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Medication adherence is a problem of widespread concern in clinical care. Poor adherence is a particular problem for patients with chronic diseases requiring long‐term medication because poor adherence can result in less successful treatment outcomes and even preventable deaths. Existing methods to collect information about patient adherence are resource‐intensive or do not successfully detect low‐adherers with high accuracy. Acknowledging that health measures recorded at clinic visits are more reliably recorded than a patient's adherence, we have developed an approach to infer medication adherence rates based on longitudinally recorded health measures that are likely impacted by time‐varying adherence behaviors. Our framework permits the inclusion of baseline health characteristics and socio‐demographic data. We employ a modular inferential approach. First, we fit a two‐component model on a training set of patients who have detailed adherence data obtained from electronic medication monitoring. One model component predicts adherence behaviors only from baseline health and socio‐demographic information, and the other predicts longitudinal health measures given the adherence and baseline health measures. Posterior draws of relevant model parameters are simulated from this model using Markov chain Monte Carlo methods. Second, we develop an approach to infer medication adherence from the time‐varying health measures using a sequential Monte Carlo algorithm applied to a new set of patients for whom no adherence data are available. We apply and evaluate the method on a cohort of hypertensive patients, using baseline health comorbidities, socio‐demographic measures, and blood pressure measured over time to infer patients' adherence to antihypertensive medication. [ABSTRACT FROM AUTHOR]

Summary: Visual inspections provide direct information about the deterioration states of each structural element within a bridge. However, when managing a network of bridges, it becomes necessary to aggregate the deterioration information from the element‐level to the bridge‐level or even the network‐level. Deterioration models that are based on state‐space models (SSM) have the capacity to model the deterioration based on visual inspections and structural attributes. Nonetheless, the application of such models has been demonstrated at the element‐level only. In this study, the SSM deterioration framework is extended to provide overall estimates for the deterioration states of bridges and of an entire network. The proposed approach also includes a framework for handling missing data and interventions. The framework's capacity is demonstrated using data from individual cases of bridges, with and without interventions, in addition to a network of B ≈ 7000 bridges in the Canadian province of Quebec. The deterioration estimates for bridges can aid in examining the effectiveness of previous interventions, the long‐term trend of the network's condition, as well as laying the groundwork for planning future maintenance actions. [ABSTRACT FROM AUTHOR]

Residual stress is closely related to the evolution process of the component fatigue state, but it can be affected by various sources. Conventional fatigue evaluation either focuses on the physical process, which is limited by the complexity of the physical process and the environment, or on monitored data to form a data-driven model, which lacks a relation to the degenerate process and is more sensitive to the quality of the data. This paper proposes a fusion-driven fatigue evaluation model based on the Gaussian process state–space model, which considers the importance of physical processes and the residuals. Through state–space theory, the probabilistic space evaluation results of the Gaussian process and linear physical model are used as the hidden state evaluation results and hidden state change observation function, respectively, to construct a complete Gaussian process state–space framework. Then, through the solution of a particle filter, the importance of the residual is inferred and the fatigue evaluation model is established. Fatigue tests on titanium alloy components were conducted to verify the effectiveness of the fatigue evaluation model. The results indicated that the proposed models could correct evaluation results that were far away from the input data and improve the stability of the prediction. [ABSTRACT FROM AUTHOR]

We introduce a novel method for online smoothing in state-space models that utilises a fixed-lag approximation to overcome the well known issue of path degeneracy. Unlike classical fixed-lag techniques that only approximate certain marginals, we introduce an online resampling algorithm, called particle stitching, that converts these marginal samples into a full posterior approximation. We demonstrate the utility of our method in the context of map-matching, the task of inferring a vehicle’s trajectory given a road network and noisy GPS observations. We develop a new state-space model for the difficult task of map-matching on dense, urban road networks. [ABSTRACT FROM AUTHOR]

Stochastic volatility processes are used in multi‐variate time series analysis to track time‐varying patterns in covariance matrices. Uhlig extended (UE) and beta‐Bartlett (BB) processes are especially convenient for analyzing high‐dimensional time series because they are conjugate with Wishart likelihoods. In this article, we show that UE and BB are closely related, but not equivalent: their hyperparameters can be matched so that they have the same forward‐filtered posteriors and one‐step ahead forecasts, but different joint (smoothed) posterior distributions. Under this circumstance, Bayes factors cannot discriminate the models and alternative approaches to model comparison are needed. We illustrate these issues in a retrospective analysis of volatilities of returns of foreign exchange rates. Additionally, we provide a backward sampling algorithm for the BB process, for which retrospective analysis had not been developed. [ABSTRACT FROM AUTHOR]

