Bayesian Time Series Analysis Research Articles

A Bayesian Structural Time Series Analysis of the Effect of Basic Income on Crime: Evidence From the Alaska Permanent Fund

AbstractThis paper examines the impact of Alaska’s Permanent Fund Dividend on crime. The Dividend has been payable annually to state residents since 1982 and is the world’s longest-running example of a basic income. Initially universal, from 1989 onwards eligibility was withdrawn from an increasing proportion of those in prison. A Bayesian structural time series estimator is used to simulate Alaskan crime rates in the counterfactual no-Dividend case. A comparison with actual rates provides an estimate of the Dividend’s impact. This does not provide strong evidence of an effect. However, incorporating information on Dividend amounts suggests the size of payments is important, with larger amounts reducing crime. There is no evidence that this effect is reinforced by the 1989 change to eligibility. The results demonstrate the potential for a basic income to encourage positive outcomes and lend support to payment being universal rather than conditional.

Effect of Strict and Soft Policy Interventions on Laboratory Diagnostic Testing in Ontario, Canada: A Bayesian Structural Time Series Analysis

Applications of behavioral economics targeted at optimizing laboratory utilization among physicians have been implemented in Ontario through different types of nonfinancial interventions. Strict policy interventions restrict Ontario Health Insurance Plan (OHIP) payment for tests to patients with specific conditions or limit ordering to particular physician specialties, while soft policy interventions involve modifications to the laboratory requisition form. This study evaluates the effectiveness of these interventions in terms of changing physician ordering behavior for eight tests that were subject to a strict or soft policy intervention during the study period. We use a Bayesian structural time series model applied to Ontario laboratory claims data for FY2006 through FY2017. Results show a 16–75% reduction in laboratory services with a strict policy intervention and an 8–36% reduction in laboratory services with a soft policy intervention. Although the overall magnitude of change was smaller for soft policy interventions, interventions designed with soft or strict policy mechanisms addressing laboratory utilization management are effective at influencing physicians’ test ordering behavior.

Effects of lake warming on the seasonal risk of toxic cyanobacteria exposure

AbstractIncidence of elevated harmful algal blooms and concentrations of microcystin are increasing globally as a result of human‐mediated changes in land use and climate. However, few studies document changes in the seasonal and interannual concentrations of microcystin in lakes. Here, we modeled 11 yr of biweekly microcystin data from six lakes to characterize the seasonal patterns in microcystin concentration and to ascertain if there were pronounced changes in the patterns of potential human exposure to microcystin in lakes of central North America. Bayesian time series analysis with generalized additive models found evidence for a regional increase in microcystin maxima and duration but recorded high variation among lakes. During the past decade, warmer temperatures, but not nutrient levels, led to a marked increase in the number of days when concentrations exceeded drinking and recreational water thresholds set by the World Health Organization and United States Environmental Protection Agency.

Beyond Whittle: Nonparametric Correction of a Parametric Likelihood with a Focus on Bayesian Time Series Analysis

Nonparametric Bayesian inference has seen a rapid growth over the last decade but only few nonparametric Bayesian approaches to time series analysis have been developed. Most existing approaches use Whittle’s likelihood for Bayesian modelling of the spectral density as the main nonparametric characteristic of stationary time series. It is known that the loss of efficiency using Whittle’s likelihood can be substantial. On the other hand, parametric methods are more powerful than nonparametric methods if the observed time series is close to the considered model class but fail if the model is misspecified. Therefore, we suggest a nonparametric correction of a parametric likelihood that takes advantage of the efficiency of parametric models while mitigating sensitivities through a nonparametric amendment. We use a nonparametric Bernstein polynomial prior on the spectral density with weights induced by a Dirichlet process and prove posterior consistency for Gaussian stationary time series. Bayesian posterior computations are implemented via an MH-within-Gibbs sampler and the performance of the nonparametrically corrected likelihood for Gaussian time series is illustrated in a simulation study and in three astronomy applications, including estimating the spectral density of gravitational wave data from the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO).

Bayesian dynamic modeling and monitoring of network flows

AbstractIn the context of a motivating study of dynamic network flow data on a large-scale e-commerce website, we develop Bayesian models for online/sequential analysis for monitoring and adapting to changes reflected in node–node traffic. For large-scale networks, we customize core Bayesian time series analysis methods using dynamic generalized linear models (DGLMs). These are integrated into the context of multivariate networks using the concept of decouple/recouple that was recently introduced in multivariate time series. This method enables flexible dynamic modeling of flows on large-scale networks and exploitation of partial parallelization of analysis while maintaining coherence with an over-arching multivariate dynamic flow model. This approach is anchored in a case study on Internet data, with flows of visitors to a commercial news website defining a long time series of node–node counts on over 56,000 node pairs. Central questions include characterizing inherent stochasticity in traffic patterns, understanding node–node interactions, adapting to dynamic changes in flows and allowing for sensitive monitoring to flag anomalies. The methodology of dynamic network DGLMs applies to many dynamic network flow studies.

