Bayesian Dynamic Linear Model Research Articles

Drift versus Shift: Decoupling Trends and Changepoint Analysis

We introduce a new approach for decoupling trends (drift) and changepoints (shifts) in time series. Our locally adaptive model-based approach for robustly decoupling combines Bayesian trend filtering and machine learning based regularization. An over-parameterized Bayesian dynamic linear model (DLM) is first applied to characterize drift. Then a weighted penalized likelihood estimator is paired with the estimated DLM posterior distribution to identify shifts. We show how Bayesian DLMs specified with so-called shrinkage priors can provide smooth estimates of underlying trends in the presence of complex noise components. However, their inability to shrink exactly to zero inhibits direct changepoint detection. In contrast, penalized likelihood methods are highly effective in locating changepoints. However, they require data with simple patterns in both signal and noise. The proposed decoupling approach combines the strengths of both, that is, the flexibility of Bayesian DLMs with the hard thresholding property of penalized likelihood estimators, to provide changepoint analysis in complex, modern settings. The proposed framework is outlier robust and can identify a variety of changes, including in mean and slope. It is also easily extended for analysis of parameter shifts in time-varying parameter models like dynamic regressions. We illustrate the flexibility and contrast the performance and robustness of our approach with several alternative methods across a wide range of simulations and application examples.

Trend and Variance Adaptive Bayesian Changepoint Analysis and Local Outlier Scoring

We adaptively estimate both changepoints and local outlier processes in a Bayesian dynamic linear model with global-local shrinkage priors in a novel model we call Adaptive Bayesian Changepoints with Outliers (ABCO). We use a state-space approach to identify a dynamic signal in the presence of outliers and measurement error with stochastic volatility. We find that global state equation parameters are inadequate for most real applications and we include local parameters to track noise at each time-step. This setup provides a flexible framework to detect unspecified changepoints in complex series, such as those with large interruptions in local trends, with robustness to outliers and heteroscedastic noise. Finally, we compare our algorithm against several alternatives to demonstrate its efficacy in diverse simulation scenarios and two empirical examples on the U.S. economy.

Performance Prediction for Steel Bridges Using SHM Data and Bayesian Dynamic Regression Linear Model: A Novel Approach

Performance Prediction for Steel Bridges Using SHM Data and Bayesian Dynamic Regression Linear Model: A Novel Approach

Tropical Atmospheric Intraseasonal Oscillations Leading to Sea Level Extremes in Coastal Indonesia during Recent Decades

Abstract Coastal flooding induced by sea surface high extreme (HEX) events is an increasing risk to human society and infrastructure as both urban growth in coastal areas and anthropogenic sea level rise continue, especially for island nations like Indonesia. This paper investigates the role of atmospheric intraseasonal oscillations (ISOs), which are dominated by the Madden–Julian oscillation (MJO), in forcing HEXs on the coasts of Indonesia bordering the Indian Ocean. We use satellite altimetry data from 1993 to 2021 and tide gauge observations to detect HEXs, and modeling experiments using both the Regional Ocean Modeling System and a Bayesian dynamic linear model to understand the forcing and processes. We find that HEXs exhibit strong seasonality, with most events occurring during boreal winter (December–February) and spring (March–May) that are dominated by seasonal-to-decadal and intraseasonal variability respectively. In 32% of the 56 HEX events detected, the amplitude of ISO-induced sea level anomalies (SLAs) exceeds that of seasonal-to-decadal SLAs. Surface wind stress associated with atmospheric ISOs is the major forcing for intraseasonal SLAs, and both the remote westerly wind stress from the Indian Ocean equator and northwesterly longshore wind stress at the Indonesian coasts play important roles in driving the HEXs. The MJO is the dominant cause of ISO-dominated HEXs and its impact shows strong seasonal differences. Spring MJOs are associated with stronger convective anomalies over the eastern Indian Ocean equator that drive stronger zonal winds across the equatorial basin that lead to more HEX events compared to winter MJOs when the convection is shifted southward.