Increases in natural mortality have been suggested as a potential driver for both the collapse and lack of recovery for the American plaice (Hippoglossoides platessoides) population on the Grand Bank of Newfoundland in NAFO Divisions 3LNO. However, natural mortality is among the most difficult parameters to estimate since it can be confounded with other parameters and model misspecifications. One method used to avoid this confounding involves modeling unfished components of a population where total mortality and natural mortality are equal. Here, we use a state-space metapopulation dynamics model to investigate whether there is evidence that natural mortality rates for unfished juvenile American plaice have varied since the population collapse. In addition, our model examined the degree of synchrony in age-1 recruitment signals between each management Division. The best fitting model included temporal variability in natural mortality rates, but estimates did not frequently differ from zero. This indicates that change in natural mortality rates is not an important driver of current juvenile 3LNO American plaice stock dynamics. Instead, this model identified that juvenile stock dynamics were mainly affected by variations in age-1 recruitment. Furthermore, a correlation analysis of the temporal variations in recruitment showed that trends were somewhat dissimilar between NAFO Divisions 3L and 3NO. Overall, although increases in M have been suggested by recent studies, we did not find strong evidence for this in juvenile fish. [ABSTRACT FROM AUTHOR]

This letter is concerned with solvingcontinuous-discrete Gaussian smoothing problems by using the Taylor moment expansion (TME) scheme. In the proposed smoothing method, we apply the TME method to approximate the transition density of the stochastic differential equation in the dynamic model. Furthermore, we derive a theoretical error bound (in the mean square sense) of the TME smoothing estimates showing that the smoother is stable under weak assumptions. Numerical experiments show that the proposed smoother outperforms a number of baseline smoothers. [ABSTRACT FROM AUTHOR]

We propose a generalized non‐linear state‐space model for count‐valued time series of COVID‐19 fatalities. To capture the dynamic changes in daily COVID‐19 death counts, we specify a latent state process that involves second‐order differencing and an AR(1)‐ARCH(1) model. These modelling choices are motivated by the application and validated by model assessment. We consider and fit a progression of Bayesian hierarchical models under this general framework. Using COVID‐19 daily death counts from New York City's five boroughs, we evaluate and compare the considered models through predictive model assessment. Our findings justify the elements included in the proposed model. The proposed model is further applied to time series of COVID‐19 deaths from the four most populous counties in Texas. These model fits illuminate dynamics associated with multiple dynamic phases and show the applicability of the framework to localities beyond New York City. [ABSTRACT FROM AUTHOR]

Random walks, intrinsic autoregression, state‐space models, smoothing splines, and so on have been widely used in various areas of statistics. However, practitioners wanting to fit these models using existing packages for random‐effects models are often faced with the difficulty that their covariance matrices are not uniquely determined. Unfortunately, different specifications of the model lead to different covariance structures, giving different analyses. Even if we make a decision on specification it is not immediately obvious how to make inferences from these models. There have been various suggestions on how to overcome such difficulties. However, they differ, implying that there is as yet no agreed remedy. In this article we provide a unified view on these alternatives and show how the analysis can be made invariant with respect to the choice of covariance by inclusion of a suitable set of covariates. Several examples are used to illustrate the approach. [ABSTRACT FROM AUTHOR]

Spatio-temporal datasets are rapidly growing in size. For example, environmental variables are measured with increasing resolution by increasing numbers of automated sensors mounted on satellites and aircraft. Using such data, which are typically noisy and incomplete, the goal is to obtain complete maps of the spatio-temporal process, together with uncertainty quantification. We focus here on real-time filtering inference in linear Gaussian state-space models. At each time point, the state is a spatial field evaluated on a very large spatial grid, making exact inference using the Kalman filter computationally infeasible. Instead, we propose a multi-resolution filter (MRF), a highly scalable and fully probabilistic filtering method that resolves spatial features at all scales. We prove that the MRF matrices exhibit a particular block-sparse multi-resolution structure that is preserved under filtering operations through time. We describe connections to existing methods, including hierarchical matrices from numerical mathematics. We also discuss inference on time-varying parameters using an approximate Rao-Blackwellized particle filter, in which the integrated likelihood is computed using the MRF. Using a simulation study and a real satellite-data application, we show that the MRF strongly outperforms competing approaches. include Python code for reproducing the simulations, some detailed properties of the MRF and auxiliary theoretical results. [ABSTRACT FROM AUTHOR]

