Bayesian Analysis Of Time Series Research Articles

Bayesian variable selection for matrix autoregressive models

A Bayesian method is proposed for variable selection in high-dimensional matrix autoregressive models which reflects and exploits the original matrix structure of data to (a) reduce dimensionality and (b) foster interpretability of multidimensional relationship structures. A compact form of the model is derived which facilitates the estimation procedure and two computational methods for the estimation are proposed: a Markov chain Monte Carlo algorithm and a scalable Bayesian EM algorithm. Being based on the spike-and-slab framework for fast posterior mode identification, the latter enables Bayesian data analysis of matrix-valued time series at large scales. The theoretical properties, comparative performance, and computational efficiency of the proposed model is investigated through simulated examples and an application to a panel of country economic indicators.

Bayesian modeling of multivariate time series of counts

AbstractIn this article, we present an overview of recent advances in Bayesian modeling and analysis of multivariate time series of counts. We discuss basic modeling strategies including integer valued autoregressive processes, multivariate Poisson time series and dynamic latent factor models. In so doing, we make a connection with univariate modeling frameworks such as dynamic generalized models, Poisson state space models with gamma evolution and present Bayesian approaches that extend these frameworks to multivariate setting. During our development, recent Bayesian approaches to the analysis of integer valued autoregressive processes and multivariate Poisson models are highlighted and concepts such as “decouple/recouple” and “common random environment” are presented. The role that these concepts play in Bayesian modeling and analysis of multivariate time series are discussed. Computational issues associated with Bayesian inference and forecasting from these models are also considered.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical Models > Time Series Models

Adaptive Bayesian Spectral Analysis of High-Dimensional Nonstationary Time Series

This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious representation of spectral matrices from a large number of simultaneously observed time series. Real and imaginary parts of the factor loading matrices are modeled independently using a prior that is formulated from the tensor product of penalized splines and multiplicative gamma process shrinkage priors, allowing for infinitely many factors with loadings increasingly shrunk toward zero as the column index increases. Formulated in a fully Bayesian framework, the time series is adaptively partitioned into approximately stationary segments, where both the number and locations of partition points are assumed unknown. Stochastic approximation Monte Carlo techniques are used to accommodate the unknown number of segments, and a conditional Whittle likelihood-based Gibbs sampler is developed for efficient sampling within segments. By averaging over the distribution of partitions, the proposed method can approximate both abrupt and slowly varying changes in spectral matrices. Performance of the proposed model is evaluated by extensive simulations and demonstrated through the analysis of high-density electroencephalography. Supplementary materials for this article are available online.

Towards reduction in bias in epidemic curves due to outcome misclassification through Bayesian analysis of time-series of laboratory test results: case study of COVID-19 in Alberta, Canada and Philadelphia, USA

BackgroundDespite widespread use, the accuracy of the diagnostic test for SARS-CoV-2 infection is poorly understood. The aim of our work was to better quantify misclassification errors in identification of true cases of COVID-19 and to study the impact of these errors in epidemic curves using publicly available surveillance data from Alberta, Canada and Philadelphia, USA.MethodsWe examined time-series data of laboratory tests for SARS-CoV-2 viral infection, the causal agent for COVID-19, to try to explore, using a Bayesian approach, the sensitivity and specificity of the diagnostic test.ResultsOur analysis revealed that the data were compatible with near-perfect specificity, but it was challenging to gain information about sensitivity. We applied these insights to uncertainty/bias analysis of epidemic curves under the assumptions of both improving and degrading sensitivity. If the sensitivity improved from 60 to 95%, the adjusted epidemic curves likely falls within the 95% confidence intervals of the observed counts. However, bias in the shape and peak of the epidemic curves can be pronounced, if sensitivity either degrades or remains poor in the 60–70% range. In the extreme scenario, hundreds of undiagnosed cases, even among the tested, are possible, potentially leading to further unchecked contagion should these cases not self-isolate.ConclusionThe best way to better understand bias in the epidemic curves of COVID-19 due to errors in testing is to empirically evaluate misclassification of diagnosis in clinical settings and apply this knowledge to adjustment of epidemic curves.

