Projecting environmental niche models through time is a common goal when studying species response to climatic change. Species distribution models (SDMs) are commonly used to estimate a species' niche from observed patterns of occurrence and environmental predictors. However, a species niche is also shaped by non-environmental factors--including biotic interactions and dispersal barrier—truncating SDM estimates. Though truncated SDMs may accurately predict present-day species niche, projections through time are often biased by environmental condition change. Modeling niche in a phylogenetic framework leverages a clade's shared evolutionary history to pull species estimates closer towards phylogenetic conserved values and farther away from species specific biases. We propose a new Bayesian model of phylogenetic niche implemented in R. Under our model, species SDM parameters are transformed into biologically interpretable continuous parameters of environmental niche optimum, breadth, and tolerance evolving under multivariate Brownian motion random walk. Through simulation analyses, we demonstrated model accuracy and precision that improved as phylogeny size increased. We also demonstrated our model on a clade of eastern United States Plethodontid salamanders by accurately estimating species niche, even when no occurrence data is present. Our model demonstrates a novel framework where niche changes can be studied forwards and backwards through time to understand ancestral ranges, patterns of environmental specialization, and niche in data deficient species. / Master of Science / As many species face increasing pressure in a changing climate, it is crucial to understand the set of environmental conditions that shape species' ranges--known as the environmental niche--to guide conservation and land management practices. Species distribution models (SDMs) are common tools that are used to model species' environmental niche. These models treat a species' probability of occurrence as a function of environmental conditions. SDM niche estimates can predict a species' range given climate data, paleoclimate, or projections of future climate change to estimate species range shifts from the past to the future. However, SDM estimates are often biased by non-environmental factors shaping a species' range including competitive divergence or dispersal barriers. Biased SDM estimates can result in range predictions that get worse as we extrapolate beyond the observed climatic conditions. One way to overcome these biases is by leveraging the shared evolutionary history amongst related species to "fill in the gaps". Species that are more closely phylogenetically related often have more similar or "conserved" environmental niches. By estimating environmental niche over all species in a clade jointly, we can leverage niche conservatism to produce more biologically realistic estimates of niche. However, currently a methodological gap exists between SDMs estimates and macroevolutionary models, prohibiting them from being estimated jointly. We propose a novel model of evolutionary niche called PhyNE (Phylogenetic Niche Evolution), where biologically realistic environmental niches are fit across a set of species with occurrence data, while simultaneously fitting and leveraging a model of evolution across a portion of the tree of life. We evaluated model accuracy, bias, and precision through simulation analyses. Accuracy and precision increased with larger phylogeny size and effectively estimated model parameters. We then applied PhyNE to Plethodontid salamanders from Eastern North America. This ecologically-important and diverse group of lungless salamanders require cold and wet conditions and have distributions that are strongly affected by climatic conditions. Species within the family vary greatly in distribution, with some species being wide ranging generalists, while others are hyper-endemics that inhabit specific mountains in the Southern Appalachians with restricted thermal and hydric conditions. We fit PhyNE to occurrence data for these species and their associated average annual precipitation and temperature data. We identified no correlations between species environmental preference and specialization. Pattern of preference and specialization varied among Plethodontid species groups, with more aquatic species possessing a broader environmental niche, likely due to the aquatic microclimate facilitating occurrence in a wider range of conditions. We demonstrated the effectiveness of PhyNE's evolutionarily-informed estimates of environmental niche, even when species' occurrence data is limited or even absent. PhyNE establishes a proof-of-concept framework for a new class of approaches for studying niche evolution, including improved methods for estimating niche for data-deficient species, historical reconstructions, future predictions under climate change, and evaluation of niche evolutionary processes across the tree of life. Our approach establishes a framework for leveraging the rapidly growing availability of biodiversity data and molecular phylogenies to make robust eco-evolutionary predictions and assessments of species' niche and distributions in a rapidly changing world.

Forward and inverse modeling studies of the relationship between tree ring width and bivariate climate are performed using a model called VS-Lite. The monthly time-step model incorporates two simple but realistic nonlinearities in its description of the transformation of climate variability into ring width index. These features ground VS-Lite in scientific principles and make it more complex than empirically-derived statistical models commonly used to simulate tree ring width. At the same time, VS-Lite is vastly simpler and more efficient than pre-existing numerical models that simulate detailed biological aspects of tree growth. A forward modeling validation study shows that VS-Lite simulates a set of observed chronologies across the continental United States with comparable or better skill than simulations derived from a standard, linear regression based approach. This extra skill derives from VS-Lite's basis in mechanistic principles, which makes it more robust than the statistical methodology to climatic nonstationarity. A Bayesian parameterization approach is also developed that incorporates scientific information into the choice of locally optimal VS-Lite parameters. The parameters derived using the scheme are found to be interpretable in terms of the climate controls on growth, and so provide a means to guide applications of the model across varying climatologies. The first reconstructions of paleoclimate that assimilate scientific understanding of the ring width formation process are performed using VS-Lite to link the proxy data to potential climate histories. Bayesian statistical methods invert VS-Lite conditional on a given dendrochronolgy to produce probabilistic estimates of local bivariate climate. Using VS-Lite in this manner produces skillful estimates, but does not present advantages compared another set of probabilistic reconstructions that invert a simpler, linear, empirical forward model. This result suggests that future data-assimilation based reconstructions will need to integrate as many data sources as possible, both across space and proxy types, in order to benefit from information provided by mechanistic models of proxy formation.

