This thesis considers two distinct topics in phylogenetic analysis. The first is construction of empirical rate matrices for amino acid models. The second topic, which constitutes the majority of the thesis, involves analysis of and extensions to the BH model of Barry and Hartigan (1987). There are a number of rate matrices used for phylogenetic analysis including the PAM (Dayhoff et al. 1979), JTT (Jones et al. 1992) and WAG (Whelan and Goldman 2001). The construction of each of these has difficulties. To avoid adjusting for multiple substitutions, the PAM and JTT matrices were constructed using only a subset of the data consisting of closely related species. The WAG model used an incomplete maximum likelihood estimation to reduce computational cost. We develop a modification of the pairwise methods first described in Arvestad and Bruno that better adjusts for some of the sparseness difficulties that arise with amino acid data. The BH model is very flexible, allowing separate discrete-time Markov processes to occur along different edges. We show, however, that an identifiability problem arises for the BH model making it difficult to estimate character state frequencies at internal nodes. To obtain such frequencies and edge-lengths for BH model fits, we define a nonstationary GTR (NSGTR) model along an edge, and find the NSGTR model that best approximates the fitted BH model. The NSGTR model is slightly more restrictive but allows for estimation of internal node frequencies and interpretable edge lengths. While adjusting for rates-across-sites variation is now common practice in phylogenetic analyses, it is widely recognized that in reality evolutionary processes can change over both sites and lineages. As an adjustment for this, we introduce a BH mixture model that not only allows completely different models along edges of a topology, but also allows for different site classes whose evolutionary dynamics can take any form.

No description available.

<p>In this dissertation, we develop a novel methodology for characterizing and simulating nonstationary, full-field, stochastic turbulent wind fields. </p><p>In this new method, nonstationarity is characterized and modeled via temporal coherence, which is quantified in the discrete frequency domain by probability distributions of the differences in phase between adjacent Fourier components.</p><p>The empirical distributions of the phase differences can also be extracted from measured data, and the resulting temporal coherence parameters can quantify the occurrence of nonstationarity in empirical wind data.</p><p>This dissertation (1) implements temporal coherence in a desktop turbulence simulator, (2) calibrates empirical temporal coherence models for four wind datasets, and (3) quantifies the increase in lifetime wind turbine loads caused by temporal coherence.</p><p>The four wind datasets were intentionally chosen from locations around the world so that they had significantly different ambient atmospheric conditions.</p><p>The prevalence of temporal coherence and its relationship to other standard wind parameters was modeled through empirical joint distributions (EJDs), which involved fitting marginal distributions and calculating correlations.</p><p>EJDs have the added benefit of being able to generate samples of wind parameters that reflect the characteristics of a particular site.</p><p>Lastly, to characterize the effect of temporal coherence on design loads, we created four models in the open-source wind turbine simulator FAST based on the \windpact turbines, fit response surfaces to them, and used the response surfaces to calculate lifetime turbine responses to wind fields simulated with and without temporal coherence.</p><p>The training data for the response surfaces was generated from exhaustive FAST simulations that were run on the high-performance computing (HPC) facilities at the National Renewable Energy Laboratory.</p><p>This process was repeated for wind field parameters drawn from the empirical distributions and for wind samples drawn using the recommended procedure in the wind turbine design standard \iec.</p><p>The effect of temporal coherence was calculated as a percent increase in the lifetime load over the base value with no temporal coherence.</p> / Dissertation

No description available.

In the face of spatially correlated data, Gaussian process regression is a very common modeling approach. Given observational data, kriging equations will provide the best linear unbiased predictor for the mean at unobserved locations. However, when a computer model provides a complete grid of forecasted values, kriging will not apply. To develop an approach to quantify uncertainty of computer model output in this setting, we leverage information from a collection of computer model runs (e.g., historical forecast and observation pairs for tropical cyclone precipitation totals) through a Bayesian hierarchical framework. This framework allows us to combine information and account for the spatial correlation within and across computer model output. Using maximum likelihood estimates and the corresponding Hessian matrices for Gaussian process parameters, these are input to a Gibbs sampler which provides posterior distributions for parameters of interest. These samples are used to generate predictions which provide uncertainty quantification for a given computer model run (e.g., tropical cyclone precipitation forecast). We then extend this framework using deep Gaussian processes to allow for nonstationary covariance structure, applied to multiple computer model runs from a cosmology application. We also perform sensitivity analyses to understand which parameter inputs most greatly impact cosmological computer model output. / Doctor of Philosophy / A crucial theme when analyzing spatial data is that locations that are closer together are more likely to have similar output values (for example, daily precipitation totals). For a particular event, common modeling approach of spatial data is to observe data at numerous locations, and make predictions for locations that were unobserved. In this work, we extend this within-event modeling approach by additionally learning about the uncertainty across different events. Through this extension, we are able to quantify uncertainty for a particular computer model (which may be modeling tropical cyclone precipitation, for example) that does not provide any uncertainty on its own. This framework can be utilized to quantify uncertainty across a vast array of computer model outputs where more than one event or model run has been obtained. We also study how inputting different values into a computer model can influence the values it produces.

No description available.

