealed importance sampling with subset simulation, focusing on low-dimensional problems. The second strategy aims to solve high-dimensional problems by leveraging spherical sampling and scaling techniques. Both methods are desirable for fragility analysis in performance-based engineering, as they can produce the entire fragility surface in a single run of the sampling algorithm. Three numerical examples, including a 1000-dimensional stochastic dynamic problem, are studied to demonstrate the proposed methods

Patient-Specific Method of Generating Parametric Maps of Patlak K(i) without Blood Sampling or Metabolite Correction: A Feasibility Study.

Currently, kinetic analyses using dynamic positron emission tomography (PET) experience very limited use despite their potential for improving quantitative accuracy in several clinical and research applications. For targeted volume applications, such as radiation treatment planning, treatment monitoring, and cerebral metabolic studies, the key to implementation of these methods is the determination of an arterial input function, which can include time-consuming analysis of blood samples for metabolite correction. Targeted kinetic applications would become practical for the clinic if blood sampling and metabolite correction could be avoided. To this end, we developed a novel method (Patlak-P) of generating parametric maps that is identical to Patlak K(i) (within a global scalar multiple) but does not require the determination of the arterial input function or metabolite correction. In this initial study, we show that Patlak-P (a) mimics Patlak K(i) images in terms of visual assessment and target-to-background (TB) ratios of regions of elevated uptake, (b) has higher visual contrast and (generally) better image quality than SUV, and (c) may have an important role in improving radiotherapy planning, therapy monitoring, and neurometabolism studies

An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates

In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov’s theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a nonequilibrium dynamics which is used to sample the equilibrium quantities

Miniaturised air sampling techniques for analysis of volatile organic compounds in air

Growing concern about the effects of atmospheric pollutants on climate and human health has accelerated the development of novel analytical methods, including sampling systems, for the determination of atmospheric volatile organic compounds (VOCs). Miniaturised air sampling (MAS) techniques have attracted wide attention in the past two decades due to their advantages (ease of operation, time-integrated sampling, small/no organic solvent consumption, and potential for automation). This review focuses on the latest developments in these techniques, including needle trap microextraction (NTME), in-tube extraction (ITEX), sorption trap, solid-phase microextraction (SPME fibre, SPME Arrow, and retracted SPME fibre), thin-film microextraction (TFME), solid-phase dynamic extraction (SPDE), and stir bar sorptive extraction (SBSE). Further, their benefits, drawbacks, and applicability to air sampling are discussed. The applications of MAS techniques for the analysis of atmospheric air, indoor air, breath air, and emissions of plants and foods are summarised and discussed.Peer reviewe

Information-based Preprocessing of PLC Data for Automatic Behavior Modeling

Cyber-physical systems (CPS) offer immense optimization potential for manufacturing processes through the availability of multivariate time series data of actors and sensors. Based on automated analysis software, the deployment of adaptive and responsive measures is possible for time series data. Due to the complex and dynamic nature of modern manufacturing, analysis and modeling often cannot be entirely automated. Even machine- or deep learning approaches often depend on a priori expert knowledge and labelling. In this paper, an information-based data preprocessing approach is proposed. By applying statistical methods including variance and correlation analysis, an approximation of the sampling rate in event-based systems and the utilization of spectral analysis, knowledge about the underlying manufacturing processes can be gained prior to modeling. The paper presents, how statistical analysis enables the pruning of a dataset's least important features and how the sampling rate approximation approach sets the base for further data analysis and modeling. The data's underlying periodicity, originating from the cyclic nature of an automated manufacturing process, will be detected by utilizing the fast Fourier transform. This information-based preprocessing method will then be validated for process time series data of cyber-physical systems' programmable logic controllers (PLC)