Bayesian statistical analysis of bacterial diversity

Bacteria play an important role in many ecological systems. The molecular characterization of bacteria using either cultivation-dependent or cultivation-independent methods reveals the large scale of bacterial diversity in natural communities, and the vastness of subpopulations within a species or genus. Understanding how bacterial diversity varies across different environments and also within populations should provide insights into many important questions of bacterial evolution and population dynamics. This thesis presents novel statistical methods for analyzing bacterial diversity using widely employed molecular fingerprinting techniques. The first objective of this thesis was to develop Bayesian clustering models to identify bacterial population structures. Bacterial isolates were identified using multilous sequence typing (MLST), and Bayesian clustering models were used to explore the evolutionary relationships among isolates. Our method involves the inference of genetic population structures via an unsupervised clustering framework where the dependence between loci is represented using graphical models. The population dynamics that generate such a population stratification were investigated using a stochastic model, in which homologous recombination between subpopulations can be quantified within a gene flow network. The second part of the thesis focuses on cluster analysis of community compositional data produced by two different cultivation-independent analyses: terminal restriction fragment length polymorphism (T-RFLP) analysis, and fatty acid methyl ester (FAME) analysis. The cluster analysis aims to group bacterial communities that are similar in composition, which is an important step for understanding the overall influences of environmental and ecological perturbations on bacterial diversity. A common feature of T-RFLP and FAME data is zero-inflation, which indicates that the observation of a zero value is much more frequent than would be expected, for example, from a Poisson distribution in the discrete case, or a Gaussian distribution in the continuous case. We provided two strategies for modeling zero-inflation in the clustering framework, which were validated by both synthetic and empirical complex data sets. We show in the thesis that our model that takes into account dependencies between loci in MLST data can produce better clustering results than those methods which assume independent loci. Furthermore, computer algorithms that are efficient in analyzing large scale data were adopted for meeting the increasing computational need. Our method that detects homologous recombination in subpopulations may provide a theoretical criterion for defining bacterial species. The clustering of bacterial community data include T-RFLP and FAME provides an initial effort for discovering the evolutionary dynamics that structure and maintain bacterial diversity in the natural environment.

Statistical and Information-Theoretic Methods for Data-Analysis

In this Thesis, we develop theory and methods for computational data analysis. The problems in data analysis are approached from three perspectives: statistical learning theory, the Bayesian framework, and the information-theoretic minimum description length (MDL) principle. Contributions in statistical learning theory address the possibility of generalization to unseen cases, and regression analysis with partially observed data with an application to mobile device positioning. In the second part of the Thesis, we discuss so called Bayesian network classifiers, and show that they are closely related to logistic regression models. In the final part, we apply the MDL principle to tracing the history of old manuscripts, and to noise reduction in digital signals.

Learning Nonlinear Visual Processing from Natural Images

The paradigm of computational vision hypothesizes that any visual function -- such as the recognition of your grandparent -- can be replicated by computational processing of the visual input. What are these computations that the brain performs? What should or could they be? Working on the latter question, this dissertation takes the statistical approach, where the suitable computations are attempted to be learned from the natural visual data itself. In particular, we empirically study the computational processing that emerges from the statistical properties of the visual world and the constraints and objectives specified for the learning process. This thesis consists of an introduction and 7 peer-reviewed publications, where the purpose of the introduction is to illustrate the area of study to a reader who is not familiar with computational vision research. In the scope of the introduction, we will briefly overview the primary challenges to visual processing, as well as recall some of the current opinions on visual processing in the early visual systems of animals. Next, we describe the methodology we have used in our research, and discuss the presented results. We have included some additional remarks, speculations and conclusions to this discussion that were not featured in the original publications. We present the following results in the publications of this thesis. First, we empirically demonstrate that luminance and contrast are strongly dependent in natural images, contradicting previous theories suggesting that luminance and contrast were processed separately in natural systems due to their independence in the visual data. Second, we show that simple cell -like receptive fields of the primary visual cortex can be learned in the nonlinear contrast domain by maximization of independence. Further, we provide first-time reports of the emergence of conjunctive (corner-detecting) and subtractive (opponent orientation) processing due to nonlinear projection pursuit with simple objective functions related to sparseness and response energy optimization. Then, we show that attempting to extract independent components of nonlinear histogram statistics of a biologically plausible representation leads to projection directions that appear to differentiate between visual contexts. Such processing might be applicable for priming, \ie the selection and tuning of later visual processing. We continue by showing that a different kind of thresholded low-frequency priming can be learned and used to make object detection faster with little loss in accuracy. Finally, we show that in a computational object detection setting, nonlinearly gain-controlled visual features of medium complexity can be acquired sequentially as images are encountered and discarded. We present two online algorithms to perform this feature selection, and propose the idea that for artificial systems, some processing mechanisms could be selectable from the environment without optimizing the mechanisms themselves. In summary, this thesis explores learning visual processing on several levels. The learning can be understood as interplay of input data, model structures, learning objectives, and estimation algorithms. The presented work adds to the growing body of evidence showing that statistical methods can be used to acquire intuitively meaningful visual processing mechanisms. The work also presents some predictions and ideas regarding biological visual processing.