Bayesian nonparametric analysis of multivariate time series: A matrix Gamma Process approach

Many Bayesian nonparametric approaches to multivariate time series rely on Whittle’s Likelihood, involving the second order structure of a stationary time series by means of its spectral density matrix. In this work, we model the spectral density matrix by means of random measures that are constructed in such a way that positive definiteness is ensured. This is in line with existing approaches for the univariate case, where the normalized spectral density is modeled similar to a probability density, e.g. with a Dirichlet process mixture of Beta densities. We present a related approach for multivariate time series, with matrix-valued mixture weights induced by a Hermitian positive definite Gamma process. The latter has not been considered in the literature, allows to include prior knowledge and possesses a series representation that will be used in MCMC methods. We establish posterior consistency and contraction rates and small sample performance of the proposed procedure is shown in a simulation study and for real data.

Bayesian comparative study on binary time series

ABSTRACTIn this paper, we consider the Bayesian analysis of binary time series with different priors, namely normal, Students' t, and Jeffreys prior, and compare the results with the frequentist methods through some simulation experiments and one real data on daily rainfall in inches at Mount Washington, NH. Among Bayesian methods, our results show that the Jeffreys prior perform better in most of the situations for both the simulation and the rainfall data. Furthermore, among weakly informative priors considered, Student's t prior with 7 degrees of freedom fits the data most adequately.

Dynamics & sparsity in latent threshold factor models: A study in multivariate EEG signal processing

We discuss Bayesian analysis of multivariate time series with dynamic factor models that exploit time-adaptive sparsity in model parametrizations via the latent threshold approach. One central focus is on the transfer responses of multiple interrelated series to underlying, dynamic latent factor processes. Structured priors on model hyper-parameters are key to the efficacy of dynamic latent thresholding, and MCMC-based computation enables model fitting and analysis. A detailed case study of electroencephalographic (EEG) data from experimental psychiatry highlights the use of latent threshold extensions of time-varying vector autoregressive and factor models. This study explores a class of dynamic transfer response factor models, extending prior Bayesian modeling of multiple EEG series and highlighting the practical utility of the latent thresholding concept in multivariate, non-stationary time series analysis.

Conditional adaptive Bayesian spectral analysis of nonstationary biomedical time series.

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely ignored due to a lack of methods that can assess the changing nature of the relationship through time. This article introduces a method for the simultaneous and automatic analysis of the association between the time-varying power spectrum and covariates, which we refer to as conditional adaptive Bayesian spectrum analysis (CABS). The procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines. CABS is formulated in a fully Bayesian framework, in which the number and locations of partition points are random, and fit using reversible jump Markov chain Monte Carlo techniques. Estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes. The proposed methodology is used to analyze the association between the time-varying spectrum of heart rate variability and self-reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse.

Bayesian analysis of hydrological time series based on MCMC algorithm

In this paper we consider Bayesian analysis of the possible changes in hydrological time series by Markov chain Monte Carlo (MCMC) algorithm. We consider multiple change-points and various possible situations. The approach of Bayesian stochastic search selection is used for detecting and estimating the number and positions of possible change-point in a piecewise constant model. MCMC algorithm is used to estimate the posterior distributions of parameters. The result of the analysis is applied to the hydrological data sets of the major river net area of Shunde in China and the data set of Nile River. In order to further investigate the trends in each segment of the hydrological data sets, we consider the analysis of change-point regression model via MCMC algorithm.

System Priors for Econometric Time Series

The paper introduces “system priors”, their use in Bayesian analysis of econometric time series, and provides a simple and illustrative application. System priors were devised by Andrle and Benes (2013) as a tool to incorporate prior knowledge into an economic model. Unlike priors about individual parameters, system priors offer a simple and efficient way of formulating well-defined and economically-meaningful priors about high-level model properties. The generality of system priors are illustrated using an AR(2) process with a prior that most of its dynamics comes from business-cycle frequencies.

