Modern statistical models for forensic fingerprint examinations : a critical review

Over the last decade, the development of statistical models in support of forensic fingerprint identification has been the subject of increasing research attention, spurned on recently by commentators who claim that the scientific basis for fingerprint identification has not been adequately demonstrated. Such models are increasingly seen as useful tools in support of the fingerprint identification process within or in addition to the ACE-V framework. This paper provides a critical review of recent statistical models from both a practical and theoretical perspective. This includes analysis of models of two different methodologies: Probability of Random Correspondence (PRC) models that focus on calculating probabilities of the occurrence of fingerprint configurations for a given population, and Likelihood Ratio (LR) models which use analysis of corresponding features of fingerprints to derive a likelihood value representing the evidential weighting for a potential source.

Properties of ideal composite knots.

The shortest tube of constant diameter that can form a given knot represents the 'ideal' form of the knot. Ideal knots provide an irreducible representation of the knot, and they have some intriguing mathematical and physical features, including a direct correspondence with the time-averaged shapes of knotted DNA molecules in solution. Here we describe the properties of ideal forms of composite knots-knots obtained by the sequential tying of two or more independent knots (called factor knots) on the same string. We find that the writhe (related to the handedness of crossing points) of composite knots is the sum of that of the ideal forms of the factor knots. By comparing ideal composite knots with simulated configurations of knotted, thermally fluctuating DNA, we conclude that the additivity of writhe applies also to randomly distorted configurations of composite knots and their corresponding factor knots. We show that composite knots with several factor knots may possess distinct structural isomers that can be interconverted only by loosening the knot.

The Limits of Discrete Time Repeated Games:Some Notes and Comments

This paper studies the limits of discrete time repeated games with public monitoring. We solve and characterize the Abreu, Milgrom and Pearce (1991) problem. We found that for the "bad" ("good") news model the lower (higher) magnitude events suggest cooperation, i.e., zero punishment probability, while the highrt (lower) magnitude events suggest defection, i.e., punishment with probability one. Public correlation is used to connect these two sets of signals and to make the enforceability to bind. The dynamic and limit behavior of the punishment probabilities for variations in ... (the discount rate) and ... (the time interval) are characterized, as well as the limit payo¤s for all these scenarios (We also introduce uncertainty in the time domain). The obtained ... limits are to the best of my knowledge, new. The obtained ... limits coincide with Fudenberg and Levine (2007) and Fudenberg and Olszewski (2011), with the exception that we clearly state the precise informational conditions that cause the limit to converge from above, to converge from below or to degenerate. JEL: C73, D82, D86. KEYWORDS: Repeated Games, Frequent Monitoring, Random Pub- lic Monitoring, Moral Hazard, Stochastic Processes.

Bayesian tools for zero counts in compositional data

The log-ratio methodology makes available powerful tools for analyzing compositionaldata. Nevertheless, the use of this methodology is only possible for those data setswithout null values. Consequently, in those data sets where the zeros are present, aprevious treatment becomes necessary. Last advances in the treatment of compositionalzeros have been centered especially in the zeros of structural nature and in the roundedzeros. These tools do not contemplate the particular case of count compositional datasets with null values. In this work we deal with \count zeros" and we introduce atreatment based on a mixed Bayesian-multiplicative estimation. We use the Dirichletprobability distribution as a prior and we estimate the posterior probabilities. Then weapply a multiplicative modi¯cation for the non-zero values. We present a case studywhere this new methodology is applied.Key words: count data, multiplicative replacement, composition, log-ratio analysis

Bandwidth allocation based on real time calculations using the convolution approach

This paper focuses on one of the methods for bandwidth allocation in an ATM network: the convolution approach. The convolution approach permits an accurate study of the system load in statistical terms by accumulated calculations, since probabilistic results of the bandwidth allocation can be obtained. Nevertheless, the convolution approach has a high cost in terms of calculation and storage requirements. This aspect makes real-time calculations difficult, so many authors do not consider this approach. With the aim of reducing the cost we propose to use the multinomial distribution function: the enhanced convolution approach (ECA). This permits direct computation of the associated probabilities of the instantaneous bandwidth requirements and makes a simple deconvolution process possible. The ECA is used in connection acceptance control, and some results are presented

The subjectivist interpretation of probability and the problem of individualisation in forensic science

This paper presents and discusses further aspects of the subjectivist interpretation of probability (also known as the 'personalist' view of probabilities) as initiated in earlier forensic and legal literature. It shows that operational devices to elicit subjective probabilities - in particular the so-called scoring rules - provide additional arguments in support of the standpoint according to which categorical claims of forensic individualisation do not follow from a formal analysis under that view of probability theory.