<p>Phosphorus load reduction and dreissenid invasion are the two most important factors that influence europhication dynamics in the Great Lakes. The 1978 amendments to the Great Lakes Water Quality Agreement (GLWQA) between the United States and Canada established target phosphorus loads for the lakes, leading to reductions in external phosphorus loading to the Great Lakes. With diminished phosphorus levels, further nutrient management was a minor concern until the proliferation of invasive dreissenid mussels. Dreissenid mussels were first documented in the Laurentian Great Lakes in the late 1980s. Zebra mussels (<italic>Dreissena polymorpha</italic>) spread quickly into shallow, hard-substrate areas; quagga mussels (<italic>Dreissena rostriformis bugensis</italic>) spread more slowly and are currently colonizing deep, offshore areas. These mussels have the potential to modify biogeochemical processes and food web structure, altering nutrient cycling and availability. Following the mussel invasion, cyanobacterial blooms and nuisance benthic algal growth have reappeared in many nearshore areas of the Great Lakes.</p><p>This dissertation characterizes long-term patterns of phosphorus loading and mussel populations for Saginaw Bay, and estimates the effects of load reductions and dreissenid invasion on several aspects of pelagic water quality, focusing on phosphorus flux and cycling in Saginaw Bay. Bayesian approaches were used to quantify the impacts of load reduction and mussel invasion, while at the same time addressing model parameter uncertainty and prediction uncertainty associated with long-term observational data. Annual total phosphorus load estimates suggest a decreasing trend until the late 1970s to early 1980s, reflecting the effectiveness of point source controls implemented pursuant to GLWQA. Despite the decrease, however, the annual loads have not likely met the 440 tonne yr-1 target established for Saginaw Bay. In 1990 zebra mussels were discovered in the bay and by 1992 they were widespread and peaked with densities of >30,000 m<super>-2</super>. Following the peak, mean densities dropped and modeling results predict that the density will reach equilibria at ~600 m<super>-2</super>. When mussels appeared, the proportion of tributary phosphorus retained in Saginaw Bay increased from ~0.5 to ~0.7, reducing phosphorus export to the main body of Lake Huron. The combined effects of increased phosphorus retention and decreased phosphorus loading have caused an ~60% decrease in phosphorus export from Saginaw Bay to Lake Huron. The analysis of long-term patterns of pelagic water quality highlights the sustained effects of mussel invasion on altering water quality parameters in Saginaw Bay; there was a consistent decrease in chlorophyll concentrations by ~46%, and total phosphorus concentrations by ~25%, and an increase in secchi depths by ~15% over ~20 year invasion of mussels. A comparison of chlorophyll-phospohrus relationship between pre- and post-invasion periods suggest the reduced chlorophyll yield for a given phosphorus concentration after the mussel invasion. Further, decreases in both total phosphorus and chlorophyll concentrations were found in the majority of 24 mussel-invaded US lakes in addition to Saginaw Bay, and modeling results predict less chlorophyll yields per unit phosphorus level that ranges from oligo- to mesotrophic conditions. All lines of evidence presented in the dissertation point to the important roles of load reductions and invasive mussels affecting eutrophication dynamics in lake ecosystems.</p> / Dissertation

<p>The first part of the thesis focuses on the development of Bayesian modeling motivated by geophysics applications. In Chapter 2, we model the frequency of pyroclastic flows collected from the Soufriere Hills volcano. Multiple change points within the dataset reveal several limitations of existing methods in literature. We propose Bayesian hierarchical models (BBH) by introducing an extra level of hierarchy with hyper parameters, adding a penalty term to constrain close consecutive rates, and using a mixture prior distribution to more accurately match certain circumstances in reality. We end the chapter with a description of the prediction procedure, which is the biggest advantage of the BBH in comparison with other existing methods. In Chapter 3, we develop new statistical techniques to model and relate three complex processes and datasets: the process of extrusion of magma into the lava dome, the growth of the dome as measured by its height, and the rockfalls as an indication of the dome's instability. First, we study the dynamic Negative Binomial branching process and use it to model the rockfalls. Moreover, a generalized regression model is proposed to regress daily rockfall numbers on the extrusion rate and dome height. Furthermore, we solve an inverse problem from the regression model and predict extrusion rate based on rockfalls and dome height.</p><p>The other focus of the thesis is adaptive Markov chain Monte Carlo (MCMC) method. In Chapter 4, we improve upon the Wang-Landau (WL) algorithm. The WL algorithm is an adaptive sampling scheme that modifies the target distribution to enable the chain to visit low-density regions of the state space. However, the approach relies heavily on a partition of the state space that is left to the user to specify. As a result, the implementation and the use of the algorithm are time-consuming and less automatic. We propose an automatic, adaptive partitioning scheme which continually refines the initial partition as needed during sampling. We show that this overcomes the limitations of the input user-specified partition, making the algorithm significantly more automatic and user-friendly while also making the performance dramatically more reliable and robust. In Chapter 5, we consider the convergence and autocorrelation aspects of MCMC. We propose an Exploration/Exploitation (XX) approach to constructing adaptive MCMC algorithms, which combines adaptation schemes of distinct types. The exploration piece uses adaptation strategies aiming at exploring new regions of the target distribution and thus improving the rate of convergence to equilibrium. The exploitation piece involves an adaptation component which decreases autocorrelation for sampling among regions already discovered. We demonstrate that the combined XX algorithm significantly outperforms either original algorithm on difficult multimodal sampling problems.</p> / Dissertation