Treasurer's reports of Hayman Levy

Digital image

Statistical methods for analysis of multi-harvest data from perennial pasture variety selection trials

Variety selection in perennial pasture crops involves identifying best varieties from data collected from multiple harvest times in field trials. For accurate selection, the statistical methods for analysing such data need to account for the spatial and temporal correlation typically present. This paper provides an approach for analysing multi-harvest data from variety selection trials in which there may be a large number of harvest times. Methods are presented for modelling the variety by harvest effects while accounting for the spatial and temporal correlation between observations. These methods provide an improvement in model fit compared to separate analyses for each harvest, and provide insight into variety by harvest interactions. The approach is illustrated using two traits from a lucerne variety selection trial. The proposed method provides variety predictions allowing for the natural sources of variation and correlation in multi-harvest data.

Statistical analysis of spectral data: A methodology for designing an intelligent monitoring system for the diabetic foot

Early detection of (pre-)signs of ulceration on a diabetic foot is valuable for clinical practice. Hyperspectral imaging is a promising technique for detection and classification of such (pre-)signs. However, the number of the spectral bands should be limited to avoid overfitting, which is critical for pixel classification with hyperspectral image data. The goal was to design a detector/classifier based on spectral imaging (SI) with a small number of optical bandpass filters. The performance and stability of the design were also investigated. The selection of the bandpass filters boils down to a feature selection problem. A dataset was built, containing reflectance spectra of 227 skin spots from 64 patients, measured with a spectrometer. Each skin spot was annotated manually by clinicians as "healthy" or a specific (pre-)sign of ulceration. Statistical analysis on the data set showed the number of required filters is between 3 and 7, depending on additional constraints on the filter set. The stability analysis revealed that shot noise was the most critical factor affecting the classification performance. It indicated that this impact could be avoided in future SI systems with a camera sensor whose saturation level is higher than 106, or by postimage processing.

Second-order statistical structure of geomagnetic field reversals

From the autocorrelation function of geomagnetic polarity intervals, it is shown that the field reversal intervals are not independent but form a process akin to the Markov process, where the random input to the model is itself a moving average process. The input to the moving average model is, however, an independent Gaussian random sequence. All the parameters in this model of the geomagnetic field reversal have been estimated. In physical terms this model implies that the mechanism of reversal possesses a memory.