Simulating a Two-Arm Random Allocation Model Using a Bayesian Dynamic Linear Model Approach

Simulating a Two-Arm Random Allocation Model Using a Bayesian Dynamic Linear Model Approach

Understanding climate modes’ impact on the Indian Ocean decadal upwelling variability

<p align="justify">This study explores the spatial pattern and climate modes’ impact on the Indian Ocean decadal upwelling variability by using observational dataset, Static Linear Regression Model (SLM) and Bayesian Dynamic Linear Model (BDLM). Our analysis shows that the Indian Ocean decadal upwellings averaged in the Eastern and Western Indian Ocean (EIO and WIO) regions are positively correlated. Moreover, the BDLM that represents the temporal modulations of the El Niño and Southern Ocean (ENSO) and Indian Ocean Dipole (IOD) impacts, reproduces the time series of the EIO and WIO upwellings more realistically than a conventional SLM does. BD<span style="font-family: 'Times New Roman';">L</span>M simulations further suggest that in both EIO and WIO, IOD is more important than ENSO impact. The time-varying regression coefficients in BDLM indicate that the observed shift of the IOD impact on the EIO upwelling around 1985 is mainly associated with the changes of <span style="font-family: 'Times New Roman';">alongshore </span>wind stress forcing <span style="font-family: 'Times New Roman';">and </span>the sensitivity of the upper <span style="font-family: 'Times New Roman';">ocean </span>temperature <span style="font-family: 'Times New Roman';">in the </span>E<span style="font-family: 'Times New Roman';">IO</span> through the surface warming tendency and the enhanced ocean stratification. This suggests that climate models need to consider the time-varying impact of different climate modes in order to simulate the Indian Ocean dynamics correctly.<strong></strong></p>

Real-Time Malfunction Detection of Maglev Suspension Controllers

This study aims to develop a track-side online monitoring system for malfunction detection in the suspension controllers of maglev trains during their in-service operation. The hardware module of the system includes two arrays of accelerometers deployed on an F-type rail and a data acquisition unit. The software module of the system consists of codes for three functions: (i) the identification of time intervals in relation to the passage of each suspension controller via synchrosqueezing transform; (ii) the extraction of a feature index (FI) sequence synthesized by modulating the response amplitude, frequency, and running speed; and (iii) the formulation of a Bayesian dynamic linear model for real-time malfunction detection in maglev suspension controllers. For verification of the proposed monitoring system and malfunction detection algorithm, full-scale tests have been conducted on an maglev test line using the devised system, where a maglev train was run at different speeds with malfunction occurring in the suspension controllers. The malfunction detection results of the proposed approach are exemplified via comparison with the recorded suspension gaps after the trial run of the maglev train. The fidelity of the results obtained using the extracted FI sequence and using the raw monitoring data are compared. The superiority of the proposed malfunction detection algorithm is also discussed via comparison with the results of the different train speeds.

Data-driven time-variant reliability assessment of bridge girders based on deep learning

This article presents a new data-driven reliability analysis framework through combining the sample convolution and interaction network (SCINet) with Bayesian probability recursion to predict the time-variant reliability of bridge girders. The structural response predicted by SCINet and the state parameter (i.e., the variance of normal distribution) estimated by Bayesian dynamic linear model (BDLM) are used to form the limit state function to predict time-variant reliability. The results with a practical bridge show that the proposed method can predict future structural responses and time-variant reliability more accurately than BDLM, long short-term memory (LSTM), and long- and short-term time-series network (LSTNet) methods.

Decadal modulation of ENSO and IOD impacts on the Indian Ocean upwelling

The decadal modulations are observed in impacts of El Niño and Southern Ocean (ENSO) and Indian Ocean Dipole (IOD) on the tropical Indian Ocean upwelling. Here, we explore important contributors to the decadal modulations by combining the observational data since 1958 and statistical model simulations. A Bayesian Dynamic Linear Model (BDLM), which represents the temporal modulations of the IOD and ENSO impacts, reproduces the timeseries of the eastern and western Indian Ocean (EIO and WIO) upwellings more realistically than a conventional Static Linear regression Model does. The time-varying regression coefficients in BDLM indicate that the observed shift of the IOD impact on the EIO upwelling around 1980 is mainly due to the changes of alongshore wind stress forcing and the sensitivity of the upper ocean temperature in the EIO through the surface warming tendency and the enhanced ocean stratification. In contrast, the impacts of ENSO and IOD on the WIO are modulated in relation to the decadal variability of the tropical Pacific Ocean. When the eastern tropical Pacific Ocean is observed warmer on decadal timescales, the accompanying changes of the dominant ENSO flavors contribute to modulating the strengths of the atmospheric convective activity over the Indian-Pacific warm pool and the easterly wind variations in the equatorial Indian Ocean.