Bayesian analysis of time series using granular computing approach

The soft computing methods, especially data mining, usually enable to describe large datasets in a human-consistent way with the use of some generic and conceptually meaningful information entities like information granules. However, such information granules may be applied not only for the descriptive purposes, but also for prediction. We review the main developments and challenges of the application of the soft computing methods in the time series analysis and forecasting, and we provide a conceptual framework for the Bayesian time series forecasting using the granular computing approach. Within the proposed approach, the information granules are successfully incorporated into the Bayesian posterior simulation process. The approach is evaluated with a set of experiments on the artificial and benchmark real-life time series datasets.

Automated Detection of Oscillating Regions in the Solar Atmosphere

Recently observed oscillations in the solar atmosphere have been interpreted and modeled as magnetohydrodynamic wave modes. This has allowed the estimation of parameters that are otherwise hard to derive, such as the coronal magnetic-field strength. This work crucially relies on the initial detection of the oscillations, which is commonly done manually. The volume of Solar Dynamics Observatory (SDO) data will make manual detection inefficient for detecting all of the oscillating regions. An algorithm is presented which automates the detection of areas of the solar atmosphere that support spatially extended oscillations. The algorithm identifies areas in the solar atmosphere whose oscillation content is described by a single, dominant oscillation within a user-defined frequency range. The method is based on Bayesian spectral analysis of time-series and image filtering. A Bayesian approach sidesteps the need for an a-priori noise estimate to calculate rejection criteria for the observed signal, and it also provides estimates of oscillation frequency, amplitude and noise, and the error in all these quantities, in a self-consistent way. The algorithm also introduces the notion of quality measures to those regions for which a positive detection is claimed, allowing simple post-detection discrimination by the user. The algorithm is demonstrated on two Transition Region and Coronal Explorer (TRACE) datasets, and comments regarding its suitability for oscillation detection in SDO are made.

Estimating Sparse Gene Regulatory Networks Using a Bayesian Linear Regression

In this paper, we propose a gene regulatory network (GRN) estimation method, which assumes that such networks are typically sparse, using time-series microarray datasets. We represent the regulatory relationships between the genes using weights, with the "net" regulation influence on a gene's expression being the summation of the independent regulatory inputs. We estimate the weights using a Bayesian linear regression method for sparse parameter vectors. We apply our proposed method to the extraction of differential gene expression software selected genes of a human buffy-coat microarray expression profile dataset of ventilator-associated pneumonia (VAP), and compare the estimation result with the GRNs estimated using both a correlation coefficient method and a database-based method ingenuity pathway analysis. A biological analysis of the resulting consensus network that is derived using the GRNs, estimated with both our and the correlation-coefficient methods results in four biologically meaningful subnetworks. Also, our method performs either better than or competitively with the existing well-established GRN estimation methods. Moreover, it performs comparatively with respect to: 1) the ground-truth GRNs for the in silico 50- and 100-gene datasets reported recently in the DREAM3 challenge and 2) the GRN estimated using a mutual information-based method for the top-ranked Bayesian analysis of time series (a Bayesian user-friendly software for analyzing time-series microarray experiments) selected genes of the VAP dataset.

Bayesian wavelet-based analysis of functional magnetic resonance time series

Wavelet methods for image regularization offer a data-driven alternative to Gaussian smoothing in functional magnetic resonance (fMRI) analysis. Their impact has been limited by the difficulties in integrating regularization in the wavelet domain and inference in the image domain, precluding the probabilistic decision on which areas are activated by a task. Here we present an integrated framework for Bayesian estimation and regularization in wavelet space that allows the usual voxelwise hypothesis testing. This framework is flexible, being an adaptation to fMRI time series of a more general wavelet-based functional mixed-effect model. Through testing on a combination of simulated and real fMRI data, we show evidence of improved signal recovery, without compromising test accuracy in image space.