Indices of relative abundance are routinely used to monitor and manage wildlife, yet all indices contain observation error and have unknown relationships with true abundance. State-space models (SSM) allow estimation of observation error while concordance in trends among multiple indices from different sampling methods may reflect true trends in abundance. We used multiple decades of data from roadkill surveys, nocturnal spotlight surveys, and observations from hunters along with trapper harvest data for six mesopredators in Illinois, USA, to evaluate concordance (i.e., similarity in trend direction and magnitude) across count- and harvest-based indices, while controlling for observation error using Bayesian SSM. We assumed that increased concordance among trends from different sampling methods would increasingly mirror trends in true abundance. We observed positive trends for raccoon and coyote, negative trends for gray and red fox, and stable trends for skunk, consistent with spatiotemporal patterns of distribution and abundance of these species within midwestern USA. Concordance among count-based indices and harvest-based indices adjusted for temporal changes in trapper numbers was generally high. In contrast, total annual trapper harvest often showed discordance with other trends. Sampling variability was similar across methods but was highest across the shortest time series highlighting the importance of methodologically or analytically controlling for sampling variability. Our results suggest that concordant broad-scale (e.g., statewide) trends in index data may be best used for evaluating relatively general trends and using relatively drastic changes as justification for more in-depth studies. [ABSTRACT FROM AUTHOR]

A growing interest in non-Gaussian time series, particularly in series comprised of nonnegative integers (counts), is taking place in today's statistics literature. Count series naturally arise in fields, such as agriculture, economics, epidemiology, finance, geology, meteorology, and sports. Unlike stationary Gaussian series where autoregressive moving-averages are the primary modeling vehicle, no single class of models dominates the count landscape. As such, the literature has evolved somewhat ad-hocly, with different model classes being developed to tackle specific situations. This article is an attempt to summarize the current state of count time series modeling. The article first reviews models having prescribed marginal distributions, including some recent developments. This is followed by a discussion of state-space approaches. Multivariate extensions of the methods are then studied and Bayesian approaches to the problem are considered. The intent is to inform researchers and practitioners about the various types of count time series models arising in the modern literature. While estimation issues are not pursued in detail, reference to this literature is made. [ABSTRACT FROM AUTHOR]

Head movement is an important but often overlooked component of emotion and social interaction. Examination of regularity and differences in head movements of infant-mother dyads over time and across dyads can shed light on whether and how mothers and infants alter their dynamics over the course of an interaction to adapt to each others. One way to study these emergent differences in dynamics is to allow parameters that govern the patterns of interactions to change over time, and according to person- and dyad-specific characteristics. Using two estimation approaches to implement variations of a vector-autoregressive model with time-varying coefficients, we investigated the dynamics of automatically-tracked head movements in mothers and infants during the Face-Face/Still-Face Procedure (SFP) with 24 infant-mother dyads. The first approach requires specification of a confirmatory model for the time-varying parameters as part of a state-space model, whereas the second approach handles the time-varying parameters in a semi-parametric ("mostly" model-free) fashion within a generalized additive modeling framework. Results suggested that infant-mother head movement dynamics varied in time both within and across episodes of the SFP, and varied based on infants' subsequently-assessed attachment security. Code for implementing the time-varying vector-autoregressive model using two R packages, dynr and mgcv, is provided. [ABSTRACT FROM AUTHOR]

Summary: The 'Endangered' Cape Vulture Gyps coprotheres has been monitored across its range for decades through disparate studies varying in geographical scope and length. Yet, no long-term, range-wide survey exists for the species. Coordinated monitoring across the range of the Cape Vulture would be logistically challenging but provide a holistic view of population dynamics in this long-lived species that forages across much of southern Africa. Here, we report breeding pair counts from seven colonies in the Cape Vulture's north-eastern breeding region from 2010 to 2019. We used state-space models to assess population growth across time. Manutsa, Soutpansberg, and Nooitgedacht colonies increased significantly over the study period, with three other colonies having positive estimates of population growth, but 95% credible intervals overlapped zero. The smallest colony at Moletjie is declining toward extirpation; only one breeding pair remained in 2019. Our results suggest the north-eastern population has been stable or increasing since 2010 with our 2019 surveys counting 2,241 breeding pairs across all sites. Indeed, there is an 89% chance that the population across the colonies we monitored increased from 2010 to 2019. Coordinated, range-wide, full-cycle monitoring is needed to thoroughly assess conservation status and efficacy of conservation actions taken for this endangered species. [ABSTRACT FROM AUTHOR]

This paper develops a Rao-Blackwellized particle filter with variational inference for jointly estimating state and time-varying parameters in non-linear state-space models (SSM) with non-Gaussian measurement noise. Depending on the availability of the conjugate prior for the unknown parameters, the joint posterior distribution of the state and unknown parameters is approximated by using an auxiliary particle filter with a probabilistic changepoint model. The distribution of the SSM parameters conditionally on each particle is then updated by using variational Bayesian inference. Experiments are first conducted on a modified nonlinear benchmark model to compare the performance of the proposed approach with other state-of-the-art approaches. Finally, in the context of GNSS multipath mitigation, the proposed approach is evaluated based on data obtained from a measurement campaign conducted in a street urban canyon.