This thesis proposes novel methods to address specific challenges in analyzing the frequency- and time-domain properties of nonstationary time series data motivated by the study of electrophysiological signals. A new method is proposed for the simultaneous and automatic analysis of the association between the time-varying power spectrum and covariates. The procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines. The approach is formulated in a fully Bayesian framework, in which the number and locations of partition points are random, and fit using reversible jump Markov chain Monte Carlo techniques. Estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes. The new methodology is used to analyze the association between the time-varying spectrum of heart rate variability and self-reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse. Another method proposed in this dissertation develops a unique framework for automatically identifying bands of frequencies exhibiting similar nonstationary behavior. This proposal provides a standardized, unifying approach to constructing customized frequency bands for different signals under study across different settings. A frequency-domain, iterative cumulative sum procedure is formulated to identify frequency bands that exhibit similar nonstationary patterns in the power spectrum through time. A formal hypothesis testing procedure is also developed to test which, if any, frequency bands remain stationary. This method is shown to consistently estimate the number of frequency bands and the location of the upper and lower bounds defining each frequency band. This method is used to estimate frequency bands useful in summarizing nonstationary behavior of full night heart rate variability data. / Statistics

This paper examines the components of the Capital Asset Pricing Model and the model's uses to analyze portfolios returns. It also looks at subsequent versions of the CAPM including a multi-variable CAPM with the inclusion of selected macro-variables as well as a non-stationary beta CAPM to estimate portfolio returns. A new model is proposed that combines the multi-variable component together with the non-stationary beta component to derive a new CAPM that is more effective at capturing current market conditions than the traditional CAPM with the fixed beta coefficient. The multi-variable CAPM with non-stationary beta is applied, together with the select macro-variables, to estimate the returns of a portfolio of assets in the oil-sector of the economy. It looks at returns during the period of 1995-2001 when the economy exhibited a wide range of variation in market returns. This paper tests the hypothesis that adapting the traditional CAPM to include beta non-stationarity will better estimate portfolio returns in a fluid market environment. The empirical results suggest that the new model is statistically significant at measuring portfolio returns. This model is estimated with an Ordinary Least Square (OLS) estimations process and identifies three factors that are statistically significant. These include quarterly changes in the Gross Domestic Product (GDP), the Unemployment Rate and the Consumer Price Index (CPI). / Master of Arts

In this dissertation, we develop a model selection and estimation methodology for nonstationary spatial fields. Large, spatially correlated data often cover a vast geographical area. However, local spatial regions may have different mean and covariance structures. Our methodology accomplishes three goals: (1) cluster locations into small regions with distinct, stationary models, (2) perform Bayesian model selection within each cluster, and (3) correlate the model selection and estimation in nearby clusters. We utilize the Conditional Autoregressive (CAR) model and Ising distribution to provide intra-cluster correlation on the linear effects and model inclusion indicators, while modeling inter-cluster correlation with separate Gaussian processes. We apply our model selection methodology to a dataset involving the prediction of Brook trout presence in subwatersheds across Pennsylvania. We find that our methodology outperforms the stationary spatial model and that different regions in Pennsylvania are governed by separate Gaussian process regression models. / Ph. D. / In this dissertation, we develop a statistical methodology for analyzing data where observations are related to each other due to spatial proximity. Our overall goal is to determine which attributes are important when predicting the response of interest. However, the effect and importance of an attribute may differ depending on the spatial location of the observation. Our methodology accomplishes three goals: (1) partition the observations into small spatial regions, (2) determine which attributes are important within each region, and (3) enforce that the importance of variables should be similar in regions that are near each other. We apply our technique to a dataset involving the prediction of Brook trout presence in subwatersheds across Pennsylvania.

Speech is a fundamental means of human communication. In the last several decades, much effort has been devoted to the efficient transmission and storage of speech signals. With advances in technology making mobile communication ubiquitous, communications anywhere has become a reality. The freedom and flexibility offered by mobile technology brings with it new challenges, one of which is robustness to acoustic background noise. Speech enhancement systems form a vital front-end for mobile telephony in noisy environments such as in cars, cafeterias, subway stations, etc., in hearing aids, and to improve the performance of speech recognition systems. In this thesis, which consists of four research articles, we discuss both single and multi-microphone approaches to speech enhancement. The main contribution of this thesis is a framework to exploit available prior knowledge about both speech and noise. The physiology of speech production places a constraint on the possible shapes of the speech spectral envelope, and this information s captured using codebooks of speech linear predictive (LP) coefficients obtained from a large training database. Similarly, information about commonly occurring noise types is captured using a set of noise codebooks, which can be combined with sound environment classi¯cation to treat different environments differently. In paper A, we introduce maximum-likelihood estimation of the speech and noise LP parameters using the codebooks. The codebooks capture only the spectral shape. The speech and noise gain factors are obtained through a frame-by-frame optimization, providing good performance in practical nonstationary noise environments. The estimated parameters are subsequently used in a Wiener filter. Paper B describes Bayesian minimum mean squared error estimation of the speech and noise LP parameters and functions there-of, while retaining the in- stantaneous gain computation. Both memoryless and memory-based estimators are derived. While papers A and B describe single-channel techniques, paper C describes a multi-channel Bayesian speech enhancement approach, where, in addition to temporal processing, the spatial diversity provided by multiple microphones s also exploited. In paper D, we introduce a multi-channel noise reduction technique motivated by blind source separation (BSS) concepts. In contrast to standard BSS approaches, we use the knowledge that one of the signals is speech and that the other is noise, and exploit their different characteristics. / QC 20100929