It is evident that the study of proteins is crucial for a deeper understanding of how drug treatments affect the body. However, differential protein expression analysis, which can be described as the method of finding which proteins are affected by a treatment, faces some major challenges. First of all, because proteomics data typically comprise several thousand different proteins for just a small number of biological tissues, there are both problems concerning multiple comparisons and low statistical power. Secondly, proteomics data are prone to suffer high rates of missing values, which could bias the results. One approach to handle these issues, which is gaining popularity, is to apply Bayesian hierarchical modeling in order to pool information from the complete dataset of all proteins when making inferences for each protein individually. Yet, in practice, there seems to be essentially only one Bayesian hierarchical model that currently is being employed, which uses a conjugate prior for the error variances but has no prior for the coefficients or the missing values. Given this, the aim of the thesis is to investigate how the model can be improved by adding priors for the coefficients and the missing values. The results show that by adding a hierarchical prior for the coefficients prediction accuracy may be increased. Furthermore, the results show that by adding a prior for the missing values differently expressed proteins can be detected that otherwise would have been overlooked.

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In many environmental and climate applications, extreme data are spatial by nature, and hence statistics of spatial extremes is currently an important and active area of research dedicated to developing innovative and flexible statistical models that determine the location, intensity, and magnitude of extreme events. In particular, the development of flexible sub-asymptotic models is in trend due to their flexibility in modeling spatial high threshold exceedances in larger spatial dimensions and with little or no effects on the choice of threshold, which is complicated with classical extreme value processes, such as Pareto processes. In this thesis, we develop new flexible sub-asymptotic extreme value models for modeling spatial and spatio-temporal extremes that are combined with carefully designed gradient-based Markov chain Monte Carlo (MCMC) sampling schemes and that can be exploited to address important scientific questions related to risk assessment in a wide range of environmental applications. The methodological developments are centered around two distinct themes, namely (i) sub-asymptotic Bayesian models for extremes; and (ii) flexible marked point process models with sub-asymptotic marks. In the first part, we develop several types of new flexible models for light-tailed and heavy-tailed data, which extend a hierarchical representation of the classical generalized Pareto (GP) limit for threshold exceedances. Spatial dependence is modeled through latent processes. We study the theoretical properties of our new methodology and demonstrate it by simulation and applications to precipitation extremes in both Germany and Spain. In the second part, we construct new marked point process models, where interest mostly lies in the extremes of the mark distribution. Our proposed joint models exploit intrinsic CAR priors to capture the spatial effects in landslide counts and sizes, while the mark distribution is assumed to take various parametric forms. We demonstrate that having a sub-asymptotic distribution for landslide sizes provides extra flexibility to accurately capture small to large and especially extreme, devastating landslides.

abstract: Although models for describing longitudinal data have become increasingly sophisticated, the criticism of even foundational growth curve models remains challenging. The challenge arises from the need to disentangle data-model misfit at multiple and interrelated levels of analysis. Using posterior predictive model checking (PPMC)—a popular Bayesian framework for model criticism—the performance of several discrepancy functions was investigated in a Monte Carlo simulation study. The discrepancy functions of interest included two types of conditional concordance correlation (CCC) functions, two types of R2 functions, two types of standardized generalized dimensionality discrepancy (SGDDM) functions, the likelihood ratio (LR), and the likelihood ratio difference test (LRT). Key outcomes included effect sizes of the design factors on the realized values of discrepancy functions, distributions of posterior predictive p-values (PPP-values), and the proportion of extreme PPP-values. In terms of the realized values, the behavior of the CCC and R2 functions were generally consistent with prior research. However, as diagnostics, these functions were extremely conservative even when some aspect of the data was unaccounted for. In contrast, the conditional SGDDM (SGDDMC), LR, and LRT were generally sensitive to the underspecifications investigated in this work on all outcomes considered. Although the proportions of extreme PPP-values for these functions tended to increase in null situations for non-normal data, this behavior may have reflected the true misfit that resulted from the specification of normal prior distributions. Importantly, the LR and the SGDDMC to a greater extent exhibited some potential for untangling the sources of data-model misfit. Owing to connections of growth curve models to the more fundamental frameworks of multilevel modeling, structural equation models with a mean structure, and Bayesian hierarchical models, the results of the current work may have broader implications that warrant further research. / Dissertation/Thesis / Doctoral Dissertation Educational Psychology 2015