Abstract Background Species distribution models have shown that blue whales (Balaenoptera musculus) occur seasonally in high densities in the most biologically productive regions of the California Current Ecosystem (CCE). Satellite telemetry studies have additionally shown that blue whales in the CCE regularly switch between behavioral states consistent with area-restricted searching (ARS) and transiting, indicative of foraging in and moving among prey patches, respectively. However, the relationship between the environmental correlates that serve as a proxy of prey relative to blue whale movement behavior has not been quantitatively assessed. Methods We investigated the association between blue whale behavioral state and environmental predictors in the coastal environments of the CCE using a long-term satellite tracking data set (72 tagged whales; summer-fall months 1998–2008), and predicted the likelihood of ARS behavior at tracked locations using nonparametric multiplicative regression models. The models were built using data from years of cool, productive conditions and validated against years of warm, low-productivity conditions. Results The best model contained four predictors: chlorophyll-a, sea surface temperature, and seafloor aspect and depth. This model estimated highest ARS likelihood (> 0.8) in areas with high chlorophyll-a levels (> 0.65 mg/m3), intermediate sea surface temperatures (11.6-17.5 °C), and shallow depths (

This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm (and the particle filter within) together with the reader. This final implementation is also available as the package pmhtutorial from the Comprehensive R Archive Network (CRAN) repository. Throughout the tutorial, we provide some intuition as to how the algorithm operates and discuss some solutions to problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian state-space model with synthetic data and a nonlinear stochastic volatility model with real-world data.

Every month, teachers face the dilemma of what exercises their students should practice, and what their consequences are regarding long-term learning. Since teachers prefer to pose their own exercises, this generates a large number of questions, each one attempted by a small number of students. Thus, we could not use models based on big data, such as deep learning. Instead, we developed a simple-to-understand state-space model that predicts end-of-year national test scores. We used 2386 online fourth-grade mathematics questions designed by teachers, each attempted by some of the 500 students in 24 low socioeconomic schools. We found that the state-space model predictions improved month by month and that in most months, it outperformed linear regression models. Moreover, the state-space estimator provides for each month a direct mechanism to simulate different practice strategies and compute their impact on the end-of-year standardized national test. We built iso-impact curves based on two critical variables: the number of questions solved correctly in the first attempt and the total number of exercises attempted. This allows the teacher to visualize the trade-off between asking students to perform exercises more carefully or perform more exercises. To the best of our knowledge, this model is the first of its kind in education. It is a novel tool that supports teachers drive whole classes to achieve long-term learning targets.

Pedestrian movements during large crowded events naturally consist of different modes of movement behaviour. Despite its importance for understanding crowd dynamics, intermittent movement behaviour is an aspect missing in the existing crowd behaviour literature. Here we analyse movement data generated from nearly 600 Wi-Fi sensors during large entertainment events in the Johan Cruijff ArenA football stadium in Amsterdam. We use the state-space modeling framework to investigate intermittent motion patterns. Movement models from the field of movement ecology are used to analyse individual pedestrian movement. Joint estimation of multiple movement tracks allows us to investigate statistical properties of measured movement metrics. We show that behavioural switching is not independent of external events, and the probability of being in one of the behavioural states changes over time. In addition, we show that the distribution of waiting times deviates from the exponential and is best fit by a heavy-tailed distribution. The heavy-tailed waiting times are indicative of bursty movement dynamics, which are here for the first time shown to characterise pedestrian movements in dense crowds. Bursty crowd behaviour has important implications for various diffusion-related processes, such as the spreading of infectious diseases. [ABSTRACT FROM AUTHOR]

The linear time invariant state–space model representation is common to systems from several areas ranging from engineering to biochemistry. We address the problem of systematic optimal experimental design for this class of model. We consider two distinct scenarios: (i) steady-state model representations and (ii) dynamic models described by discrete-time representations. We use our approach to construct locally D-optimal designs by incorporating the calculation of the determinant of the Fisher Information Matrix and the parametric sensitivity computation in a Nonlinear Programming formulation. A global optimization solver handles the resulting numerical problem. The Fisher Information Matrix at convergence is used to determine model identifiability. We apply the methodology proposed to find approximate and exact optimal experimental designs for static and dynamic experiments for models representing a biochemical reaction network where the experimental purpose is to estimate kinetic constants. [ABSTRACT FROM AUTHOR]

Summary: The early detection of anomalies associated with changes in the behavior of structures is important for ensuring their serviceability and safety. Identifying anomalies from monitoring data is prone to false and missed alarms due to the uncertain nature of the infrastructure responses' dependency on external factors such as temperature and loading. Existing anomaly detection strategies typically rely on univariate threshold values and disregard the planning horizon in the context of decision making. This paper proposes an anomaly detection framework that combines the interpretability of existing Bayesian dynamic linear models, a particular form of state‐space models, with the long‐term planning ability of reinforcement learning. The new framework provides (a) reinforcement learning formalism for anomaly detection in Bayesian dynamic linear models, (b) a method for simulating anomalies with respect to its height, duration, and time of occurrence, and (c) a method for quantifying anomaly detectability. The potential of the new framework is demonstrated on monitoring data collected on a bridge in Canada. The results show that the framework is able to detect real anomalies that were known to have occurred, as well as synthetic anomalies. [ABSTRACT FROM AUTHOR]

