A guide to state-space modeling of ecological time series
Marie Auger-Méthé, Ken Newman, Diana Cole, Fanny Empacher, Rowenna Gryba, Aaron A. King, Vianney Leos-Barajas, Joanna Mills Flemming, Anders Nielsen, Giovanni Petris, Len Thomas
State-space models (SSMs) are an important modeling framework for analyzing ecological time series. These hierarchical models are commonly used to model population dynamics, animal movement, and capture-recapture data, and are now increasingly being used to model other ecological processes. SSMs are popular because they are flexible and they model the natural variation in ecological processes separately from observation error. Their flexibility allows ecologists to model continuous, count, binary, and categorical data with linear or nonlinear processes that evolve in discrete or continuous time. Modeling the two sources of stochasticity separately allows researchers to differentiate between biological variation (e.g., in birth processes) and imprecision in the sampling methodology, and generally provides better estimates of the ecological quantities of interest than if only one source of stochasticity is directly modeled. Since the introduction of SSMs, a broad range of fitting procedures have been proposed. However, the variety and complexity of these procedures can limit the ability of ecologists to formulate and fit their own SSMs. We provide the knowledge for ecologists to create SSMs that are robust to common, and often hidden, estimation problems, and the model selection and validation tools that can help them assess how well their models fit their data. In this paper, we present a review of SSMs that will provide a strong foundation to ecologists interested in learning about SSMs, introduce new tools to veteran SSM users, and highlight promising research directions for statisticians interested in ecological applications. The review is accompanied by an in-depth tutorial that demonstrates how SSMs models can be fitted and validated in R. Together, the review and tutorial present an introduction to SSMs that will help ecologists to formulate, fit, and validate their models.
Mathematical Institute of the S.A.S.A（塞尔维亚科学与艺术学院数学研究所）；Technical Faculty in Bor, University of Belgrade（贝尔格莱德大学博尔技术学院）；DIMES, University of Calabria（卡拉布里亚大学DIMES）
Sustainability became the most important component of world development, as countries worldwide fight the battle against the climate change. To understand the effects of climate change, the ecological footprint, along with the biocapacity should be observed. The big part of the ecological footprint, the carbon footprint, is most directly associated with the energy, and specifically fuel sources. This paper develops a time series vector autoregression prediction model of the ecological footprint based on energy parameters. The objective of the paper is to forecast the EF based solely on energy …
Analyzing ecological data often requires modeling the autocorrelation created by spatial and temporal processes. Many of the statistical methods used to account for autocorrelation can be viewed as regression models that include basis functions. Understanding the concept of basis functions enables ecologists to modify commonly used ecological models to account for autocorrelation, which can improve inference and predictive accuracy. Understanding the properties of basis functions is essential for evaluating the fit of spatial or time-series models, detecting a hidden form of multicollinearity,…
In order to describe more accurately the time relationships between daily satellite imagery time series of precipitation and NDVI we propose an estimator which takes into account the sparsity naturally observed in precipitation. We conducted a series of simulation studies and show that the proposed estimator's variance is smaller than the canonical's (Pearson-based), in particular, when the signal-to-noise ratio is rather low. Also, the proposed estimator's variance was found smaller than the canonical's one when we applied them to stacks of images (2002-2016) taken on some ecological regions …
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation p…
We present a multivariate hierarchical space-time model to describe the joint series of monthly extreme temperatures and amounts of rainfall. Data are available for 360 monitoring stations over 60 years, with missing data affecting almost all series. Model components account for spatio-temporal dependence with annual cycles, dependence on covariates and between responses. The very large amount of data is tackled modeling the spatio-temporal dependence by the nearest neighbor Gaussian process. Response multivariate dependencies are described using the linear model of coregionalization, while an…
Exploring adversarial attack vectors and studying their effects on machine learning algorithms has been of interest to researchers. Deep neural networks working with time series data have received lesser interest compared to their image counterparts in this context. In a recent finding, it has been revealed that current state-of-the-art deep learning time series classifiers are vulnerable to adversarial attacks. In this paper, we introduce two local gradient based and one spectral density based time series data augmentation techniques. We show that a model trained with data obtained using our …
VISTA-SSM: Varying and Irregular Sampling Time-series Analysis via State Space Models
Johns Hopkins University（约翰斯·霍普金斯大学）；Institute for Psycholinguistics and Digital Health, United States of America（美国心理语言学和健康数字研究所）；New York University School of Medicine（纽约大学医学院）；University of Houston（休斯顿大学）
Label-Guided Imputation via Forest-Based Proximities for Improved Time Series Classification
1 Department of Statistics, Brigham Young University, Provo, UT, USA Emails；2 Department of Computer Science, Brigham Young University, Provo, UT, USA Email；3 Department of Public Health, Brigham Young University, Provo, UT, USA Email；4 Department of Neurology, Vagelos College of Physicians \& Surgeons, Columbia University, New York, NY, USA Email；5 Department of Neurology, Miller School of Medicine, University of Miami, Miami, FL, USA Email；6 Elmhurst Hospital Center, NYC Health + Hospitals, New York, NY, USA Email；7 Department of Mathematics \& Statistics, Utah State University, Logan, UT, USA Email
Neural networks have become a powerful tool in pattern recognition and part of their success is due to generalization from using large datasets. However, unlike other domains, time series classification datasets are often small. In order to address this problem, we propose a novel time series data augmentation called guided warping. While many data augmentation methods are based on random transformations, guided warping exploits the element alignment properties of Dynamic Time Warping (DTW) and shapeDTW, a high-level DTW method based on shape descriptors, to deterministically warp sample patte…
Damage detection in active-sensing, guided-waves-based Structural Health Monitoring (SHM) has evolved through multiple eras of development during the past decades. Nevertheless, there still exists a number of challenges facing the current state-of-the-art approaches, both in the industry as well as in research and development, including low damage sensitivity, lack of robustness to uncertainties, need for user-defined thresholds, and non-uniform response across a sensor network. In this work, a novel statistical framework is proposed for active-sensing SHM based on the use of ultrasonic guided…
An active area of research interest is the inference of ecological models of complex microbial communities. Inferring such ecological models entails understanding the interactions between microbes and how they affect each other's growth. This dissertation employs a statistical perspective to contribute further to the knowledge currently addressing this problem. Part I explains how high-throughput droplet-based microfluidics technology can be used to screen for microbial interactions. An explicit, statistical framework is motivated and developed that can guide the analysis of data from such exp…
This paper introduces a simple framework of counterfactual estimation for causal inference with time-series cross-sectional data, in which we estimate the average treatment effect on the treated by directly imputing counterfactual outcomes for treated observations. We discuss several novel estimators under this framework, including the fixed effects counterfactual estimator, interactive fixed effects counterfactual estimator, and matrix completion estimator. They provide more reliable causal estimates than conventional twoway fixed effects models when treatment effects are heterogeneous or uno…
With rapid development of techniques to measure brain activity and structure, statistical methods for analyzing modern brain-imaging play an important role in the advancement of science. Imaging data that measure brain function are usually multivariate time series and are heterogeneous across both imaging sources and subjects, which lead to various statistical and computational challenges. In this paper, we propose a group-based method to cluster a collection of multivariate time series via a Bayesian mixture of smoothing splines. Our method assumes each multivariate time series is a mixture o…