Fast calculation of the CAC convolution algorithm using the multinomial distribution function

The authors focus on one of the methods for connection acceptance control (CAC) in an ATM network: the convolution approach. With the aim of reducing the cost in terms of calculation and storage requirements, they propose the use of the multinomial distribution function. This permits direct computation of the associated probabilities of the instantaneous bandwidth requirements. This in turn makes possible a simple deconvolution process. Moreover, under certain conditions additional improvements may be achieved

Incidence of HIV-1 drug resistance among antiretroviral treatment-naive individuals starting modern therapy combinations.

BACKGROUND: Estimates of drug resistance incidence to modern first-line combination antiretroviral therapies against human immunodeficiency virus (HIV) type 1 are complicated by limited availability of genotypic drug resistance tests (GRTs) and uncertain timing of resistance emergence. METHODS: Five first-line combinations were studied (all paired with lamivudine or emtricitabine): efavirenz (EFV) plus zidovudine (AZT) (n = 524); EFV plus tenofovir (TDF) (n = 615); lopinavir (LPV) plus AZT (n = 573); LPV plus TDF (n = 301); and ritonavir-boosted atazanavir (ATZ/r) plus TDF (n = 250). Virological treatment outcomes were classified into 3 risk strata for emergence of resistance, based on whether undetectable HIV RNA levels were maintained during therapy and, if not, whether viral loads were >500 copies/mL during treatment. Probabilities for presence of resistance mutations were estimated from GRTs (n = 2876) according to risk stratum and therapy received at time of testing. On the basis of these data, events of resistance emergence were imputed for each individual and were assessed using survival analysis. Imputation was repeated 100 times, and results were summarized by median values (2.5th-97.5th percentile range). RESULTS: Six years after treatment initiation, EFV plus AZT showed the highest cumulative resistance incidence (16%) of all regimens (<11%). Confounder-adjusted Cox regression confirmed that first-line EFV plus AZT (reference) was associated with a higher median hazard for resistance emergence, compared with other treatments: EFV plus TDF (hazard ratio [HR], 0.57; range, 0.42-0.76), LPV plus AZT (HR, 0.63; range, 0.45-0.89), LPV plus TDF (HR, 0.55; range, 0.33-0.83), ATZ/r plus TDF (HR, 0.43; range, 0.17-0.83). Two-thirds of resistance events were associated with detectable HIV RNA level ≤500 copies/mL during treatment, and only one-third with virological failure (HIV RNA level, >500 copies/mL). CONCLUSIONS: The inclusion of TDF instead of AZT and ATZ/r was correlated with lower rates of resistance emergence, most likely because of improved tolerability and pharmacokinetics resulting from a once-daily dosage.

Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocksbased on compositional statistics is introduced. It improves and generalizes the commonjoins-count statistics known from map analysis in geographic information systems.Assigning phases independently to objects in RD is modelled by a single-trial multinomialrandom function Z(x), where the probabilities of phases add to one and areexplicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistenciesof the tests based on the conventional joins{count statistics and their possiblycontradictory interpretations are avoided. In practical applications we assume that theprobabilities of phases do not depend on the location but are identical everywhere inthe domain of de nition. Thus, the model involves the sum of r independent identicalmultinomial distributed 1-trial random variables which is an r-trial multinomialdistributed random variable. The probabilities of the distribution of the r counts canbe considered as a composition in the Q-part simplex SQ. They span the so calledHardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This isa generalisation of the well-known Hardy-Weinberg law of genetics. If the assignmentof phases accounts for some kind of spatial dependence, then the r-trial probabilitiesdo not remain on H. This suggests the use of the Aitchison distance between observedprobabilities to H to test dependence. Moreover, when there is a spatial uctuation ofthe multinomial probabilities, the observed r-trial probabilities move on H. This shiftcan be used as to check for these uctuations. A practical procedure and an algorithmto perform the test have been developed. Some cases applied to simulated and realdata are presented.Key words: Spatial distribution of crystals in rocks, spatial distribution of phases,joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinbergmanifold, Aitchison geometry