One of the most challenging problems in the study of complex dynamical systems is to find the statistical interdependencies among the system components. Granger causality (GC) represents one of the most employed approaches, based on modeling the system dynamics with a linear vector autoregressive (VAR) model and on evaluating the information flow between two processes in terms of prediction error variances. In its most advanced setting, GC analysis is performed through a state-space (SS) representation of the VAR model that allows to compute both conditional and unconditional forms of GC by solving only one regression problem. While this problem is typically solved through Ordinary Least Square (OLS) estimation, a viable alternative is to use Artificial Neural Networks (ANNs) implemented in a simple structure with one input and one output layer and trained in a way such that the weights matrix corresponds to the matrix of VAR parameters. In this work, we introduce an ANN combined with SS models for the computation of GC. The ANN is trained through the Stochastic Gradient Descent L1 (SGD-L1) algorithm, and a cumulative penalty inspired from penalized regression is applied to the network weights to encourage sparsity. Simulating networks of coupled Gaussian systems, we show how the combination of ANNs and SGD-L1 allows to mitigate the strong reduction in accuracy of OLS identification in settings of low ratio between number of time series points and of VAR parameters. We also report how the performances in GC estimation are influenced by the number of iterations of gradient descent and by the learning rate used for training the ANN. We recommend using some specific combinations for these parameters to optimize the performance of GC estimation. Then, the performances of ANN and OLS are compared in terms of GC magnitude and statistical significance to highlight the potential of the new approach to reconstruct causal coupling strength and network topology even in challenging conditions of data paucity. The results highlight the importance of of a proper selection of regularization parameter which determines the degree of sparsity in the estimated network. Furthermore, we apply the two approaches to real data scenarios, to study the physiological network of brain and peripheral interactions in humans under different conditions of rest and mental stress, and the effects of the newly emerged concept of remote synchronization on the information exchanged in a ring of electronic oscillators. The results highlight how ANNs provide a mesoscopic description of the information exchanged in networks of multiple interacting physiological systems, preserving the most active causal interactions between cardiovascular, respiratory and brain systems. Moreover, ANNs can reconstruct the flow of directed information in a ring of oscillators whose statistical properties can be related to those of physiological networks.

Species that migrate long distances or between distinct habitats— for example, anadromous or catadromous fish—experience the consequences of climate change in each habitat and are therefore particularly at risk in a changing world. Studies of anadromous species often focus on freshwater despite the ocean's disproportionate influence on survival and growth. To understand a prominent anadromous species' response to ocean climate, we use a new spatio‐temporal model jointly estimating the ocean distribution of all major fall‐run Chinook salmon (Oncorhynchus tshawytscha, Salmonidae) stocks from California to British Columbia over 40 years. We model hundreds of millions of tagged individuals, finding that different stocks have fundamentally different ocean distributions, distinct associations with sea surface temperature (SST), and contrasting distributional responses to historical ocean SST variation. We show species‐level estimates of ocean distribution that ignore among‐stock variation will lead to errant predictions of spatial distribution. Using future (2030–2090) SST projections to model focal stocks of fisheries importance we predict substantial ocean redistribution in response to SST change. Predicted aggregate distributional changes do not follow a simple, poleward shift. Instead, we predict net movement into some ocean regions (British Columbia, central California) but net movement out of others (northern California, Washington). Distribution shifts have implications for both major fisheries and marine mammal predators of Chinook salmon. We focus on the consequences of spatial changes in ocean distribution, but our approach provides a general structure to link marine and freshwater components of anadromous species under climate change. [ABSTRACT FROM AUTHOR]

When prediction intervals are constructed using unobserved component models (UCM), problems can arise due to the possible existence of components that may or may not be conditionally heteroscedastic. Accurate coverage depends on correctly identifying the source of the heteroscedasticity. Different proposals for testing heteroscedasticity have been applied to UCM; however, in most cases, these procedures are unable to identify the heteroscedastic component correctly. The main issue is that test statistics are affected by the presence of serial correlation, causing the distribution of the statistic under conditional homoscedasticity to remain unknown. We propose a nonparametric statistic for testing heteroscedasticity based on the well-known Wilcoxon's rank statistic. We study the asymptotic validation of the statistic and examine bootstrap procedures for approximating its finite sample distribution. Simulation results show an improvement in the size of the homoscedasticity tests and a power that is clearly comparable with the best alternative in the literature. We also apply the test on real inflation data. Looking for the presence of a conditionally heteroscedastic effect on the error terms, we arrive at conclusions that almost all cases are different than those given by the alternative test statistics presented in the literature. [ABSTRACT FROM AUTHOR]

