Electromyogram (EMG) is an established tool to study operation of neuromuscular systems. In analysing EMG signals, accurate detection of the movement-related events in the signal is frequently necessary. I explored the application of change-point detection algorithm proposed by Moskvina et. al., 2003 to EMG event detection, and evaluated the technique’s performance comparing it to two common threshold-based event detection methods and to the visual estimates of the EMG events performed by trained practitioners in the field. The algorithm was implemented in MATLAB and applied to EMG segments recorded from wrist and trunk muscles. The quality and frequency of successful detection were assessed for all methods, using the average visual estimate as the baseline, against which techniques were evaluated. The application showed that the change-point detection can successfully locate multiple changes in the EMG signal, but the maximum value of the detection statistic did not always identify the muscle activation onset.

<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

Electromyogram (EMG) is an established tool to study operation of neuromuscular systems. In analysing EMG signals, accurate detection of the movement-related events in the signal is frequently necessary. I explored the application of change-point detection algorithm proposed by Moskvina et. al., 2003 to EMG event detection, and evaluated the technique’s performance comparing it to two common threshold-based event detection methods and to the visual estimates of the EMG events performed by trained practitioners in the field. The algorithm was implemented in MATLAB and applied to EMG segments recorded from wrist and trunk muscles. The quality and frequency of successful detection were assessed for all methods, using the average visual estimate as the baseline, against which techniques were evaluated. The application showed that the change-point detection can successfully locate multiple changes in the EMG signal, but the maximum value of the detection statistic did not always identify the muscle activation onset.

Monte Carlo simulation methods are becoming increasingly important for solving difficult optimization problems. Monte Carlo methods are often used when it is infeasible to determine an exact result via a deterministic algorithm, such as with NP or #P problems. Several recent Monte Carlo techniques employ the idea of importance sampling; examples include the Cross-Entropy method and sequential importance sampling. The Cross-Entropy method is a relatively new Monte Carlo technique that has been successfully applied to a wide range of optimization and estimation problems since introduced by R. Y. Rubinstein in 1997. However, as the problem size increases, the Cross-Entropy method, like many heuristics, can take an exponentially increasing amount of time before it returns a solution. For large problems this can lead to an impractical amount of running time. A main aim of this thesis is to develop the Cross-Entropy method for large-scale parallel computing, allowing the running time of a Cross-Entropy program to be significantly reduced by the use of additional computing resources. The effectiveness of the parallel approach is demonstrated via a number of numerical studies. A second aim is to apply the Cross-Entropy method and sequential importance sampling to biological problems, in particular the multiple change-point problem for DNA sequences. The multiple change-point problem in a general setting is the problem of identifying, given a particular sequence of numbers/characters, a point along that sequence where some property of interest changes abruptly. An example in a biological setting, is identifying points in a DNA sequence where there is a significant change in the proportion of the nucleotides G and C with respect to the nucleotides A and T. We show that both sequential importance sampling and the Cross-Entropy approach yield significant improvements in time and/or accuracy over existing techniques.

Thesis (Ph.D.)--Baylor University, 2008. / Includes bibliographical references (p.84-86)

The main subject of this thesis is a change point detection in stationary vector autoregressions. Various test statistics are proposed for the retrospective break point detection in the parameters of such models, in particular, the derivation of their asymptotic distribution under the null hypothesis of no change. Testing procedures are based on the maximum like- lihood principle and are derived under normality, nevertheless the asymptotic results are valid for broader class of distributions and involve also the models with certain form of dependence. Simulation studies document the quality of the results.

This thesis deals with the detection of change in the intercept in panel data re- gression model. We are interested in testing a null hypothesis that there was no change in the intercept during the observation period in case with no depen- dency between panels and with the number of panels and observations in each panel going to infinity. Based on the results for simplified case with no additional regressors we propose a statistical test and show its properties. We also derive a consistent estimate of the parameter of change based on the least squares me- thod. The main contribution of the thesis is the derivation of theoretical results of the proposed test while variances of errors are known and its modification for unknown variance parameters. A large simulation study is conducted to examine the results. Then we present an application to real data, particularly we use four factor CAPM model to detect change in monthly returns of US mutual funds during an observation period 2004-2011 and show a significant change during the sub-prime crisis in 2007-2008. This work expands existing results for de- tecting changes in the mean in panel data and offers many directions for further beneficial research. 1