Rate of gene sequence evolution and species diversification in flowering plants: a re-evaluation

Barraclough and co-workers (in a paper published in 1996) observed that there was a significant positive correlation between the rate of evolution of the rbcL chloroplast gene within families of flowering plants and the number of species in those families. We tested three additional data sets of our own (based on both plastid and nuclear genes) and used methods designed specifically for the comparison of sister families (based on random speciation and extinction). We show that, over all sister groups, the correlation between the rate of gene evolution and an increased diversity is not always present. Despite tending towards a positive association, the observation of individual probabilities presents a U-shaped distribution of association (i.e. it can be either significantly positive or negative). We discuss the influence of both phylogenetic sampling and applied taxonomies on the results.

Implementing statistical learning methods through Bayesian networks (Part 2): bayesian evaluations for results of black toner analyses in forensic document examination

This paper presents and discusses the use of Bayesian procedures - introduced through the use of Bayesian networks in Part I of this series of papers - for 'learning' probabilities from data. The discussion will relate to a set of real data on characteristics of black toners commonly used in printing and copying devices. Particular attention is drawn to the incorporation of the proposed procedures as an integral part in probabilistic inference schemes (notably in the form of Bayesian networks) that are intended to address uncertainties related to particular propositions of interest (e.g., whether or not a sample originates from a particular source). The conceptual tenets of the proposed methodologies are presented along with aspects of their practical implementation using currently available Bayesian network software.

The Farm, the city, and the emergence of social security

We study the social, demographic and economic origins of social security. The data for the U.S. and for a cross section of countries suggest that urbanization and industrialization are associated with the rise of social insurance. We describe an OLG model in which demographics, technology, and social security are linked together in a political economy equilibrium. In the model economy, there are two locations (sectors), the farm (agricultural) and the city (industrial) and the decision to migrate from rural to urban locations is endogenous and linked to productivity differences between the two locations and survival probabilities. Farmers rely on land inheritance for their old age and do not support a pay-as-you-go social security system. With structural change, people migrate to the city, the land loses its importance and support for social security arises. We show that a calibrated version of this economy, where social security taxes are determined by majority voting, is consistent with the historical transformation in the United States.

Driven fragmentation of granular gases

The dynamics of homogeneously heated granular gases which fragment due to particle collisions is analyzed. We introduce a kinetic model which accounts for correlations induced at the grain collisions and analyze both the kinetics and relevant distribution functions these systems develop. The work combines analytical and numerical studies based on direct simulation Monte Carlo calculations. A broad family of fragmentation probabilities is considered, and its implications for the system kinetics are discussed. We show that generically these driven materials evolve asymptotically into a dynamical scaling regime. If the fragmentation probability tends to a constant, the grain number diverges at a finite time, leading to a shattering singularity. If the fragmentation probability vanishes, then the number of grains grows monotonously as a power law. We consider different homogeneous thermostats and show that the kinetics of these systems depends weakly on both the grain inelasticity and driving. We observe that fragmentation plays a relevant role in the shape of the velocity distribution of the particles. When the fragmentation is driven by local stochastic events, the longvelocity tail is essentially exponential independently of the heating frequency and the breaking rule. However, for a Lowe-Andersen thermostat, numerical evidence strongly supports the conjecture that the scaled velocity distribution follows a generalized exponential behavior f (c)~exp (−cⁿ), with n ≈1.2, regarding less the fragmentation mechanisms

Combined impact of negative lifestyle factors on cardiovascular risk in children: a randomized prospective study.