Biodiversity indicators summarise extensive, complex ecological data sets and are important in influencing government policy. Component data consist of time-varying indices for each of a number of different species. However, current biodiversity indicators suffer from multiple statistical shortcomings. We describe a state-space formulation for new multispecies biodiversity indicators, based on rates of change in the abundance or occupancy probability of the contributing individual species. The formulation is flexible and applicable to different taxa. It possesses several advantages, including the ability to accommodate the sporadic unavailability of data, incorporate variation in the estimation precision of the individual species' indices when appropriate, and allow the direct incorporation of smoothing over time. Furthermore, model fitting is straightforward in Bayesian and classical implementations, the latter adopting either efficient Hidden Markov modelling or the Kalman filter. Conveniently, the same algorithms can be adopted for cases based on abundance or occupancy data—only the subsequent interpretation differs. The procedure removes the need for bootstrapping which can be prohibitive. We recommend which of two alternatives to use when taxa are fully or partially sampled. The performance of the new approach is demonstrated on simulated data, and through application to three diverse national UK data sets on butterflies, bats and dragonflies. We see that uncritical incorporation of index standard errors should be avoided. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

Summary: Successful forecasting models strike a balance between parsimony and flexibility. This is often achieved by employing suitable shrinkage priors that penalize model complexity but also reward model fit. In this article, we modify the stochastic volatility in mean (SVM) model by introducing state‐of‐the‐art shrinkage techniques that allow for time variation in the degree of shrinkage. Using a real‐time inflation forecast exercise, we show that employing more flexible prior distributions on several key parameters sometimes improves forecast performance for the United States, the United Kingdom, and the euro area (EA). Comparing in‐sample results reveals that our proposed model yields qualitatively similar insights to the original version of the model. [ABSTRACT FROM AUTHOR]

This study modelled and estimated climatic data using the state-space model. The study was specifically to identify the pattern of the trend movement i.e., increase or decrease in the occurrence of the climatic change; to use of Univariate Kalman Filter for the computation of the likelihood function for climatic projections; to modelling the climatic dataset using the state-space model and to assess the forecasting power of the state-space models. The data used for the work includes temperature and rainfall for periods January 1991 to December 2017. The data are tested for normality. Shapiro-Wilk, Anderson-Darling and Kolmogorov-Smirnov test of normality for the climatic data all showed that the variables are not normally distributed. The work spans the use of breaking trend regression model to fit climatic data to estimate the slopes which show much increase in climatic data has been recorded from the initial time data collection until the present. Investigations and diagnostic are carried out by checking for corrections in the residuals and also checking for periodicity in the residuals. The results of this investigation show significant autocorrelation in the residuals indicating the presence of underlying noise terms which is not accounted for. By treating the residual as an autoregressive moving average (ARMA) process whereby we can obtain its spectral density, the result from the parametric spectral estimate shows underlying periodic patterns for monthly data, thus, leads to a discussion on the need to treat climatic data as a structural time series model. We select appropriate models by considering the goodness of fit of the model by comparing the Akaike information criterion (AIC) values. Parameters are estimated and accomplished with some measures of precision.

The degree to which predation is an additive vs. compensatory source of mortality is fundamental to understanding the effects of predation on prey populations and evaluating the efficacy of predator management actions. In the Columbia River basin, USA, predation by Caspian Terns (Hydroprogne caspia) on U.S. Endangered Species Act (ESA)‐listed juvenile salmonids (smolts; Oncorhynchus spp.) has led to predator management actions to reduce predation; however, the assumption that reduced predation translates into greater salmonid survival, either within the life stage where predation occurs or across their lifetime, has remained untested. To address this critical uncertainty, we analyzed a long‐term (2008–2018) mark–recapture–recovery data set of ESA‐listed steelhead trout (O. mykiss) that were tagged (n = 78,409) and subsequently exposed to predation during smolt out‐migration through multiple river reaches (spatial scales), jointly estimating weekly probabilities of steelhead survival, mortality due to bird predation, and mortality due to other causes. This concurrent estimation across time‐stratified cohorts allowed for the direct measurement of the strength, magnitude, and direction of relationships between survival and Caspian Tern predation. Estimates of Tern predation on steelhead were substantial in most years, with cumulative annual estimates ranging from 0.075 (95% creditable interval = 0.058–0.099) to 0.375 (0.290–0.461). Increases in Tern predation probabilities were associated with statistically significant decreases in steelhead survival probabilities in all evaluated years and salmonid life stages (smolt out‐migration and smolt‐to‐adult returns). Results provide novel evidence that predation by Caspian Terns may have been a super‐additive source of mortality during the smolt life stage and a partially additive source of mortality to the adult life stage. Annual estimates of the difference between observed survival and baseline survival (i.e., in the absence of Tern predation) ranged from 0.052 (0.017–0.103) to 0.314 (0.172–0.459) during the steelhead smolt life stage and from 0.011 (0.001–0.029) to 0.049 (0.025–0.078) to the adult life stage. The estimated levels of compensation have important implications for predator management actions aimed at increasing the survival of endangered salmonids, and the modeling approach developed herein provides a framework to directly quantify the impacts of source‐specific mortality factors on prey populations. [ABSTRACT FROM AUTHOR]