Dynamic Shrinkage Processes

SummaryWe propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on a global–local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular global–local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modelling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólya–gamma scale mixture representation of the process proposed. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than do competing methods, and we apply the model for irregular curve fitting of minute-by-minute Twitter central processor unit usage data. In addition, we develop an adaptive time varying parameter regression model to assess the efficacy of the Fama–French five-factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that, with the exception of the market risk, no other risk factors are significant except for brief periods.

Change of access to emergency care in a repopulated village after the 2011 Fukushima nuclear disaster: a retrospective observational study

ObjectivesSustaining emergency care access is of great concern. The aim of this study is to evaluate access to emergency care in a repopulated village following the 2011 Fukushima disaster.DesignThis research...

The perspectives of politicians on tobacco control in Turkey.

BackgroundTobacco use is a leading but preventable cause of non-communicable diseases and premature death. The legislature has a key role in setting tobacco control policies. Smoking trends are decreasing thanks to the introduction of effective tobacco control policies in Turkey and these policies may have been shaped by how politicians’ interpreted social problems that were prominent during the development and implementation of tobacco regulations.AimThis paper explores the long-term national relationship between tobacco consumption, tobacco control policies and the associated political discourse in Turkey, considering the varying influences through national leadership on this important public health agenda. This relationship is studied by comparing a time series analysis of tobacco consumption trends with a policy analysis of the minutes of deliberations at the Grand National Assembly of Turkey (GNAT).MethodsThis study uses Bayesian time series analysis in order investigate whether the tobacco control policies and related activities influenced the annual per adult cigarette consumption in Turkey. We used a novel method to identify change points in tobacco trends and whether they correspond with key policy changes intended to alter usage after adjusting for the effect of other non-policy related covariates, such as the purchasing power. The policy analysis included an examination of the minutes of deliberations at the GNAT—which is the Turkish parliament and unicameral Turkish legislature—1 year before and 1 year after the break years associated with an increase or decrease in tobacco consumption.Results and recommendationsTobacco consumption increased with the encouragement of tobacco production and the entrance of multinational companies in the country in 1976 and 1993, respectively. The National Tobacco Law of 1996 and comprehensive amendments in 2008, including smoke-free public places and tax increases, appear to have helped reduce tobacco consumption in Turkey. The focus of Parliamentary discussions throughout this period changed, becoming less supportive of tobacco over time. However, throughout the period there remained discussions focussing on concerns around the implications for the economy and the privatization agenda, national agriculture and the welfare of farmers. Effective control appears to require certain political ingredients to be implemented: politicians who are well informed on tobacco control measures and understand the range of issues surrounding the policies (not only those directly health-related); and supportive public health information in the community. Evidence-based public health policy should be introduced to the politicians.

Online condition assessment of high-speed trains based on Bayesian forecasting approach and time series analysis

High-speed rail (HSR) has been in operation and development in many countries worldwide. The explosive growth of HSR has posed great challenges for operation safety and ride comfort. Among various technological demands on high-speed trains, vibration is an inevitable problem caused by rail/wheel imperfections, vehicle dynamics, and aerodynamic instability. Ride comfort is a key factor in evaluating the operational performance of high-speed trains. In this study, online monitoring data have been acquired from an in-service high-speed train for condition assessment. The measured dynamic response signals at the floor level of a train cabin are processed by the Sperling operator, in which the ride comfort index sequence is used to identify the train\'s operation condition. In addition, a novel technique that incorporates salient features of Bayesian inference and time series analysis is proposed for outlier detection and change detection. The Bayesian forecasting approach enables the prediction of conditional probabilities. By integrating the Bayesian forecasting approach with time series analysis, one-step forecasting probability density functions (PDFs) can be obtained before proceeding to the next observation. The change detection is conducted by comparing the current model and the alternative model (whose mean value is shifted by a prescribed offset) to determine which one can well fit the actual observation. When the comparison results indicate that the alternative model performs better, then a potential change is detected. If the current observation is a potential outlier or change, Bayes factor and cumulative Bayes factor are derived for further identification. A significant change, if identified, implies that there is a great alteration in the train operation performance due to defects. In this study, two illustrative cases are provided to demonstrate the performance of the proposed method for condition assessment of high-speed trains.