Intensification of heatwaves in China in recent decades: Roles of climate modes

Modes of climate variability can affect weather extremes, posing intractable challenges to our environment. However, to what extent climate modes can modulate heatwaves in China under a warming background remains poorly understood. Here, we examine the changes in heatwave intensity in seven distinct regions: three East, two middle, and two west regions over China and systematically explore the impacts of climate modes, by analyzing observations and performing model experiments using a Bayesian dynamic linear model and an atmospheric general circulation model (AGCM). Abrupt increases in heatwave intensity are detected across China during a transition period of 1993–2000, and the intensification remains robust in northern and western China after the warming trend being removed. The combined impacts of the El Niño–Southern Oscillation (ENSO), Atlantic Multidecadal Oscillation (AMO), and Indian Ocean Dipole (IOD) explain 62.35–70.01% of the observed heatwave intensification in East I, Middle I, West I, and West II regions. Decadal changes of atmospheric circulations associated with the negative phase transition of the Interdecadal Pacific Oscillation (IPO), which is highly correlated with the decadal variability of ENSO, combined with the positive phase transition of the AMO around the mid-1990s increase surface air temperature and enhance atmospheric internal variability and climate modes’ impacts, resulting in the abrupt increase of heatwaves in the past two decades. These results highlight the importance of the concurrent phase transitions of decadal climate modes in regulating heatwaves.

Atmospheric Dispersion Modeling Using a Stochastic Wind Model

In this work, we propose a stochastic wind field based on the Bayesian dynamic linear model to account for the wind flow field in the transient advection-diffusion partial differential equation (PDE). The resulting dispersion model accounts for the time variation in the wind field and meteorological variables, allowing the simulation of a transient regime. The main advantage of using such a wind field model over a Fourier series to fit wind time series is its potential to make predictions. In addition, a suitable methodology is necessary to solve the resulting dispersion model. In this work, we use a finite element formulation appropriate to solve transient advection-diffusion PDEs. We verify the accuracy of the proposed methodology by reproducing a case study considering a field tracer experiment. The model evaluation against experimental data shows the good performance of the proposed dispersion model.

SHM-informed life-cycle intelligent maintenance of fatigue-sensitive detail using Bayesian forecasting and Markov decision process

Civil and maritime engineering systems must be efficiently managed to control the failure risk at an acceptable level as their performance is gradually degraded throughout the operational life, caused by fatigue and corrosion. Structural health monitoring develops a timely capability to assess the structural condition and performance metrics. However, using actual long-term monitoring data to guide the life-cycle management under stochastic environments has not been sufficiently studied. To realize an optimal maintenance strategy within the service life, an integrated monitoring-based optimal management framework is developed on the basis of the partially observable Markov decision processes (POMDPs) and Bayesian forecasting. In the proposed framework, the stochastic fatigue processes are quantified by the state transition matrix. The Bayesian dynamic linear model is embedded in POMDPs as a continuous observation part to forecast the cycling impacts and estimate the deterioration rate using long-term dynamic strain responses. In addition, making use of the special features of the problem considered in this paper, an adaptive discretization strategy is proposed to alleviate the complexity of large discrete observed spaces in the POMDP. The applicability and feasibility of the framework are evaluated by intelligent maintenance of fatigue-sensitive components with real-world monitoring data. After solving the POMDP by an efficient offline solver, the results obtained in this paper demonstrate that structural interventions are uneconomical to extend the life when a welded detail is approaching its end of life due to the normal service. Furthermore, if multiple interventions are available, the framework can find optimal maintenance actions based on the trade-off between long-term utility and the corresponding cost. This framework as the prototype could also be adjusted to aid life-cycle intelligent maintenance of other types of components under different deterioration scenarios.

A novel Bayesian blind source separation approach for extracting non-stationary and discontinuous components from structural health monitoring data

We propose a new method to explore the blind source separation (BSS) of heterogeneous structural health monitoring (SHM) data containing non-stationary and temporally discontinuous components in the framework of Bayesian inference. Specifically, Gaussian process (GP) with a specially defined time-varying kernel function is introduced to encode the prior information about the unknown sources. The time-varying kernel function encompasses a state indicator hyperparameter which enables the expressivity of intermittently active and inactive source signals and incorporates smooth switch and composite kernels catering for the interpretation of complex sources. With the likelihood function elicited from monitoring data alongside with the priors for sources, mixing matrix and noise, the unknown sources are extracted from the posterior distributions formalized by Bayes’ theorem, where a sequential Metropolis − Hasting sampling algorithm is adopted to numerically compute the source statistics in a high-dimensional realm. Numerical simulations demonstrate that the proposed method performs satisfactorily in (i) extracting intermittently active and inactive (abruptly appearing and disappearing) non-stationary source signals, (ii) estimating inconsistent levels of noise contaminated in different sensors, and (iii) handling unknown number of sources. In the verification using real-world strain monitoring data collected from the Tsing Ma Bridge carrying both highway and railway traffic, it is shown that the proposed method well extracts the railway-induced non-stationary strain component with intermittence, and the structural condition index formulated by the Bayesian dynamic linear model (BDLM) is more robust when adopting the separated highway-induced strain data than using the combined railway- and highway-induced strain data. The results obtained by the proposed method are also compared with those by the two most common BSS techniques — the independent component analysis (ICA) and second-order statistics (SOS) methods.