There are no gold standard methods that perform well in every situation when it comes to the analysis of multiple time series of counts. In this paper, we consider a positively correlated bivariate time series of counts and propose a parameter-driven Poisson regression model for its analysis. In our proposed model, we employ a latent autoregressive process, AR(p) to accommodate the temporal correlations in the two series. We compute the familiar maximum likelihood estimators of the model parameters and their standard errors via a Bayesian data cloning approach. We apply the model to the analysis of a bivariate time series arising from asthma-related visits to emergency rooms across the Canadian province of Ontario. [ABSTRACT FROM AUTHOR]

Prices of agricultural products often vary in relatively stable patterns around their long‐run trends. These variations translate into fluctuations of selling prices as well as farm revenues. We provide an overview of the current literature on agricultural price cycles. Using a transparent and reproducible model selection process and the Kalman filter, we select optimal models and estimate the cyclic patterns of hog and cattle prices for Brazil, Chile and Uruguay. Durations of those cycles are found to be about three years and seven years, respectively. These durations are in line with the literature and the biological characteristics of livestock production. Our results can inform producers forecasts on price developments in the short and medium run. They are useful for guiding policy makers on the timing of policy interventions for influencing the duration or the amplitudes of cycles. [ABSTRACT FROM AUTHOR]

Summary: Visual inspections is a common approach for the network‐scale monitoring of bridges. One of the main challenges when interpreting visual inspections is the observations being subjective and thus the observation uncertainty varies among different inspectors. In addition, observations uncertainties can be dependent on the structural element condition. These two factors introduce difficulties in differentiating between measurement errors and legitimate changes in a structure's condition. This study proposes a state‐space model suited for the network‐scale analyses of transportation infrastructure. The formulation of the proposed framework enables quantifying the uncertainty associated with each inspector. In addition, the proposed model accounts for the uncertainty of visual inspections based on the structure condition as well as the uncertainty specific to each inspector. The predictive capacity and robustness of the proposed model are verified with synthetic inspection data, where the true deterioration state is known. Following the verification step, the proposed model is validated with real data taken from a visual inspections database. [ABSTRACT FROM AUTHOR]

In many scenarios, a state-space model depends on a parameter which needs to be inferred from data. Using stochastic gradient search and the optimal filter first-order derivatives, the parameter can be estimated online. To analyze the asymptotic behavior of such methods, it is necessary to establish results on the existence and stability of the optimal filter higher-order derivatives. These properties are studied here. Under regularity conditions, we show that the optimal filter higher-order derivatives exist and forget initial conditions exponentially fast. We also show that the same derivatives are geometrically ergodic. [ABSTRACT FROM AUTHOR]

Effective conservation and management of animal populations requires knowledge of abundance and trends. For many species, these quantities are estimated using systematic visual surveys. Additional individual‐level data are available for some species. Integrated population modeling (IPM) offers a mechanism for leveraging these data sets into a single estimation framework. IPMs that incorporate both population‐ and individual‐level data have previously been developed for birds, but have rarely been applied to cetaceans. Here, we explore how IPMs can be used to improve the assessment of cetacean populations. We combined three types of data that are typically available for cetaceans of conservation concern: population‐level visual survey data, individual‐level capture–recapture data, and data on anthropogenic mortality. We used this IPM to estimate the population dynamics of the Cook Inlet population of beluga whales (CIBW; Delphinapterus leucas) as a case study. Our state‐space IPM included a population process model and three observational submodels: (1) a group detection model to describe group size estimates from aerial survey data; (2) a capture–recapture model to describe individual photographic capture–recapture data; and (3) a Poisson regression model to describe historical hunting data. The IPM produces biologically plausible estimates of population trajectories consistent with all three data sets. The estimated population growth rate since 2000 is less than expected for a recovering population. The estimated juvenile/adult survival rate is also low compared to other cetacean populations, indicating that low survival may be impeding recovery. This work demonstrates the value of integrating various data sources to assess cetacean populations and serves as an example of how multiple, imperfect data sets can be combined to improve our understanding of a population of interest. The model framework is applicable to other cetacean populations and to other taxa for which similar data types are available. [ABSTRACT FROM AUTHOR]