PURPOSE: Negative lifestyle factors are known to be associated with increased cardiovascular risk (CVR) in children, but research on their combined impact on a general population of children is sparse. Therefore, we aimed to quantify the combined impact of easily assessable negative lifestyle factors on the CVR scores of randomly selected children after 4 years. METHODS: Of the 540 randomly selected 6- to 13-year-old children, 502 children participated in a baseline health assessment, and 64% were assessed again after 4 years. Measures included anthropometry, fasting blood samples, and a health assessment questionnaire. Participants scored one point for each negative lifestyle factor at baseline: overweight; physical inactivity; high media consumption; little outdoor time; skipping breakfast; and having a parent who has ever smoked, is inactive, or overweight. A CVR score at follow-up was constructed by averaging sex- and age-related z-scores of waist circumference, blood pressure, glucose, inverted high-density lipoprotein, and triglycerides. RESULTS: The age-, sex-, pubertal stage-, and social class-adjusted probabilities (95% confidence interval) for being in the highest CVR score tertile at follow-up for children who had at most one (n = 48), two (n = 64), three (n = 56), four (n = 41), or five or more (n = 14) risky lifestyle factors were 15.4% (8.9-25.3), 24.3% (17.4-32.8), 36.0% (28.6-44.2), 49.8% (38.6-61.0), and 63.5% (47.2-77.2), respectively. CONCLUSIONS: Even in childhood, an accumulation of negative lifestyle factors is associated with higher CVR scores after 4 years. These negative lifestyle factors are easy to assess in clinical practice and allow early detection and prevention of CVR in childhood.

Event-related potential analyses via single-subject topographic classification.

Introduction: Responses to external stimuli are typically investigated by averaging peri-stimulus electroencephalography (EEG) epochs in order to derive event-related potentials (ERPs) across the electrode montage, under the assumption that signals that are related to the external stimulus are fixed in time across trials. We demonstrate the applicability of a single-trial model based on patterns of scalp topographies (De Lucia et al, 2007) that can be used for ERP analysis at the single-subject level. The model is able to classify new trials (or groups of trials) with minimal a priori hypotheses, using information derived from a training dataset. The features used for the classification (the topography of responses and their latency) can be neurophysiologically interpreted, because a difference in scalp topography indicates a different configuration of brain generators. An above chance classification accuracy on test datasets implicitly demonstrates the suitability of this model for EEG data. Methods: The data analyzed in this study were acquired from two separate visual evoked potential (VEP) experiments. The first entailed passive presentation of checkerboard stimuli to each of the four visual quadrants (hereafter, "Checkerboard Experiment") (Plomp et al, submitted). The second entailed active discrimination of novel versus repeated line drawings of common objects (hereafter, "Priming Experiment") (Murray et al, 2004). Four subjects per experiment were analyzed, using approx. 200 trials per experimental condition. These trials were randomly separated in training (90%) and testing (10%) datasets in 10 independent shuffles. In order to perform the ERP analysis we estimated the statistical distribution of voltage topographies by a Mixture of Gaussians (MofGs), which reduces our original dataset to a small number of representative voltage topographies. We then evaluated statistically the degree of presence of these template maps across trials and whether and when this was different across experimental conditions. Based on these differences, single-trials or sets of a few single-trials were classified as belonging to one or the other experimental condition. Classification performance was assessed using the Receiver Operating Characteristic (ROC) curve. Results: For the Checkerboard Experiment contrasts entailed left vs. right visual field presentations for upper and lower quadrants, separately. The average posterior probabilities, indicating the presence of the computed template maps in time and across trials revealed significant differences starting at ~60-70 ms post-stimulus. The average ROC curve area across all four subjects was 0.80 and 0.85 for upper and lower quadrants, respectively and was in all cases significantly higher than chance (unpaired t-test, p<0.0001). In the Priming Experiment, we contrasted initial versus repeated presentations of visual object stimuli. Their posterior probabilities revealed significant differences, which started at 250ms post-stimulus onset. The classification accuracy rates with single-trial test data were at chance level. We therefore considered sub-averages based on five single trials. We found that for three out of four subjects' classification rates were significantly above chance level (unpaired t-test, p<0.0001). Conclusions: The main advantage of the present approach is that it is based on topographic features that are readily interpretable along neurophysiologic lines. As these maps were previously normalized by the overall strength of the field potential on the scalp, a change in their presence across trials and between conditions forcibly reflects a change in the underlying generator configurations. The temporal periods of statistical difference between conditions were estimated for each training dataset for ten shuffles of the data. Across the ten shuffles and in both experiments, we observed a high level of consistency in the temporal periods over which the two conditions differed. With this method we are able to analyze ERPs at the single-subject level providing a novel tool to compare normal electrophysiological responses versus single cases that cannot be considered part of any cohort of subjects. This aspect promises to have a strong impact on both basic and clinical research.