Forecasting two-horse races in new democracies: Accuracy, precision and error

The purpose of this article is to explore electoral forecasting in two-horse races in new democracies. Specifically, it applies a Bayesian dynamic linear model (coined the Two-Stage Model, TSM) to look at the 2020 Chilean two-question national plebiscite. The ultimate objective is to test the TSM in terms of accuracy (how close the forecast is to the election results), precision (how close the forecast is to other methods of prediction) and error (how the forecast deviates from perfect accuracy/precision). The article finds that while the TSM does appear to be a stable estimator, its accuracy and precision is affected under certain conditions. Using the difference in the results for each of the two questions, the article discusses how sharp and unexpected shifts in electoral preferences can affect forecasts.

Revisiting the PPP puzzle: Nominal exchange rate rigidity and region of inaction

The paper revisits the purchasing power parity (PPP) puzzle and investigates potential sources of rigidity in the real exchange rate convergence. We propose two hypotheses on the slow convergence estimates in previous studies, and re-estimate the convergence rates to test the hypotheses. First, the slow convergence estimation is potentially from the forex market intervention by the central banks which claim to freely float their exchanges. Second, the real exchange rates may not show any convergence if they are already converged and within the “region of inaction.” We identify the regions of inaction (1) by creating bands around averages of real exchange rates, assuming that the PPP forms around the long-run averages, and (2) by using a Bayesian Dynamic Linear Model (DLM), assuming that real exchange rates converge to the different levels over time. We use a standard fixed effect estimation as well as a mean group panel estimation to handle aggregation biases in standard panel estimation. The results confirm the propositions and make the puzzle less puzzling; we find approximately 30%–65% shorter half-life estimates than the standard fixed effects estimates in previous studies.

Bayesian dynamic linear model framework for structural health monitoring data forecasting and missing data imputation during typhoon events

A Bayesian dynamic linear model (BDLM) framework for data modeling and forecasting is proposed to evaluate the performance of an operational cable-stayed bridge, that is, Ting Kau Bridge in Hong Kong, by using SHM strain field data acquired. One of the major challenges in dealing with the existing in-service bridge under extreme typhoon loads is to forecast structural behavior using the typhoon response exhibiting non-stationarity, large data fluctuations and strong randomness. The first attempt for SHM data modeling during extreme events, that is, typhoons, using BDLM framework, was conducted in this study. The data from multiple sensors are analyzed for one-step, multi-step ahead forecasting and missing data imputation. The overall bridge behavior is incorporated into a forecasting model by superposition of forecasting results of trend (representing the structural baseline response), periodic component (response component evolving regularly over time), and autoregressive component (time-dependent error) through BDLM algorithm. The results demonstrate that the BDLM framework yielded more accurate calculations compared with Gaussian process and Variational Heteroscedasticity Gaussian Process methods with respect to one-step ahead forecasting for strain data under typhoons. Multi-step ahead forecasting was successfully carried out both for non-typhoon and typhoon responses within an acceptable precision range. The correlation between periodic component and temperature was also investigated. Regarding missing data imputation, BLDM algorithm can generate robust results due to making full use of the monitoring data both before and after the missing segments.

Bayesian dynamic extreme value modeling for conflict-based real-time safety analysis

Real-time safety analysis and optimization using surrogate safety measures such as traffic conflicts and techniques such extreme value theory (EVT) models is an emerging research topic in the context of proactive traffic safety management. However, the predictive performance and temporal transferability of the existing real-time safety analysis EVT models are subject to the assumption of invariant model parameters, which do not account for the temporal variability and is not suitable for real-time traffic data analysis. This study proposes a Bayesian dynamic extreme value modeling approach for conflict-based real-time safety analysis which integrates a Bayesian dynamic linear model with the extreme value distribution. The proposed approach has several unique advantages as it: 1) allows the model parameters to be time-varying; 2) integrates the newer data with prior information to recursively update the model parameters and account for state-space changes and react to sudden trend changes; 3) accounts for temporal variability and non-stationarity in conflict extremes; and 4) quantitatively evaluates the real-time safety levels of a road facility. The proposed approach is applied for cycle-by-cycle safety analysis at four signalized intersections in the city of Surrey, British Columbia. Traffic conflicts are characterized by the modified time to collision indicator. Three traffic parameters (traffic volume, shock wave area, and platoon ratio) at the signal cycle level are considered as covariates to account for non-stationarity. Several Bayesian dynamic and static extreme value models are developed and two safety indices, namely risk of crash (RC) and return level (RL), are generated to quantitatively represent the cycle-level safety. The RC directly reflects whether a cycle is risky while the RL can evaluate the safety levels of individual cycles. The results show that the dynamic model can identify more crash-risk cycles with either a positive RC or a positive RL than the static model and is more capable of differentiating the safety levels for individual cycles in terms of RL. Overall, the dynamic model outperforms the static model in terms of the statistical fit and aggregate crash estimation accuracy.