Empirical Analysis of Competition in Procurement Auctions

A vast amount of public services and goods are contracted through procurement auctions. Therefore it is very important to design these auctions in an optimal way. Typically, we are interested in two different objectives. The first objective is efficiency. Efficiency means that the contract is awarded to the bidder that values it the most, which in the procurement setting means the bidder that has the lowest cost of providing a service with a given quality. The second objective is to maximize public revenue. Maximizing public revenue means minimizing the costs of procurement. Both of these goals are important from the welfare point of view. In this thesis, I analyze field data from procurement auctions and show how empirical analysis can be used to help design the auctions to maximize public revenue. In particular, I concentrate on how competition, which means the number of bidders, should be taken into account in the design of auctions. In the first chapter, the main policy question is whether the auctioneer should spend resources to induce more competition. The information paradigm is essential in analyzing the effects of competition. We talk of a private values information paradigm when the bidders know their valuations exactly. In a common value information paradigm, the information about the value of the object is dispersed among the bidders. With private values more competition always increases the public revenue but with common values the effect of competition is uncertain. I study the effects of competition in the City of Helsinki bus transit market by conducting tests for common values. I also extend an existing test by allowing bidder asymmetry. The information paradigm seems to be that of common values. The bus companies that have garages close to the contracted routes are influenced more by the common value elements than those whose garages are further away. Therefore, attracting more bidders does not necessarily lower procurement costs, and thus the City should not implement costly policies to induce more competition. In the second chapter, I ask how the auctioneer can increase its revenue by changing contract characteristics like contract sizes and durations. I find that the City of Helsinki should shorten the contract duration in the bus transit auctions because that would decrease the importance of common value components and cheaply increase entry which now would have a more beneficial impact on the public revenue. Typically, cartels decrease the public revenue in a significant way. In the third chapter, I propose a new statistical method for detecting collusion and compare it with an existing test. I argue that my test is robust to unobserved heterogeneity unlike the existing test. I apply both methods to procurement auctions that contract snow removal in schools of Helsinki. According to these tests, the bidding behavior of two of the bidders seems consistent with a contract allocation scheme.

Conceptual and statistical modelling of environmental effects in population dynamics

Population dynamics are generally viewed as the result of intrinsic (purely density dependent) and extrinsic (environmental) processes. Both components, and potential interactions between those two, have to be modelled in order to understand and predict dynamics of natural populations; a topic that is of great importance in population management and conservation. This thesis focuses on modelling environmental effects in population dynamics and how effects of potentially relevant environmental variables can be statistically identified and quantified from time series data. Chapter I presents some useful models of multiplicative environmental effects for unstructured density dependent populations. The presented models can be written as standard multiple regression models that are easy to fit to data. Chapters II IV constitute empirical studies that statistically model environmental effects on population dynamics of several migratory bird species with different life history characteristics and migration strategies. In Chapter II, spruce cone crops are found to have a strong positive effect on the population growth of the great spotted woodpecker (Dendrocopos major), while cone crops of pine another important food resource for the species do not effectively explain population growth. The study compares rate- and ratio-dependent effects of cone availability, using state-space models that distinguish between process and observation error in the time series data. Chapter III shows how drought, in combination with settling behaviour during migration, produces asymmetric spatially synchronous patterns of population dynamics in North American ducks (genus Anas). Chapter IV investigates the dynamics of a Finnish population of skylark (Alauda arvensis), and point out effects of rainfall and habitat quality on population growth. Because the skylark time series and some of the environmental variables included show strong positive autocorrelation, the statistical significances are calculated using a Monte Carlo method, where random autocorrelated time series are generated. Chapter V is a simulation-based study, showing that ignoring observation error in analyses of population time series data can bias the estimated effects and measures of uncertainty, if the environmental variables are autocorrelated. It is concluded that the use of state-space models is an effective way to reach more accurate results. In summary, there are several biological assumptions and methodological issues that can affect the inferential outcome when estimating environmental effects from time series data, and that therefore need special attention. The functional form of the environmental effects and potential interactions between environment and population density are important to deal with. Other issues that should be considered are assumptions about density dependent regulation, modelling potential observation error, and when needed, accounting for spatial and/or temporal autocorrelation.

Constructing the ideal victim in the United States of America's annual trafficking in persons reports

Human trafficking as a global phenomenon continues to elude accurate quantitative measure, and remains a controversial policy domain significantly influenced by anecdotal evidence. Drawing on the policy analysis framework of Bacchi (1999; 2007) the problem representation of trafficking through narratives can be considered a direct antecedent of contemporary anti-human trafficking policy. This article explores the construction of human trafficking within the Trafficking in Persons Reports, published annually by the United States of America’s Department of State. An examination of the victim and offender narratives contained within the reports published between 2001 and 2012 demonstrates that human trafficking is predominantly represented as a crime committed by ideal offenders against idealized victims, consistent with Christie’s (1986) landmark criteria of ideal victimization. This representation of an ideal prototype has the potential to inform policy that diverts focus from the causative role of global socioeconomic injustice towards criminal justice policies targeting individual offenders.

