Integrated Systems for Inducing Spatio-Temporal Process Models.

Research on inductive process modeling combines background knowledge with time-series data to construct explanatory models, but previous work has placed few constraints on search through the model space. We present an extended formalism that organizes process knowledge in a hierarchical manner, and we describe HIPM, a system that carries out constrained search for hierarchical process models. We report experiments that suggest this approach produces more accurate and plausible models with less effort. We conclude by discussing related research and directions for future work.

Journal of Symbolic Computation, 1996

Granularity of time is an important issue for the understanding of how actions performed at coarse levels of time interact with others, working at finer levels. However, it has not received much attention from most AI work on temporal logic. In simpler domains of application we may not need to consider it a problem but it becomes important in more complex domains, such as ecological modelling. In this domain, aggregation of processes working at different time granularities (and sometimes cyclically) is very difficult to achieve reliably. We have proposed a new time granularity theory based on modular temporal classes, and have developed a temporal reasoning system to specify cyclical processes of simulation models in ecology at many levels of time.

Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2008

With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. Over the last decade, hierarchical models implemented through Markov chain Monte Carlo methods have become especially popular for spatial modelling, given their flexibility and power to fit models that would be infeasible with classical methods as well as their avoidance of possibly inappropriate asymptotics. However, fitting hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases in cubic order with the number of spatial locations, rendering such models infeasible for large spatial data sets. This computational burden is exacerbated in multivariate settings with several spatially dependent response variables. It is also aggravated when data are collected at frequent time points and spatiotemporal process models are used. With regard to this challenge, our contribution is to work with what we call predictive process models for spatial and spatiotemporal data. Every spatial (or spatiotemporal) process induces a predictive process model (in fact, arbitrarily many of them). The latter models project process realizations of the former to a lower dimensional subspace, thereby reducing the computational burden. Hence, we achieve the flexibility to accommodate non-stationary, non-Gaussian, possibly multivariate, possibly spatiotemporal processes in the context of large data sets. We discuss attractive theoretical properties of these predictive processes. We also provide a computational template encompassing these diverse settings. Finally, we illustrate the approach with simulated and real data sets.

Electronic Proceedings in Theoretical Computer Science, 2012

We propose PALPS, a Process Algebra with Locations for Population Systems. PALPS allows us to produce spatially-explicit, individual-based models and to reason about their behavior. Our calculus has two levels: at the first level we may define the behavior of an individual of a population while, at the second level, we may specify a system as the collection of individuals of various species located in space, moving through their life cycle while changing their location, if they so wish, and interacting with each other in various ways such as preying on each other. Furthermore, we propose a probabilistic temporal logic for reasoning about the behavior of PALPS processes. We illustrate our framework via models of dispersal in metapopulations.

Journal of Statistical Software, 2015

In this paper we detail the reformulation and rewrite of core functions in the spBayes R package. These efforts have focused on improving computational efficiency, flexibility, and usability for point-referenced data models. Attention is given to algorithm and computing developments that result in improved sampler convergence rate and efficiency by reducing parameter space; decreased sampler run-time by avoiding expensive matrix computations, and; increased scalability to large datasets by implementing a class of predictive process models that attempt to overcome computational hurdles by representing spatial processes in terms of lower-dimensional realizations. Beyond these general computational improvements for existing model functions, we detail new functions for modeling data indexed in both space and time. These new functions implement a class of dynamic spatio-temporal models for settings where space is viewed as continuous and time is taken as discrete.

Environmetrics, 2005

There is a considerable literature in spatiotemporal modelling. The approach adopted here applies to the setting where space is viewed as continuous but time is taken to be discrete. We view the data as a time series of spatial processes and work in the setting of dynamic models, achieving a class of dynamic models for such data. We seek rich, flexible, easy-to-specify, easy-to-interpret, computationally tractable specifications which allow very general mean structures and also non-stationary association structures. Our modelling contributions are as follows. In the case where univariate data are collected at the spatial locations, we propose the use of a spatiotemporally varying coefficient form. In the case where multivariate data are collected at the locations, we need to capture associations among measurements at a given location and time as well as dependence across space and time. We propose the use of suitable multivariate spatial process models developed through coregionalization. We adopt a Bayesian inference framework. The resulting posterior and predictive inference enables summaries in the form of tables and maps, which help to reveal the nature of the spatiotemporal behaviour as well as the associated uncertainty. We illuminate various computational issues and then apply our models to the analysis of climate data obtained from the National Center for Atmospheric Research to analyze precipitation and temperature measurements obtained in Colorado in 1997.

Lecture Notes in Computer Science, 2009

Processes are central for geographic information science; yet geographic information systems (GIS) lack capabilities to represent process related information. A prerequisite to including processes in GIS software is a general method to describe geographic processes independently of application disciplines. This paper presents such a method, namely a process description language. The vocabulary of the process description language is derived formally from mathematical models. Physical processes in geography can be described in two equivalent languages: partial dierential equations or partial dierence equations, where the latter can be shown graphically and used as a method for application specialists to enter their process models. The vocabulary of the process description language comprises components for describing the general behavior of prototypical geographic physical processes. These process components can be composed by basic models of geographic physical processes, which is shown by means of an example.

2008

A framework and a software tool has been developed to execute two important steps in the model development cycle of temporal numerical models simulating geographic change using rules of cause and effect. The first step supported by the tool is the software implementation of spatio- temporal models. This can be done with the tool by combining generic operations on 2D

We define the inductive process modeling task as the automated construction of quantitative process models from time series and background knowledge. In this task, the background knowledge comprises generic processes that along with a given set of entities define the space of candidate model structures. Typically this space grows exponentially with the size of the library, so past research introduced a hierarchical organization on the processes to constrain that space to a limited set of plausible configurations. However, organizing the processes into a hierarchy takes considerable effort, leads to implicit constraints, and creates a complex relationship between the knowledge of what processes exist and the knowledge of how one can combine them. To address these problems, we developed SC-IPM 1 , an inductive process modeler that uses declarative constraints to reduce the size of the model structure space. In this paper, we describe the constraint formalism and how it guides SC-IPM's search.

2019

We model the spatial dynamics of a forest stand by using a special class of spatio-temporal point processes, the sequential spatial point process, where the spatial dimension is parameterized and the time component is atomic. The sequential spatial point processes differ from spatial point processes in the sense that the realizations are ordered sequences of spatial locations and the order of points allows us to approximate the spatial evolutionary dynamics of the process. This feature shall be useful to interpret the long-term dependence and the memory formed by the spatial history of the process. As an illustration, the sequence can represent the tree locations ordered with respect to time, or to some given quantitative marks such as tree diameters. We derive a parametric sequential spatial point process model that is expressed in terms of self-interaction of the spatial points, and then the maximum-likelihood-based inference is tractable. As an application, we apply the model obt...