BATS: a Bayesian user-friendly software for Analyzing Time Series microarray experiments

BackgroundGene expression levels in a given cell can be influenced by different factors, namely pharmacological or medical treatments. The response to a given stimulus is usually different for different genes and may depend on time. One of the goals of modern molecular biology is the high-throughput identification of genes associated with a particular treatment or a biological process of interest. From methodological and computational point of view, analyzing high-dimensional time course microarray data requires very specific set of tools which are usually not included in standard software packages. Recently, the authors of this paper developed a fully Bayesian approach which allows one to identify differentially expressed genes in a 'one-sample' time-course microarray experiment, to rank them and to estimate their expression profiles. The method is based on explicit expressions for calculations and, hence, very computationally efficient.ResultsThe software package BATS (Bayesian Analysis of Time Series) presented here implements the methodology described above. It allows an user to automatically identify and rank differentially expressed genes and to estimate their expression profiles when at least 5–6 time points are available. The package has a user-friendly interface. BATS successfully manages various technical difficulties which arise in time-course microarray experiments, such as a small number of observations, non-uniform sampling intervals and replicated or missing data.ConclusionBATS is a free user-friendly software for the analysis of both simulated and real microarray time course experiments. The software, the user manual and a brief illustrative example are freely available online at the BATS website:

Bayesian Inference and Forecasting in Dynamic Neural Networks with Fully Markov Switching ARCH Noises

We deal with one-layer feed-forward neural network for the Bayesian analysis of nonlinear time series. Noises are modeled nonlinearly and nonnormally, by means of ARCH models whose parameters are all dependent on a hidden Markov chain. Parameter estimation is performed by sampling from the posterior distribution via Evolutionary Monte Carlo algorithm, in which two new crossover operators have been introduced. Unknown parameters of the model also include the missing values which can occur within the observed series, so, considering future values as missing, it is also possible to compute point and interval multi-step-ahead predictions.

The Power of the “Objective” Bayesian Unit-Root Test

Abstract Some researchers, for example, Koop (1992), and Sims (1988), advocated forBayesian alternatives to unit-root testing over the classical approach using theaugmented Dickey-Fuller test (ADF). This paper studies the power of what Koop(1992) has called the ”Objective” Bayesian approach to unit-root testing. Koop’s”objective” Bayesian test is interesting in light of the call by Phillips (1991a,1991b) for more objective Bayesian analysis of time series. We apply the ”ob-jective” Bayesian unit-root test to a study of long-run purchasing power parity(PPP) in the post-Bretton Woods era and also Monte Carlo simulations. Overall,our results suggest that the ”objective” Bayesian test is biased in favor of trend-stationarity. We conclude that, at least for the ”objective” Bayesian test, it is notbetter than the classical ADF approach in unit-root tests, and because of its bias,the ”objective” priors suggested by Koop is not appropriate.Journal of Economic Literature Classification: C11, C22, F31I wish to thank Professor Stephen M. Miller, participants at the Southern Eco-nomic Association Annual Meetings, and Department of Economics, Universityof Connecticut, brown-bag seminar for comments on an earlier draft of this paper.Remaining errors are my sole responsibilities.

Bayesian analysis of blood glucose time series from diabetes home monitoring.

This paper describes the application of a novel Bayesian estimation technique to extract the structural components, i.e., trend and daily patterns, from blood glucose level time series coming from home monitoring of insulin dependent diabetes mellitus patients. The problem is formulated through a set of stochastic equations, and is solved in a Bayesian framework by using a Markov chain Monte Carlo technique. The potential of the method is illustrated by analyzing data coming from the home monitoring of a 14-year old male patient.

A comparison of approximate Bayesian forecasting methods for non-Gaussian time series

We present the results on the comparison of efficiency of approximate Bayesian methods for the analysis and forecasting of non-Gaussian dynamic processes. A numerical algorithm based on MCMC methods has been developed to carry out the Bayesian analysis of non-linear time series. Although the MCMC-based approach is not fast, it allows us to study the efficiency, in predicting future observations, of approximate propagation procedures that, being algebraic, have the practical advantage of being very quick. Copyright © 2000 John Wiley & Sons, Ltd.

Bayesian analysis of autoregressive time series with change points

The paper deals with the identification of a stationary autoregressive model for a time series and the contemporary detection of a change in its mean. We adopt the Bayesian approach with weak prior information on the parameters of the models under comparison and an exact form of the likelihood function. When necessary, we resort to fractional Bayes factors to choose between models, and to importance sampling to solve computational issues.