Decentralization Effects in Ecological Fiscal Transfers: A Bayesian Structural Time Series Analysis for Portugal

Portugal has a unitary system in which the central government transfers funds to lower government levels for their public functions. In 2007, Portugal introduced Ecological Fiscal Transfers (EFT), where municipalities receive transfers for hosting protected areas (PA). We study whether introducing EFT in Portugal incentivized municipalities to designate PA and has led to a decentralization of conservation decisions. We employ a Bayesian structural time series approach to estimate the effect of introducing EFT in comparison to a simulated counterfactual time series. Quantitative results show a significant increase in the ratio of municipal and national PA designations following Portugal’s EFT introduction—which we infer to be a causal consequence. The analysis furthermore places emphasis on the importance of relevant municipal conservation competencies for the functioning of the instrument. Results have important implications for conservation policy-making in terms of allocating budgets and competencies in multi-level governments.

Superharmonic priors for autoregressive models

Tanaka and Komaki (Sankhya Ser A Indian Stat Inst 73-A:162–184, 2011) proposed superharmonic priors in Bayesian time series analysis as alternative to the famous Jeffreys prior. By definition the existence of superharmonic priors on a specific time series model with finite-dimensional parameter is equivalent to that of positive nonconstant superharmonic functions on the corresponding Riemannian manifold endowed with the Fisher metric. In the autoregressive models, whose Fisher metric and its inverse have quite messy forms, we obtain superharmonic priors in an explicit manner. To derive this result, we developed a systematic way of dealing with symmetric polynomials, which are related to Schur functions.

Dynamic approach to linear statistical calibration with an application in microwave radiometry

ABSTRACTThe problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the ‘classical’ approach and the ‘inverse’ regression approach. Both of these models are static models and are used to estimate exact measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe it. The Bayesian time series analysis method of Dynamic Linear Models can be used to monitor the evolution of the measures, thus introducing a dynamic approach to statistical calibration. The research presented employs a new approach to performing statistical calibration. A simulation study in the context of microwave radiometry is conducted that compares the dynamic model to traditional static frequentist and Bayesian approaches. The focus of the study is to understand how well the dynamic statistical calibration method performs under various signal-to-noise ratios, r.

Bayesian Time Series Analysis of Structural Changes in Level and Trend

In this article we consider the problem of detecting changes in level and trend in time series model in which the number of change-points is unknown. The approach of Bayesian stochastic search model selection is introduced to detect the configuration of changes in a time series. The number and positions of change-points are determined by a sequence of change-dependent parameters. The sequence is estimated by its posterior distribution via the maximum a posteriori (MAP) estimation. Markov chain Monte Carlo (MCMC) method is used to estimate posterior distributions of parameters. Some actual data examples including a time series of traffic accidents and two hydrological time series are analyzed.

Monitoring of Proportional‐Integral Controlled Processes using a Bayesian Time Series Analysis Method

Recently, there has been interest in applying statistical process monitoring methods to processes controlled with feedback controllers in order to eliminate assignable causes and achieve reduced overall variability. In this paper, we propose a Bayesian change‐point method to monitor processes regulated with proportional‐integral controllers. The approach is based on fitting an exponential rise model to the control input actions in response to a step shift and employs a change‐point method to detect the change. Simulation studies show that the proposed method has better run‐length performance in detecting step shifts in controlled processes than Shewhart chart on individuals and special‐cause chart on residuals of time series model. Copyright © 2013 John Wiley & Sons, Ltd.

Erratum: Bayesian time series analysis of terrestrial impact cratering

Erratum: Bayesian time series analysis of terrestrial impact cratering

Bayesian Time-Series Analysis of a Repeated-Measures Poisson Outcome With Excess Zeroes

In this article, the authors demonstrate a time-series analysis based on a hierarchical Bayesian model of a Poisson outcome with an excessive number of zeroes. The motivating example for this analysis comes from the intensive care unit (ICU) of an urban university teaching hospital (New Haven, Connecticut, 2002-2004). Studies of medication use among older patients in the ICU are complicated by statistical factors such as an excessive number of zero doses, periodicity, and within-person autocorrelation. Whereas time-series techniques adjust for autocorrelation and periodicity in outcome measurements, Bayesian analysis provides greater precision for small samples and the flexibility to conduct posterior predictive simulations. By applying elements of time-series analysis within both frequentist and Bayesian frameworks, the authors evaluate differences in shift-based dosing of medication in a medical ICU. From a small sample and with adjustment for excess zeroes, linear trend, autocorrelation, and clinical covariates, both frequentist and Bayesian models provide evidence of a significant association between a specific nursing shift and dosing level of a sedative medication. Furthermore, the posterior distributions from a Bayesian random-effects Poisson model permit posterior predictive simulations of related results that are potentially difficult to model.

P2-418 Weather variability and the incidence of influenza: Bayesian time series analysis

IntroductionInfluenza is one of the most common infectious diseases in the world. Few studies have examined the quantitative relationship between weather conditions and influenza. This paper examined the potential impact...