Change-point detection aims to reveal sudden changes in sequences of data. Special attention has been paid to the detection of abrupt level shifts, and applications of such techniques can be found in a great variety of fields, such as monitoring of climate change, examination of gene expressions and quality control in the manufacturing industry. In this work, we compared the performance of two methods representing frequentist and Bayesian approaches, respectively. The frequentist approach involved a preliminary search for level shifts using a tree algorithm followed by a dynamic programming algorithm for optimizing the locations and sizes of the level shifts. The Bayesian approach involved an MCMC (Markov chain Monte Carlo) implementation of a method originally proposed by Barry and Hartigan. The two approaches were implemented in R and extensive simulations were carried out to assess both their computational efficiency and ability to detect abrupt level shifts. Our study showed that the overall performance regarding the estimated location and size of change-points was comparable for the Bayesian and frequentist approach. However, the Bayesian approach performed better when the number of change-points was small; whereas the frequentist became stronger when the change-point proportion increased. The latter method was also better at detecting simultaneous change-points in vector time series. Theoretically, the Bayesian approach has a lower computational complexity than the frequentist approach, but suitable settings for the combined tree and dynamic programming can greatly reduce the processing time.

BACKGROUND - Bipolar disorder has been postulated as an explanation for King John's inconsistencies of leadership and vagaries of character. Changes in activity, matching those in mood, are core features of the condition. METHOD - A measure of King John's activity was derived from his travelling itinerary. Change Point Analysis (CPA) was used to detect significant changes in that travelling activity and from them, to identify clinically compliant, high and low, activity time periods. The results were tested against an alternative mathematical model (Bollinger Bands™), three alternative parameters and two comparator itineraries (familial & non-familial). Using primary historical sources and published analyses, bipolar symptoms were identified and their temporal relationship to the ICD-10 compliant CPA periods evaluated. The influence of circumstances was also evaluated using primary sources and a representative sequential sample (1200-1204). RESULTS - CPA identified 83 periods of changed travelling activity. These changes were mathematically independent of the availability of the historical sources that underpin the itinerary. From these, 37 high and 22 low periods complied with current diagnostic guidelines and demonstrated descriptive and statistical similarities to those found in the bipolar literature. Analyses using alternative mathematical modelling and different parameters showed similar changes; analyses of comparator itineraries showed a possible familial trait. Of the 17 bipolar symptoms identified, all were found in CPA periods of appropriate polarity. Of the 23 sequential periods, 10 showed evidence of behaviour that was difficult to attribute to circumstances. CONCLUSIONS & OUTCOMES - The pattern of changes in King John's activity are highly suggestive of bipolar disorder with primary historical sources describing synchronous bipolar behaviour. This may alter our understanding both of King John and of Magna Carta. Change Point Analysis merits greater consideration when analysing time based data, as does the use of activity as an objective marker of human behaviour.

This thesis details several applications of Gaussian processes (GPs) for enhanced time series modeling. We first cover different approaches for using Gaussian processes in time series problems. These are extended to the state space approach to time series in two different problems. We also combine Gaussian processes and Bayesian online change point detection (BOCPD) to increase the generality of the Gaussian process time series methods. These methodologies are evaluated on predictive performance on six real world data sets, which include three environmental data sets, one financial, one biological, and one from industrial well drilling. Gaussian processes are capable of generalizing standard linear time series models. We cover two approaches: the Gaussian process time series model (GPTS) and the autoregressive Gaussian process (ARGP).We cover a variety of methods that greatly reduce the computational and memory complexity of Gaussian process approaches, which are generally cubic in computational complexity. Two different improvements to state space based approaches are covered. First, Gaussian process inference and learning (GPIL) generalizes linear dynamical systems (LDS), for which the Kalman filter is based, to general nonlinear systems for nonparametric system identification. Second, we address pathologies in the unscented Kalman filter (UKF).We use Gaussian process optimization (GPO) to learn UKF settings that minimize the potential for sigma point collapse. We show how to embed mentioned Gaussian process approaches to time series into a change point framework. Old data, from an old regime, that hinders predictive performance is automatically and elegantly phased out. The computational improvements for Gaussian process time series approaches are of even greater use in the change point framework. We also present a supervised framework learning a change point model when change point labels are available in training.