Observed changes in seasonal drought characteristics and their possible potential drivers over Pakistan

AbstractLong‐term drought monitoring and its assessment are of great importance for meteorological disaster risk management. The recurrent spells of heat waves and droughts have severely affected the environmental conditions worldwide, including Pakistan. The present work sought to investigate the spatiotemporal changes in drought characteristics over Pakistan during Rabi and Kharif cropping seasons. The role of large‐scale circulation and interannual mode of climate variability is further explored to identify the physical mechanisms associated with droughts in the region. Monthly precipitation and temperature data (1983–2019) from 53 meteorological stations were used to study drought characteristics, using the standardized precipitation evapotranspiration index (SPEI). The nonparametric Mann–Kendall, Sen's Slope, and Sequential Mann–Kendall tests were applied on the drought index to determine the statistical significance and magnitude of the historical trend. The state‐of‐the‐art Bayesian Dynamic Linear model was further used to analyse large‐scale climate drivers of droughts, revealed an increase in drought severity, mostly over arid to semiarid regions for both cropping seasons. While temperature played a significant role in defining droughts over dry and hot seasons, rainfall is influential over the western disturbances influenced region. The analysis of atmospheric circulation patterns revealed that large‐scale changes in wind speed, air temperature, relative humidity, and geopotential height anomalies are the likely drivers of droughts in the region. We found that Niño4, sea surface temperature, and multivariate El Niño‐Southern Oscillation (ENSO4.0) Index are the most influential factors for seasonal droughts across Pakistan. Overall, the findings provide a better understanding of drought‐prone areas in the region, and this information is of potential use for mitigating and managing drought risks.

Forecasting daily new infections, deaths and recovery cases due to COVID-19 in Pakistan by using Bayesian Dynamic Linear Models.

The COVID-19 has caused the deadliest pandemic around the globe, emerged from the city of Wuhan, China by the end of 2019 and affected all continents of the world, with severe health implications and as well as financial-damage. Pakistan is also amongst the top badly effected countries in terms of casualties and financial loss due to COVID-19. By 20th March, 2021, Pakistan reported 623,135 total confirmed cases and 13,799 deaths. A state space model called 'Bayesian Dynamic Linear Model' (BDLM) was used for the forecast of daily new infections, deaths and recover cases regarding COVID-19. For the estimation of states of the models and forecasting new observations, the recursive Kalman filter was used. Twenty days ahead forecast show that the maximum number of new infections are 4,031 per day with 95% prediction interval (3,319-4,743). Death forecast shows that the maximum number of the deaths with 95% prediction interval are 81 and (67-93), respectively. Maximum daily recoveries are 3,464 with 95% prediction interval (2,887-5,423) in the next 20 days. The average number of new infections, deaths and recover cases are 3,282, 52 and 1,840, respectively, in the upcoming 20 days. As the data generation processes based on the latest data has been identified, therefore it can be updated with the availability of new data to provide latest forecast.

Switching Bayesian dynamic linear model for condition assessment of bridge expansion joints using structural health monitoring data

Age-related deterioration and premature failure have been primary concerns for bridge expansion joints. It is essential to improve the understanding of their operational performance. The existing approaches mainly formulate the deterministic/probabilistic temperature-displacement relationship (TDR) model to assess the structural condition of bridge expansion joints. Nevertheless, it is not easy to guarantee a strong correlation between representative temperature and displacement. Rather than establishing the TDR model, this work uses the displacement response to evaluate the expansion joint condition by combining the Bayesian dynamic linear model (BDLM) with Markov-switching theory. The external temperature effect on the displacement is modeled by the superposition of harmonic components in BDLM. The expectation–maximization (EM) algorithm initialized by the subspace method is employed to optimize the initial parameters. The presented approach is validated through the simulated data, and then it is applied to the expansion joint of a long-span bridge. Results show that EM with the subspace method involves high computational accuracy and efficiency in estimating unknown parameters compared to the Newton-Raphson approach. The switching BDLM successfully identifies the degradation process of expansion joints and offers the transition probability from the normal to other states.