Theses and Dissertations at Montana State University (MSU)
Permanent URI for this communityhttps://scholarworks.montana.edu/handle/1/732
Browse
3 results
Search Results
Item Bayesian computing and sampling design for partially-surveyed spatial point process models(Montana State University - Bozeman, College of Letters & Science, 2020) Flagg, Kenneth Allen; Chairperson, Graduate Committee: Andrew Hoegh; Andrew Hoegh and John Borkowski were co-authors of the article, 'Modeling partially-surveyed point process data: inferring spatial point intensity of geomagnetic anomalies' in the journal 'Journal of agricultural, biological, and environmental statistics' which is contained within this dissertation.; Andrew Hoegh was a co-author of the article, 'The integrated nested laplace approximation applied to spatial log-Gaussian Cox process models' submitted to the journal 'Journal of applied statistics' which is contained within this dissertation.; John Borkowski and Andrew Hoegh were co-authors of the article, 'Log-Gaussian Cox processes and sampling paths: towards optimal design' submitted to the journal 'Spatial statistics' which is contained within this dissertation.Spatial point processes model situations such as unexploded ordnance, plant and animal populations, and celestial bodies, where events occur at distinct points in space. Point process models describe the number and distribution of these events. These models have been mathematically understood for many decades, but have not been widely used because of computational challenges. Computing advances in the last 30 years have kept interest alive, with several breakthroughs circa 2010 that have made Bayesian spatial point process models practical for many applications. There is now interest in sampling, where the process is only observed in part of the study site. My dissertation work deals with sampling along paths, a standard feature of unexploded ordnance remediation studies. In this dissertation, I introduce a data augmentation procedure to adapt a Dirichlet process mixture model to sampling situations and I provide the first comparison of a variety of sampling designs with regard to their spatial prediction performance for spatial log-Gaussian Cox process (LGCP) models. The Dirichlet process model remains computationally expensive in the sampling case while the LGCP performs well with low computing time. The sampling design study shows that paths with regular spacing perform well, with corners and direction changes being helpful when the path is short.Item Robust response surface designs against missing observations(Montana State University - Bozeman, College of Letters & Science, 2015) Srisuradetchai, Patchanok; Chairperson, Graduate Committee: John J. BorkowskiEven though an experiment is carefully planned, some observations may be lost during the process of collecting data or may be suspicious in some way. Missing observations can be the result from many causes, for example, the loss of experimental units and miscoded data where their correct values are non-trackable. The risk of losing observations usually cannot be ignored in practice. When small response surface designs are used, the effects of missing points may be substantial. The ability to estimate all parameters could be completely lost, or the variances of predicted responses could be incredibly large in a certain part of an experimental region. With respect to design optimality, designs will usually no longer be optimal when missing values exist. The robustness against a missing value of several standard response surface designs has been studied via newly proposed measures. The designs include central composite designs (CCDs), small composite designs (SCDs), hybrid designs, and exact alphabetic optimal designs. In addition, an R package has been developed to visualize the effect of missing data. The behaviors of D-, A-, G-, and IV -efficiencies for CCDs are studied, and the axial distance that makes a spherical CCD more robust to a missing point is found via a numerical search. Results show that the axial distance obtained from Min D criterion is the largest and respectively followed by Min G, Min IV , and Min A. The D-, A-, G-, and IV -optimality criteria, as well as the point-exchange algorithm, are modified for constructing optimal robust exact designs. The resulting robust exact designs are compared to existing optimal exact designs to observe how resulting designs are robust to a missing point. It is observed that D- and IV -optimal robust designs are slightly less optimal but their robustness properties are appreciably improved. The robustness of G-optimal robust designs is usually slightly improved but with considerable loss in design efficiency. The same robust optimality criteria are also applied to construct optimal robust exact mixture designs. Finally, the adaptive designs are introduced. This allows experimenters to change design points once a missing value occurs during experimentation.Item Robust and optimal design strategies for nonlinear models using genetic algorithms(Montana State University - Bozeman, College of Letters & Science, 2014) Akapame, Sydney Kwasi; Chairperson, Graduate Committee: John J. BorkowskiExperimental design pervades all areas of scientific inquiry. The central idea behind many designed experiments is to improve or optimize inference about the quantities of interest in a statistical model. Thus, the strengths of any inferences made will be dependent on the choice of the experimental design and the statistical model. Any design that optimizes some statistical property will be referred to as an optimal design. In the main, most of the literature has focused on optimal designs for linear models such as low-order polynomials. While such models are widely applicable in some areas, they are unsuitable as approximations for data generated by systems or mechanisms that are nonlinear. Unlike linear models, nonlinear models have the unique property that the optimal designs for estimating their model parameters depend on the unknown model parameters. This dissertation addresses several strategies to choose experimental designs in nonlinear model situations. Attempts at solving the nonlinear design problem have included locally optimal designs, sequential designs and Bayesian optimal designs. Locally optimal designs are optimal designs conditional on a particular guess of the parameter vector. Although these designs are useful in certain situations, they tend to be sub-optimal if the guess is far from the truth. Sequential designs are based on repeated experimentation and tend to be expensive. Bayesian optimal designs generalize locally optimal designs by averaging a design optimality criterion over a prior distribution, but tend to be sensitive to the choice of prior distribution. More importantly, in cases where multiple priors are elicited from a group of experts, designs are required that are robust to the class (or range) of prior distributions. New robust design criteria to address the issue of robustness are proposed in this dissertation. In addition, designs based on axiomatic methods for pooling prior distributions are obtained. Efficient algorithms for generating designs are also required. In this research, genetic algorithms (GAs) are used for design generation in the MATLAB® computing environment. A new genetic operator suited to the design problem is developed and used. Existing designs in the published literature are improved using GAs.