Aircraft trajectory clustering techniques using circular statistics

This paper presents a statistical aircraft trajectory clustering approach aimed at discriminating between typical manned and expected unmanned traffic patterns. First, a resampled version of each trajectory is modelled using a mixture of Von Mises distributions (circular statistics). Second, the remodelled trajectories are globally aligned using tools from bioinformatics. Third, the alignment scores are used to cluster the trajectories using an iterative k-medoids approach and an appropriate distance function. The approach is then evaluated using synthetically generated unmanned aircraft flights combined with real air traffic position reports taken over a sector of Northern Queensland, Australia. Results suggest that the technique is useful in distinguishing between expected unmanned and manned aircraft traffic behaviour, as well as identifying some common conventional air traffic patterns.

Asteroid identification using statistical orbital inversion methods

An efficient and statistically robust solution for the identification of asteroids among numerous sets of astrometry is presented. In particular, numerical methods have been developed for the short-term identification of asteroids at discovery, and for the long-term identification of scarcely observed asteroids over apparitions, a task which has been lacking a robust method until now. The methods are based on the solid foundation of statistical orbital inversion properly taking into account the observational uncertainties, which allows for the detection of practically all correct identifications. Through the use of dimensionality-reduction techniques and efficient data structures, the exact methods have a loglinear, that is, O(nlog(n)), computational complexity, where n is the number of included observation sets. The methods developed are thus suitable for future large-scale surveys which anticipate a substantial increase in the astrometric data rate. Due to the discontinuous nature of asteroid astrometry, separate sets of astrometry must be linked to a common asteroid from the very first discovery detections onwards. The reason for the discontinuity in the observed positions is the rotation of the observer with the Earth as well as the motion of the asteroid and the observer about the Sun. Therefore, the aim of identification is to find a set of orbital elements that reproduce the observed positions with residuals similar to the inevitable observational uncertainty. Unless the astrometric observation sets are linked, the corresponding asteroid is eventually lost as the uncertainty of the predicted positions grows too large to allow successful follow-up. Whereas the presented identification theory and the numerical comparison algorithm are generally applicable, that is, also in fields other than astronomy (e.g., in the identification of space debris), the numerical methods developed for asteroid identification can immediately be applied to all objects on heliocentric orbits with negligible effects due to non-gravitational forces in the time frame of the analysis. The methods developed have been successfully applied to various identification problems. Simulations have shown that the methods developed are able to find virtually all correct linkages despite challenges such as numerous scarce observation sets, astrometric uncertainty, numerous objects confined to a limited region on the celestial sphere, long linking intervals, and substantial parallaxes. Tens of previously unknown main-belt asteroids have been identified with the short-term method in a preliminary study to locate asteroids among numerous unidentified sets of single-night astrometry of moving objects, and scarce astrometry obtained nearly simultaneously with Earth-based and space-based telescopes has been successfully linked despite a substantial parallax. Using the long-term method, thousands of realistic 3-linkages typically spanning several apparitions have so far been found among designated observation sets each spanning less than 48 hours.

Process variability-aware statistical hybrid modeling of dynamic power dissipation in 65 nm CMOS designs

A generalized technique is proposed for modeling the effects of process variations on dynamic power by directly relating the variations in process parameters to variations in dynamic power of a digital circuit. The dynamic power of a 2-input NAND gate is characterized by mixed-mode simulations, to be used as a library element for 65mn gate length technology. The proposed methodology is demonstrated with a multiplier circuit built using the NAND gate library, by characterizing its dynamic power through Monte Carlo analysis. The statistical technique of Response. Surface Methodology (RSM) using Design of Experiments (DOE) and Least Squares Method (LSM), are employed to generate a "hybrid model" for gate power to account for simultaneous variations in multiple process parameters. We demonstrate that our hybrid model based statistical design approach results in considerable savings in the power budget of low power CMOS designs with an error of less than 1%, with significant reductions in uncertainty by atleast 6X on a normalized basis, against worst case design.

Author response: "Missed opportunity related to statistical methods"

"We thank MrGilder for his considered comments and suggestions for alternative analyses of our data. We also appreciate Mr Gilder’s support of our call for larger studies to contribute to the evidence base for preoperative loading with high-carbohydrate fluids..."