We propose an evolutionary state-space model (E-SSM) for analyzing high-dimensional brain signals, the statistical properties of which evolve over the course of a nonspatial memory experiment. Under the E-SSM, brain signals are modeled as mixtures of components (e.g., an AR(2) process) with oscillatory activity at predefined frequency bands. To account for the potential nonstationarity of these components (because brain responses can vary throughout an experiment), the parameters are allowed to vary over epochs. Compared with classical approaches, such as independent component analyses and filtering, the proposed method accounts for the entire temporal correlation of the components and accommodates nonstationarity. For inference purposes, we propose a novel computational algorithm based on a Kalman smoother, maximum likelihood, and blocked resampling. The E-SSM model is applied in simulation studies and applied to multi-epoch local field potential (LFP) signal data, collected from a nonspatial (olfactory) sequence memory task study. The results confirm that our method captures the evolution of the power of the components across different phases in the experiment, and identifies clusters of electrodes that behave similarly with respect to the decomposition of different sources. These findings suggest that the activity of electrodes does change over the course of an experiment in practice. Thus, treating these epoch recordings as realizations of an identical process could lead to misleading results. In summary, the proposed method underscores the importance of capturing the evolution in brain responses over the study period. [ABSTRACT FROM AUTHOR]

We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the geophysics literature, with state-space algorithms from the statistics literature. Our algorithms address a variety of estimation scenarios, including online and off-line state and parameter estimation. We take a Bayesian perspective, for which the goal is to generate samples from the joint posterior distribution of states and parameters. The key benefit of our approach is the use of ensemble Kalman methods for dimension reduction, which allows inference for high-dimensional state vectors. We compare our methods to existing ones, including ensemble Kalman filters, particle filters, and particle MCMC. Using a real data example of cloud motion and data simulated under a number of nonlinear and non-Gaussian scenarios, we show that our approaches outperform these existing methods. for this article are available online. [ABSTRACT FROM AUTHOR]

Understanding how nutrients flow through food webs is central in ecosystem ecology. Tracer addition experiments are powerful tools to reconstruct nutrient flows by adding an isotopically enriched element into an ecosystem and tracking its fate through time. Historically, the design and analysis of tracer studies have varied widely, ranging from descriptive studies to modeling approaches of varying complexity. Increasingly, isotope tracer data are being used to compare ecosystems and analyze experimental manipulations. Currently, a formal statistical framework for analyzing such experiments is lacking, making it impossible to calculate the estimation errors associated with the model fit, the interdependence of compartments, and the uncertainty in the diet of consumers. In this article we develop a method based on Bayesian hidden Markov models and apply it to the analysis of N 15 ‐NH 4 + tracer additions in two Trinidadian streams in which light was experimentally manipulated. Through this case study, we illustrate how to estimate N fluxes between ecosystem compartments, turnover rates of N within those compartments, and the associated uncertainty. We also show how the method can be used to compare alternative models of food web structure, calculate the error around derived parameters, and make statistical comparisons between sites or treatments. [ABSTRACT FROM AUTHOR]

Reliable projections of crop production are an essential tool for the design of feasible policy plans to tackle food security and land allocation, and an accurate characterization of the long-run trend in crop yield is the key ingredient in such projections. We provide several contributions adding to our current understanding of the impact of climatic factors on crop yield. First of all, reflecting the complexity of agricultural systems and the time required for any change to diffuse, we show that crop yield in Europe has historically been characterized by a stochastic trend rather than the deterministic specifications normally used in the literature. Secondly, we found that, contrary to previous studies, the trend in crop yield has slowly changed across time rather than being affected by a single abrupt permanent change. Thirdly, we provide strong evidence that climatic factors have played a major role in shaping the long-run trajectory of crop yield over the decades, by influencing both the size and the statistical nature of the trend. In other words, climatic factors are important not only for the year-to-year fluctuations in crop yield but also for its path in the long-run. Finally, we find that, for most countries in this study, the trend in temperature is responsible for a reduction in the long-run growth rate of yield in wheat, whereas a small gain is produced in maize, except for Southern European countries. [ABSTRACT FROM AUTHOR]

This paper presents a novel algorithm for efficient online estimation of the filter derivatives in general hidden Markov models. The algorithm, which has a linear computational complexity and very limited memory requirements, is furnished with a number of convergence results, including a central limit theorem with an asymptotic variance that can be shown to be uniformly bounded in time. Using the proposed filter derivative estimator, we design a recursive maximum likelihood algorithm updating the parameters according the gradient of the one-step predictor log-likelihood. The efficiency of this online parameter estimation scheme is illustrated in a simulation study. [ABSTRACT FROM AUTHOR]