On the statistical estimation of diffusion processes: a survey

Data available on continuos-time diffusions are always sampled discretely in time. In most cases, the likelihood function of the observations is not directly computable. This survey covers a sample of the statistical methods that have been developed to solve this problem. We concentrate on some recent contributions to the literature based on three di§erent approaches to the problem: an improvement of the Euler-Maruyama discretization scheme, the use of Martingale Estimating Functions and the application of Generalized Method of Moments (GMM).

On the statistical estimation of diffusion processes - a partial survey

Data available on continuous-time diffusions are always sampled discretely in time. In most cases, the likelihood function of the observations is not directly computable. This survey covers a sample of the statistical methods that have been developed to solve this problem. We concentrate on some recent contributions to the literature based on three di§erent approaches to the problem: an improvement of the Euler-Maruyama discretization scheme, the employment of Martingale Estimating Functions, and the application of Generalized Method of Moments (GMM).

The statistical estimation of throughput and turnaround functions for a university computer system /

Vita.

Notes on the theory of statistical estimation and of testing hypotheses : lectures /

"Notes prepared by Ralph J. Brookner."

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.

MAXIMUM A-POSTERIORI ESTIMATION OF MISSING SAMPLES WITH CONTINUITY CONSTRAINT IN ELECTROMAGNETIC ARTICULOGRAPHY DATA

Electromagnetic Articulography (EMA) technique is used to record the kinematics of different articulators while one speaks. EMA data often contains missing segments due to sensor failure. In this work, we propose a maximum a-posteriori (MAP) estimation with continuity constraint to recover the missing samples in the articulatory trajectories recorded using EMA. In this approach, we combine the benefits of statistical MAP estimation as well as the temporal continuity of the articulatory trajectories. Experiments on articulatory corpus using different missing segment durations show that the proposed continuity constraint results in a 30% reduction in average root mean squared error in estimation over statistical estimation of missing segments without any continuity constraint.

New directions in sparse sampling and estimation for underdetermined systems

A central objective in signal processing is to infer meaningful information from a set of measurements or data. While most signal models have an overdetermined structure (the number of unknowns less than the number of equations), traditionally very few statistical estimation problems have considered a data model which is underdetermined (number of unknowns more than the number of equations). However, in recent times, an explosion of theoretical and computational methods have been developed primarily to study underdetermined systems by imposing sparsity on the unknown variables. This is motivated by the observation that inspite of the huge volume of data that arises in sensor networks, genomics, imaging, particle physics, web search etc., their information content is often much smaller compared to the number of raw measurements. This has given rise to the possibility of reducing the number of measurements by down sampling the data, which automatically gives rise to underdetermined systems.

In this thesis, we provide new directions for estimation in an underdetermined system, both for a class of parameter estimation problems and also for the problem of sparse recovery in compressive sensing. There are two main contributions of the thesis: design of new sampling and statistical estimation algorithms for array processing, and development of improved guarantees for sparse reconstruction by introducing a statistical framework to the recovery problem.

We consider underdetermined observation models in array processing where the number of unknown sources simultaneously received by the array can be considerably larger than the number of physical sensors. We study new sparse spatial sampling schemes (array geometries) as well as propose new recovery algorithms that can exploit priors on the unknown signals and unambiguously identify all the sources. The proposed sampling structure is generic enough to be extended to multiple dimensions as well as to exploit different kinds of priors in the model such as correlation, higher order moments, etc.

Recognizing the role of correlation priors and suitable sampling schemes for underdetermined estimation in array processing, we introduce a correlation aware framework for recovering sparse support in compressive sensing. We show that it is possible to strictly increase the size of the recoverable sparse support using this framework provided the measurement matrix is suitably designed. The proposed nested and coprime arrays are shown to be appropriate candidates in this regard. We also provide new guarantees for convex and greedy formulations of the support recovery problem and demonstrate that it is possible to strictly improve upon existing guarantees.

This new paradigm of underdetermined estimation that explicitly establishes the fundamental interplay between sampling, statistical priors and the underlying sparsity, leads to exciting future research directions in a variety of application areas, and also gives rise to new questions that can lead to stand-alone theoretical results in their own right.