Bayesian time series analysis of terrestrial impact cratering

Giant impacts by comets and asteroids have probably had an important influence on terrestrial biological evolution. We know of around 180 high velocity impact craters on the Earth with ages up to 2400Myr and diameters up to 300km. Some studies have identified a periodicity in their age distribution, with periods ranging from 13 to 50Myr. It has further been claimed that such periods may be causally linked to a periodic motion of the solar system through the Galactic plane. However, many of these studies suffer from methodological problems, for example misinterpretation of p-values, overestimation of significance in the periodogram or a failure to consider plausible alternative models. Here I develop a Bayesian method for this problem in which impacts are treated as a stochastic phenomenon. Models for the time variation of the impact probability are defined and the evidence for them in the geological record is compared using Bayes factors. This probabilistic approach obviates the need for ad hoc statistics, and also makes explicit use of the age uncertainties. I find strong evidence for a monotonic decrease in the recorded impact rate going back in time over the past 250Myr for craters larger than 5km. The same is found for the past 150Myr when craters with upper age limits are included. This is consistent with a crater preservation/discovery bias modulating an otherwise constant impact rate. The set of craters larger than 35km (so less affected by erosion and infilling) and younger than 400Myr are best explained by a constant impact probability model. A periodic variation in the cratering rate is strongly disfavoured in all data sets. There is also no evidence for a periodicity superimposed on a constant rate or trend, although this more complex signal would be harder to distinguish.

Sequentially interacting Markov chain Monte Carlo methods

Sequential Monte Carlo (SMC) is a methodology for sampling approximately from a sequence of probability distributions of increasing dimension and estimating their normalizing constants. We propose here an alternative methodology named Sequentially Interacting Markov Chain Monte Carlo (SIMCMC). SIMCMC methods work by generating interacting non-Markovian sequences which behave asymptotically like independent Metropolis-Hastings (MH) Markov chains with the desired limiting distributions. Contrary to SMC, SIMCMC allows us to iteratively improve our estimates in an MCMC-like fashion. We establish convergence results under realistic verifiable assumptions and demonstrate its performance on several examples arising in Bayesian time series analysis.

Patterns in prey use among fur seals and seabirds in the Pribilof Islands

Abstract We explored correlation in diet trends for five piscivorous predators that reproduce on the Pribilof Islands as illustrative of the shifting structure of the Bering Sea ecosystem. We evaluated the size and species of prey consumed by adult female and juvenile northern fur seals ( Callorhinus ursinus ) and adults and chicks of black-legged kittiwakes ( Rissa tridactyla ), red-legged kittiwakes ( Rissa brevirostris ), thick-billed murres ( Uria lomvia ), and common murres ( Uria aalge ) from data collected between July and October 1960–2000. Sample sources included stomachs from seals and seabirds collected on pelagic foraging grounds in the eastern Bering Sea, seal scats from rookeries and seabird regurgitations and whole prey from nest sites on St. Paul and St. George Islands of the Pribilof Island archipelago. Typical prey included small fish and invertebrates (⩽20 cm for seals and ⩽12 cm for seabirds) that concentrate along frontal boundaries of the continental shelf/slope and in the epi-pelagic zone. Squids and fishes including walleye pollock ( Theragra chalcogramma ), capelin ( Mallotus villosus ), and sand lance ( Ammodytes hexapterus ) were variably important in the diet of all five predators. Some prey, such as capelin, were principal in predator diets during the 1960s (seals) and into the early 1980s (seabirds), but declined or disappeared from all predator diets thereafter while others, such as walleye pollock, occurred with increasing frequency from the 1970s forward. As the number of individuals consuming walleye pollock increased, the overall volume of pollock in seabird diets declined. This decline was coincident with a decrease in the age and body size of pollock consumed by both seabirds and fur seals. Squid and pollock were negatively correlated in the diets of their primary consumers, northern fur seals (Pearson's coefficient −0.71, p =0.016) and thick-billed murres (Pearson's coefficient=−0.74, p =0.015) from the 1970s forward. Inter-island variation in diet was evident to varying degrees for all predators, with a prevalence of fish on St. Paul Island and invertebrates on St. George Island. Bayesian time-series analysis of synthesized data described significant temporal cross-correlation in diet among northern fur seals, red- and black-legged kittiwakes, and thick-billed murres. For all correlated predators except common murres, beta-binomial modeling indicated that trends in the occurrence of four of the five primary prey (sand lance, capelin, squid, and pollock) evaluated, were significantly associated with eastern Bering Sea time-series trends in sea surface temperature, ice retreat or a combination of both. Data synthesis highlighted potential competition and a scenario for the effects of an altered prey field on the population stability of predators. The association between correlated diet changes among predators and indices of oceanographic shifts in the 1970s and the 1990s allow scrutiny of hypotheses concerning causal mechanisms in population declines.