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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Urban Studies and Planning, 1989., Vita., Includes bibliographical references (leaves 62-63)., by Robert Coleman Reeves, Jr., CPA., M.S.

Discrete Markov random field models provide a natural framework for representing images or spatial datasets. They model the spatial association present while providing a convenient Markovian dependency structure and strong edge-preservation properties. However, parameter estimation for discrete Markov random field models is difficult due to the complex form of the associated normalizing constant for the likelihood function. For large lattices, the reduced dependence approximation to the normalizing constant is based on the concept of performing computationally efficient and feasible forward recursions on smaller sublattices which are then suitably combined to estimate the constant for the whole lattice. We present an efficient computational extension of the forward recursion approach for the autologistic model to lattices that have an irregularly shaped boundary and which may contain regions with no data; these lattices are typical in applications. Consequently, we also extend the reduced dependence approximation to these scenarios enabling us to implement a practical and efficient non-simulation based approach for spatial data analysis within the variational Bayesian framework. The methodology is illustrated through application to simulated data and example images. The supplemental materials include our C++ source code for computing the approximate normalizing constant and simulation studies.

A time series method for the determination of combustion chamber resonant frequencies is outlined. This technique employs the use of Markov-chain Monte Carlo (MCMC) to infer parameters in a chosen model of the data. The development of the model is included and the resonant frequency is characterised as a function of time. Potential applications for cycle-by-cycle analysis are discussed and the bulk temperature of the gas and the trapped mass in the combustion chamber are evaluated as a function of time from resonant frequency information.

The purpose of this thesis is to examine current Command and Control planning methods and to aid in the furtherance of the Object Model Working Group's (OMWG) Core Plan Representation. Chapter I introduces the discipline of planning and its history. Chapter II discusses the theory and practice of modern Object Oriented modeling. The structure and conventions of object programming are covered as well as a method for information system abstraction. Chapter III covers the background of current Command and Control systems and gives a report on the OMWG efforts in creation of an Object Schema for Command and control. Chapter IV presents the author's submission for an Object-Oriented representation of the COMSUBPAC OPLAN 5050 based on the Core Plan Representation (CPR), http://archive.org/details/objectorientedpl109458754, Lieutenant, United States Navy, Approved for public release; distribution is unlimited.

Early detection surveillance programs aim to find invasions of exotic plant pests and diseases before they are too widespread to eradicate. However, the value of these programs can be difficult to justify when no positive detections are made. To demonstrate the value of pest absence information provided by these programs, we use a hierarchical Bayesian framework to model estimates of incursion extent with and without surveillance. A model for the latent invasion process provides the baseline against which surveillance data are assessed. Ecological knowledge and pest management criteria are introduced into the model using informative priors for invasion parameters. Observation models assimilate information from spatio-temporal presence/absence data to accommodate imperfect detection and generate posterior estimates of pest extent. When applied to an early detection program operating in Queensland, Australia, the framework demonstrates that this typical surveillance regime provides a modest reduction in the estimate that a surveyed district is infested. More importantly, the model suggests that early detection surveillance programs can provide a dramatic reduction in the putative area of incursion and therefore offer a substantial benefit to incursion management. By mapping spatial estimates of the point probability of infestation, the model identifies where future surveillance resources can be most effectively deployed.

Counterinsurgency (COIN) is essentially a human endeavor that taxes the full spectrum of human capabilities. The challenges of COIN and Full Spectrum Operations (FSO) require a complementary approach to Soldier preparation referred to here as Full Spectrum Training and Development (FSTD). The goal of the research described in this report was to develop an exemplary guide for FSTD focused on the skills and attributes needed for reconnaissance leaders in FSO. This goal was achieved by developing and evaluating a guide designed to help instructors facilitate collaborative learning. The guide incorporated principles and best practices of peer-to-peer training to directly support instructors teaching reconnaissance leader skills and attributes. During development the guide underwent iterative review by course leaders and instructors as well as behavioral research scientists. The guide was then evaluated and revised based on two operational implementations. Empirical data from the evaluations suggested the guide is a valuable and welcome resource for instructors and course leaders. The report includes suggestions for extending the methodology to other U.S. Army courses., Prepared in cooperation with U.S. Army Research Institute for the Behavioral and Social Sciences, Fort Knox, KY and Augusta State Univ., Augusta, GA.