Applications of Statistical Modeling in Iterative CT Image Reconstruction

Thesis (Master's)--University of Washington, 2015

Navigating emotion research during a paradigm shift in psychology

Human emotional responses are highly individual. A comprehensive analysis of emotion research in cognitive psychology and physiology, including laboratory-based experiments, showed that understanding human emotions requires a dynamic systems approach incorporating insights from scientific disciplines beyond psychology. Importantly, subjective and automatic evaluations of emotive information are context-sensitive and changeable, confirming the dynamic nature of emotion and role of individual differences. Furthermore, a comparison of different statistical approaches established that statistical estimation, rather than averages, best captures our highly individual emotional responses. Emotion research needs a cross-disciplinary approach.

Directed Assembly of Ultrathin Gold Nanowires over Large Area by Dielectrophoresis

Ultrathin Au nanowires (similar to 2 nm diameter) are interesting from a fundamental point of view to study structure and electronic transport and also hold promise in the field of nanoelectronics, particularly for sensing applications. Device fabrication by direct growth on various substrates has been useful in demonstrating some of the potential applications. However, the realization of practical devices requires device fabrication strategies that are fast, inexpensive, and efficient. Herein, we demonstrate directed assembly of ultrathin Au nanowires over large areas across electrodes using ac dielectrophoresis with a mechanistic understanding of the process. On the basis of the voltage and frequency, the wires either align in between or across the contact pads. We exploit this assembly to produce an array of contacting wires for statistical estimation of electrical transport with important implications for future nanoelectronic/sensor applications.

Support for Integrated Ecosystem Assessments of NOAA’s National Estuarine Research Reserves System (NERRS), Volume II: Assessment of Ecological Condition and Stressor Impacts in Subtidal Waters of the North Carolina NERRS

A study was conducted to assess the status of ecological condition and potential human-health risks in subtidal estuarine waters throughout the North Carolina National Estuarine Research Reserve System (NERRS) (Currituck Sound, Rachel Carson, Masonboro Island, and Zeke’s Island). Field work was conducted in September 2006 and incorporated multiple indicators of ecosystem condition including measures of water quality (dissolved oxygen, salinity, temperature, pH, nutrients and chlorophyll, suspended solids), sediment quality (granulometry, organic matter content, chemical contaminant concentrations), biological condition (diversity and abundances of benthic fauna, fish contaminant levels and pathologies), and human dimensions (fish-tissue contaminant levels relative to human-health consumption limits, various aesthetic properties). A probabilistic sampling design permitted statistical estimation of the spatial extent of degraded versus non-degraded condition across these estuaries relative to specified threshold levels of the various indicators (where possible). With some exceptions, the status of these reserves appeared to be in relatively good to fair ecological condition overall, with the majority of the area (about 54%) having various water quality, sediment quality, and biological (benthic) condition indicators rated in the healthy to intermediate range of corresponding guideline thresholds. Only three stations, representing 10.5% of the area, had one or more of these indicators rated as poor/degraded in all three categories. While such a conclusion is encouraging from a coastal management perspective, it should be viewed with some caution. For example, although co-occurrences of adverse biological and abiotic environmental conditions were limited, at least one indicator of ecological condition rated in the poor/degraded range was observed over a broader area (35.5%) represented by 11 of the 30 stations sampled. In addition, the fish-tissue contaminant data were not included in these overall spatial estimates; however, the majority of samples (77% of fish that were analyzed, from 79%, of stations where fish were caught) contained inorganic arsenic above the consumption limits for human cancer risks, though most likely derived from natural sources. Similarly, aesthetic indicators are not reflected in these spatial estimates of ecological condition, though there was evidence of noxious odors in sediments at many of the stations. Such symptoms reflect a growing realization that North Carolina estuaries are under multiple pressures from a variety of natural and human influences. These data also suggest that, while the current status of overall ecological condition appears to be good to fair, long-term monitoring is warranted to track potential changes in the future. This study establishes an important baseline of overall ecological condition within NC NERRS that can be used to evaluate any such future changes and to trigger appropriate management actions in this rapidly evolving coastal environment. (PDF contains 76 pages)

