Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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It is believed that fingerprints are determined in embryonic development. Unlike other personal characteristics the fingerprint appears to be a result of a random process. For example fingerprints of identical twins (whose DNA is identical) are distinct, and extensive studies have found little evidence of a genetic relationship in terms of types of fingerprint, certainly at the small scale. At a larger scale the pattern of ridges on fingerprints can be categorised as belonging to one of five basic forms: loops (left and right), whorls, arches and tented arches. The population frequencies of these types show little variation with ethnicity and a list of the types occurring on the ten digits can be used as an initial basis for identification of individuals. However, such a system would not uniquely identify an individual although the frequency of certain combinations could be extremely small. At a smaller scale various minutiae or singularities can be observed in a fingerprint. These include ridge endings and bifurcations, amongst others. Typical fingerprints have several hundred of these as well as two key points (with the exception of a simple arch) referred to as the core and delta, which are focal points of the overall pattern of ridges. Modern identification systems are based upon ridge endings and bifurcations, not least because they are the easiest to determine automatically from image analysis. The configuration of these minutiae is unique to the individual. This research explores the relationship between the locations of minutiae to determine if they can be modelled using a statistical process. In addition, since the approach is based on how fingerprints can be examined in a forensic situation an algorithm is created and tested which allows the strength of a match between a fingermark left at a crime and a fingerprint from a known suspect to be calculated. Currently the result of matching a fingermark and fingerprint is expressed as a categorical value of; match, no match or inconclusive. The method in this research allows this to be expressed as a numerical value allowing for a wider and more flexible use of fingerprint evidence.

This thesis describes the development of statistical methods for facial identification. The objective is to provide a technique which can provide answers based on probabilities to the question of whether two images of a face are from the same person or whether there could be two different people whose facial images match equally well. The aim would be to contribute to evidence that an image captured, for example, at a crime scene by CCTV, is that of a suspect in custody. The methods developed are based on the underlying mathematics of faces (specifically the shape of the configuration of identified landmarks) At present expert witnesses carry out facial comparisons to assess how alike two faces are and their declared expert opinions are inevitably subjective. To develop the method a large population study was carried out to explore facial variation. Sets of measurements of landmarks were digitally taken from ≈3000 facial images and Procrustes analyses were performed to extract the underlying face shapes and used to estimate the parameters in statistical model for the population of face shapes. This allows pairs of faces to be compared in relation to population variability using a multivariate normal likelihood ratio (MVNLR) procedure. The MVNLR technique is a recognised means for evidence evaluation, and is widely used for example on trace evidence and DNA matching. However, many modifications and adaptations were required because of unique aspects of facial data such as high dimensionality, differential reliabilities of landmark identification and differential distinctiveness within the population of certain facial features. The thesis describes techniques of selection of appropriate landmarks and novel dimensionality reduction methods to accommodate these aspects involving non-sequential selection of principal components (to avoid ephemeral facial expressions) and balancing of measures of reliability against selectivity and specificity.

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One major aim of statistics is to systematically study outcomes of interest in a population by observing the properties of a sample of that population. Some outcomes, such as the total number of people infected in an epidemic, can depend on properties of the whole population, such as the structure of contacts among the individuals, or contact network. A network is a collection of individuals as well as the pairwise connections between them. This dissertation explores how the effects of network structure on infectious outcomes yield challenges for statistical analysis, and suggests strategies to address them. In Section I, we consider an intervention to reduce the spread of an epidemic on a collection of individuals in partially-connected networks, and show how network structure and mixing across networks can reduce the probability of observing true intervention effects, or statistical power. In Section II, we show how accounting for estimated properties of an epidemic contact network can improve statistical power, and that this improvement depends on the properties of the whole network as well as the epidemic spreading through them. Finally, in Section III, we derive the conditions under which a particular kind of network - the Degree-Corrected Stochastic Blockmodel - is susceptible to extensive epidemic spread, enabling statistical analysts to estimate when and to what extent the challenges and corrections explored here require consideration. We will conclude with a discussion of how the estimates and derivations in the final two sections can be used as adjustment covariates when assessing the effect of treatment on epidemic spread. / Biostatistics

This dissertation presents three independent essays in microeconomic theory. Chapter 1 suggests an alternative to the common prior assumption, in which agents form beliefs by learning from data, possibly interpreting the data in different ways. In the limit as agents observe increasing quantities of data, the model returns strict solutions of a limiting complete information game, but predictions may diverge substantially for small quantities of data. Chapter 2 (with Jon Kleinberg and Sendhil Mullainathan) proposes use of machine learning algorithms to construct benchmarks for “achievable" predictive accuracy. The paper illustrates this approach for the problem of predicting human-generated random sequences. We find that leading models explain approximately 10-15% of predictable variation in the problem. Chapter 3 considers the problem of how to interpret inconsistent choice data, when the observed departures from the standard model (perfect maximization of a single preference) may emerge either from context-dependencies in preference or from stochastic choice error. I show that if preferences are “simple" in the sense that they consist only of a small number of context-dependencies, then the analyst can use a proposed optimization problem to recover the true number of underlying context-dependent preferences. / Economics

Studies of complex systems and agent-based models often focus on the relationship between microscopic behaviour and phenomena on a macroscopic level. Such models have applications in sociology, biology and economics. Here we study specific models in evolutionary game theory and game learning, analysing the differences between deterministic, population-level descriptions and stochastic, individual-level descriptions. We also examine the relationships between individual actions and global features in data from a financial market. Attempts to explain the emergence of altruism commonly use evolutionary game theory. Here, stochastic models can exhibit continued oscillations when the equivalent deterministic dynamics approach a fixed point. We classify the power spectra of such stochastic oscillations using an expansion of the master equation in the inverse system size. We find that the choice of update rule can have significant effects on the frequency and amplitude of these fluctuations.In light of recent experimental setups of social dilemmas to test the applicability of evolutionary theories to human players, we show that noise-induced oscillations can also be found in models of multiplayer game learning. We again perform an expansion in the noise strength to classify these oscillations analytically. We examine the effect that the parameters of the model can have on these fluctuations in both well-mixed and networked setups. We also use financial time series from the Spanish Stock Market to quantify features of the actions of individual trading firms. Examining how trades impact prices we find that the variety of individual behaviours cannot be inferred from that of the market. We test the applicability of an existing model by Bouchaud et al for reconstructing the response of the price to trades over time and show that it does not extend to describing any particular firm.

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Some of the more significant effects of global warming are manifested in the rise of temperatures and the increased intensity of hurricanes. This study analyzed data on Annual, January and July temperatures in Miami in the period spanning from 1949 to 2011; as well as data on central pressure and radii of maximum winds of hurricanes from 1944 to present. Annual Average, Maximum and Minimum Temperatures were found to be increasing with time. Also July Average, Maximum and Minimum Temperatures were found to be increasing with time. On the other hand, no significant trend could be detected for January Average, Maximum and Minimum Temperatures. No significant trend was detected in the central pressures and radii of maximum winds of hurricanes, while the radii of maximum winds for the largest hurricane of the year showed an increasing trend.