New perspectives on State Space Models (17w5120)
David Campbell (Simon Fraser University)
Marie Auger-Methe (Dalhousie University)
Len Thomas (University of St. Andrews)
Considerable progress has been made outside of SSM applications with high potential for gains through modification of the SSM framework, but collaboration between subfields of statistics has been limited in part by a lack of strong communication venues. Recent advances in opening up black box models have gained traction from fields like probabilistic numerical analysis, computer experiments, gaussian process regression. Additional advances in filtering methods and functional data analysis may permit improved semi-parametric models for process noise while improving inference and prediction from noisy data. Together, the advancements in these fields have the potential to take down some of the most difficult barriers to the progress of SSMs.
Objectives of the workshop:
This workshop will focus on new and potential methodological advances for State Space Models (SSMs). A wide spectrum of researchers will be assembled to bring advances from diverse fields to explore these tools and the modifications needed to accommodate the process noise and observation noise combination in SSMs. The goal is to develop new collaborations between distant fields and accelerate research and collaboration in SSMs for resource management purposes. As the flexibility of SSMs continues to add to their popularity, it is important to bring together the communities at this crucial stage in their development. Furthermore, in bringing together experts in a variety of sub-fields of Mathematics and Statistics permits the workshop participants to produce a ‘call to arms’ paper outlining recent advances in their respective fields with potential for high impact in SSMs and highlight the collaborative potential.
Along with exposing the diverse communities to the open problems in SSMs and the state of the art approaches in SSMs and related fields, the goal of the workshop is to encourage innovation through synthesis and development of new approaches by combining existing and currently disjoint research areas to explore important questions around SSMs, in particular:
(1) The complexity of the interaction between process noise and observation noise lead to parameter identifiability concerns. Do recent advances in parameter identifiability show promise for dealing with process and observational noise SSMs?
(2) The observation process is often opportunistic in time, for example it may coincide with the annual return of animals to their hunting or spawning grounds, or it may take observations when a GPS tag is able to send a signal. Some SSMs are built from discretized versions of differential equation models based on the theoretical dynamics of the system. Diverse communities have independently developed different strategies for modifying differential equations to allow process noise. The computer experiments community often uses an additive non-parametric model discrepancy term whereas the SSM community often uses independent discrepancy shocks acting the level of the derivative. Some groups make use of a stochastic differential equation models while others introduces a model relaxation as an approximation to the process noise. For example, the statistics community working on differential equation models often use smoothing to allow process noise, while the probabilistic numerics community models the inherent uncertainty induced by discretization of a continuous time model. What are these approaches capable of doing and when should one approach be recommended over another?
(3) The filtering community has several ways of dealing with complex models, SSMs may be linearized so that Kalman Filtering methods can be applied, or models may be adjusted discretely to suit a particle filter. Additional work has been done through iterative filtering which allows parameters to be time varying then annealed with decaying amounts of time varying flexibility. Related work in functional data analysis is designed to extract the underlying process from a particular penalized function space. How can these methods be melded?
(4) How robust are the models to treatment of nuisance parameters? SSMs often use nuisance parameters to estimate the process noise as a set of random effects. The models can therefore become extremely high dimensional. Additionally, how can robustness of SSMs be improved when dealing with equipment failures in the collection of field data?
(5) As both the complexity of SSMs and the size of the datasets are quickly expanding, computational efficiency is becoming a topic of prime interest. Technological advancements in positional recording devices are resulting in tags recording geolocations at high frequency and for increasingly long periods of time. As a result, fitting a single SSM to the movement data of a few individuals can take weeks. A few recent computational frameworks have shown significant improvements in optimizing methods and show great promise. As computational speed is often a crucial concern to the end-users, incorporating the new statistical tools developed within the workshop in such framework has the potential to revolutionize the way in which SSMs are applied to data.
It is important for young researchers to widen their community and receive diverse exposure to solve problems by combining results across fields. Considerable effort will be made to promote researchers at all levels, several of the invited researchers are currently Assistant Professor, PhD students, post-docs, or junior level in industry. As 2017 approaches additional efforts will be made to find the upcoming researchers with interests related to or already working on SSMs.
References: Auger-Méthé, M., C. Field, C. M. Albertsen, A. E. Derocher, M. A. Lewis, I. D. Jonsen, and J. M. Flemming. 2015. State-space models’ dirty little secrets: even simple linear Gaussian models can have estimation problems:1–54. arXiv: 1508.04325 Buckland, S. T., K. B. Newman, L. Thomas, and N. B. Koesters. 2004. State-space models for the dynamics of wild animal populations. Ecological Modelling 171:157–175. Jonsen, I. D., M. Basson, S. Bestley, M. V. Bravington, T. A. Patterson, M. W. Pedersen, R. Thomson, U. H. Thygesen, and S. J. Wotherspoon. 2013. State-space models for bio-loggers: A methodological road map. Deep-Sea Research Part II: Topical Studies in Oceanography 88-89:34–46. Knape, J. 2008. Estimability of density dependence in models of time series data. Ecology 89:2994–3000. McClintock, B. T., R. King, L. Thomas, J. Matthiopoulos, B. J. McConnell, and J. M. Morales. 2012. A general discrete-time modeling framework for animal movement using multistate random walks. Ecological Monographs 82:335–349. Newman, K. B., S. T. Buckland, B. J. T. Morgan, R. King, D. L. Borchers, D. J. Cole, P. Besbeas, O. Gimenez, and L. Thomas. 2014. Modelling population dynamics: model formulation, fitting and assessment using state-space methods. Springer, New York. Patterson, T. A., L. Thomas, C. Wilcox, O. Ovaskainen, and J. Matthiopoulos. 2008. State-space models of individual animal movement. Trends in Ecology and Evolution 23:87–94.