Simulation of Tail Weight Distributions in Biological Year 1986–2006 Landings of Brown Shrimp, Farfantepenaeus aztecus, from the Northern Gulf of Mexico Fishery

Size distribution within re- ported landings is an important aspect of northern Gulf of Mexico penaeid shrimp stock assessments. It reflects shrimp population characteristics such as numerical abundance of various sizes, age structure, and vital rates (e.g. recruitment, growth, and mortality), as well as effects of fishing, fishing power, fishing practices, sampling, size-grading, etc. The usual measure of shrimp size in archived landings data is count (C) the number of shrimp tails (abdomen or edible portion) per pound (0.4536 kg). Shrimp are marketed and landings reported in pounds within tail count categories. Statistically, these count categories are count class intervals or bins with upper and lower limits expressed in C. Count categories vary in width, overlap, and frequency of occurrence within the landings. The upper and lower limits of most count class intervals can be transformed to lower and upper limits (respectively) of class intervals expressed in pounds per shrimp tail, w, the reciprocal of C (i.e. w = 1/C). Age based stock assessments have relied on various algorithms to estimate numbers of shrimp from pounds landed within count categories. These algorithms required un- derlying explicit or implicit assumptions about the distribution of C or w. However, no attempts were made to assess the actual distribution of C or w. Therefore, validity of the algorithms and assumptions could not be determined. When different algorithms were applied to landings within the same size categories, they produced different estimates of numbers of shrimp. This paper demonstrates a method of simulating the distribution of w in reported biological year landings of shrimp. We used, as examples, landings of brown shrimp, Farfantepenaeus aztecus, from the northern Gulf of Mexico fishery in biological years 1986–2006. Brown shrimp biological year, Ti, is defined as beginning on 1 May of the same calendar year as Ti and ending on 30 April of the next calendar year, where subscript i is the place marker for biological year. Biological year landings encompass most if not all of the brown shrimp life cycle and life span. Simulated distributions of w reflect all factors influencing sizes of brown shrimp in the landings within a given biological year. Our method does not require a priori assumptions about the parent distributions of w or C, and it takes into account the variability in width, overlap, and frequency of occurrence of count categories within the landings. Simulated biological year distributions of w can be transformed to equivalent distributions of C. Our method may be useful in future testing of previously applied algorithms and development of new estimators based on statistical estimation theory and the underlying distribution of w or C. We also examine some applications of biological year distributions of w, and additional variables derived from them.

Shape from Contour

The problem of using image contours to infer the shapes and orientations of surfaces is treated as a problem of statistical estimation. The basis for solving this problem lies in an understanding of the geometry of contour formation, coupled with simple statistical models of the contour generating process. This approach is first applied to the special case of surfaces known to be planar. The distortion of contour shape imposed by projection is treated as a signal to be estimated, and variations of non-projective origin are treated as noise. The resulting method is then extended to the estimation of curved surfaces, and applied successfully to natural images. Next, the geometric treatment is further extended by relating countour curvature to surface curvature, using cast shadows as a model for contour generation. This geometric relation, combined with a statistical model, provides a measure of goodness-of-fit between a surface and an image contour. The goodness-of-fit measure is applied to the problem of establishing registration between an image and a surface model. Finally, the statistical estimation strategy is experimentally compared to human perception of orientation: human observers' judgements of tilt correspond closely to the estimates produced by the planar strategy.

A Geometric Approach to Slot Alignment in Wireless Sensor Networks

Traditionally, slotted communication protocols have employed guard times to delineate and align slots. These guard times may expand the slot duration significantly, especially when clocks are allowed to drift for longer time to reduce clock synchronization overhead. Recently, a new class of lightweight protocols for statistical estimation in wireless sensor networks have been proposed. This new class requires very short transmission durations (jam signals), thus the traditional approach of using guard times would impose significant overhead. We propose a new, more efficient algorithm to align slots. Based on geometrical properties of space, we prove that our approach bounds the slot duration by only a constant factor of what is needed. Furthermore, we show by simulation that this bound is loose and an even smaller slot duration is required, making our approach even more efficient.