Because aesthetics can have a profound effect upon the human relationship to the non-human environment the importance of aesthetics to ecologically sustainable designed landscapes has been acknowledged. However, in recognition that the physical forms of designed landscapes are an expression of the social values of the time, some design professionals have called for a new aesthetic ― one that reflects these current ecological concerns. To address this, some authors have suggested various theoretical design frameworks upon which such an aesthetic could be based. Within these frameworks there is an underlying theme that the patterns and processes of natural systems have the potential to form a new aesthetic for landscape design —an aesthetic based on fractal rather than Euclidean geometry. Perry, Reeves and Sim (2008) have shown that it is possible to differentiate between different landscape forms by fractal analysis. However, this research also shows that individual scenes from within very different landscape forms can possess the same fractal properties. Early data, revealed by transforming landscape images from the spatial to the frequency domain, using the fast Fourier transform, suggest that fractal patterning can have a significant effect within the landscape. In fact, it may be argued that any landscape design that includes living processes will include some design element whose ultimate form can only be expressed through the mathematics of fractal geometry. This paper will present ongoing research into the potential role of fractal geometry as a basis for a new form language – a language that may articulate an aesthetic for landscape design that echoes our ecological awakening.

Hidden Markov random field models provide an appealing representation of images and other spatial problems. The drawback is that inference is not straightforward for these models as the normalisation constant for the likelihood is generally intractable except for very small observation sets. Variational methods are an emerging tool for Bayesian inference and they have already been successfully applied in other contexts. Focusing on the particular case of a hidden Potts model with Gaussian noise, we show how variational Bayesian methods can be applied to hidden Markov random field inference. To tackle the obstacle of the intractable normalising constant for the likelihood, we explore alternative estimation approaches for incorporation into the variational Bayes algorithm. We consider a pseudo-likelihood approach as well as the more recent reduced dependence approximation of the normalisation constant. To illustrate the effectiveness of these approaches we present empirical results from the analysis of simulated datasets. We also analyse a real dataset and compare results with those of previous analyses as well as those obtained from the recently developed auxiliary variable MCMC method and the recursive MCMC method. Our results show that the variational Bayesian analyses can be carried out much faster than the MCMC analyses and produce good estimates of model parameters. We also found that the reduced dependence approximation of the normalisation constant outperformed the pseudo-likelihood approximation in our analysis of real and synthetic datasets.

Recognition that we need to live in a more ecologically sustainable way and that the physical forms of designed landscapes are an expression of the social values and cultural drivers of the time has underpinned the call by some landscape design professionals for a new design aesthetic – one that reflects modern ecological concerns. However, for an 'ecological aesthetic' to be accepted, it must be capable of generating landscape forms that are pleasurable to the general public, as it is the general public who will be responsible for delivering ecological sustainability in the long term. The growth in understanding of the mathematical properties of natural systems and processes has led some authors to suggest that fractal geometry, called the language of nature, could play a role in developing such an aesthetic. This is supported by recent research that suggests human perceptual systems have evolved to process fractal patterning and that we have a visual preference for images with certain fractal qualities. However, how fractal geometry can be used, and what form an aesthetic based on this geometry might take, remains elusive and undefined. To develop an aesthetic based on fractal geometry it is necessary to understand why fractal geometry should be considered as a potential tool and whether the application of fractal analysis can differentiate between the types of landscape forms encountered every day.

Maximum likelihood parameter estimation and sampling from Bayesian posterior distributions are problematic when the probability density for the parameter of interest involves an intractable normalising constant which is also a function of that parameter. In this paper, an auxiliary variable method is presented which requires only that independent samples can be drawn from the unnormalised density at any particular parameter value. The proposal distribution is constructed so that the normalising constant cancels from the Metropolis-Hastings ratio. The method is illustrated by producing posterior samples for parameters of the Ising model given a particular lattice realisation.

Let n S-valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r+1 of the n components in the joint distribution, we term this a lag-r model, whose normalising constant can be computed using a forward recursion in O(Sr+1) computations, as opposed to O(Sn) for the direct computation. We show how a lag-r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed.

Motivated by the autologistic model for the analysis of spatial binary data on the two-dimensional lattice, we develop efficient computational methods for calculating the normalizing constant for models for discrete data defined on the cylinder and lattice. Because the normalizing constant is generally unknown analytically, statisticians have developed various ad hoc methods to overcome this difficulty. Our aim is to provide computationally and statistically efficient methods for calculating the normalizing constant so that efficient likelihood-based statistical methods are then available for inference. We extend the so-called transition method to find a feasible computational method of obtaining the normalizing constant for the cylinder boundary condition. To extend the result to the free-boundary condition on the lattice we use an efficient path sampling Markov chain Monte Carlo scheme. The methods are generally applicable to association patterns other than spatial, such as clustered binary data, and to variables taking three or more values described by, for example, Potts models.