A Bayesian network approach to the database serch problem in criminal proceedings

Background The 'database search problem', that is, the strengthening of a case - in terms of probative value - against an individual who is found as a result of a database search, has been approached during the last two decades with substantial mathematical analyses, accompanied by lively debate and centrally opposing conclusions. This represents a challenging obstacle in teaching but also hinders a balanced and coherent discussion of the topic within the wider scientific and legal community. This paper revisits and tracks the associated mathematical analyses in terms of Bayesian networks. Their derivation and discussion for capturing probabilistic arguments that explain the database search problem are outlined in detail. The resulting Bayesian networks offer a distinct view on the main debated issues, along with further clarity. Methods As a general framework for representing and analyzing formal arguments in probabilistic reasoning about uncertain target propositions (that is, whether or not a given individual is the source of a crime stain), this paper relies on graphical probability models, in particular, Bayesian networks. This graphical probability modeling approach is used to capture, within a single model, a series of key variables, such as the number of individuals in a database, the size of the population of potential crime stain sources, and the rarity of the corresponding analytical characteristics in a relevant population. Results This paper demonstrates the feasibility of deriving Bayesian network structures for analyzing, representing, and tracking the database search problem. The output of the proposed models can be shown to agree with existing but exclusively formulaic approaches. Conclusions The proposed Bayesian networks allow one to capture and analyze the currently most well-supported but reputedly counter-intuitive and difficult solution to the database search problem in a way that goes beyond the traditional, purely formulaic expressions. The method's graphical environment, along with its computational and probabilistic architectures, represents a rich package that offers analysts and discussants with additional modes of interaction, concise representation, and coherent communication.

Inference about the number of contributors to a DNA mixture: Comparative analyses of a Bayesian network approach and the maximum allele count method.

In the forensic examination of DNA mixtures, the question of how to set the total number of contributors (N) presents a topic of ongoing interest. Part of the discussion gravitates around issues of bias, in particular when assessments of the number of contributors are not made prior to considering the genotypic configuration of potential donors. Further complication may stem from the observation that, in some cases, there may be numbers of contributors that are incompatible with the set of alleles seen in the profile of a mixed crime stain, given the genotype of a potential contributor. In such situations, procedures that take a single and fixed number contributors as their output can lead to inferential impasses. Assessing the number of contributors within a probabilistic framework can help avoiding such complication. Using elements of decision theory, this paper analyses two strategies for inference on the number of contributors. One procedure is deterministic and focuses on the minimum number of contributors required to 'explain' an observed set of alleles. The other procedure is probabilistic using Bayes' theorem and provides a probability distribution for a set of numbers of contributors, based on the set of observed alleles as well as their respective rates of occurrence. The discussion concentrates on mixed stains of varying quality (i.e., different numbers of loci for which genotyping information is available). A so-called qualitative interpretation is pursued since quantitative information such as peak area and height data are not taken into account. The competing procedures are compared using a standard scoring rule that penalizes the degree of divergence between a given agreed value for N, that is the number of contributors, and the actual value taken by N. Using only modest assumptions and a discussion with reference to a casework example, this paper reports on analyses using simulation techniques and graphical models (i.e., Bayesian networks) to point out that setting the number of contributors to a mixed crime stain in probabilistic terms is, for the conditions assumed in this study, preferable to a decision policy that uses categoric assumptions about N.

A neuron-glia signalling network in the active brain.

Glial cells are active partners of neurons in processing information and synaptic integration. They receive coded signals from synapses and elaborate modulatory responses. The active properties of glia, including long-range signalling and regulated transmitter release, are beginning to be elucidated. Recent insights suggest that the active brain should no longer be regarded as a circuitry of neuronal contacts, but as an integrated network of interactive neurons and glia.

Relevant gender differences in epidemiological profile, exposure to first antiretroviral regimen and survival in the Spanish AIDS Research Network Cohort.

BACKGROUND The possible differences in the disease spectrum and prognosis of HIV infection in women and men is a major point of concern. Women are under-represented in randomized clinical trials and in some cohorts. Discordant results have often been obtained depending on the setting. METHODS We assessed gender differences in clinical and epidemiological features, antiretroviral treatment (ART) exposure and survival in two multicentre cohorts of HIV-positive subjects in Spain: CoRIS-MD and CoRIS. Competing risk regression models were used to assess gender effect on time to start ART and time to first ART change, and a Cox regression model to estimate gender effect on time to death. RESULTS Between January 1996 and December 2008, 1,953 women and 6,072 men naive to ART at study entry were included. The trend analysis over time showed the percentage of women in the younger (<20 years) and older (>50 years) strata increased significantly (P<0.001) from 0.5% and 1.8% in 1996 to 4.9% and 4.2% in 2008, respectively. By competing risk analysis women started ART earlier than men (adjusted subhazard ratio [ASHR] 1.21, 95% CI 1.11, 1.31) in CoRIS cohort, while in CoRIS-MD none of these differences were observed. In both cohorts women showed a shorter time to the first ART change (ASHR 1.10, 95% CI 1.01, 1.19). Pregnancy and patient's/physician's decisions as reasons for changing were more frequent in women than in men in CoRIS. In the Cox regression model, gender was not associated with differences in survival. CONCLUSIONS In two large cohorts in Spain, we observed relevant gender differences in epidemiological characteristics and antiretroviral exposure outcomes, while survival differences were not attributable to gender.

From SNPs to pathways: integration of functional effect of sequence variations on models of cell signalling pathways

Background: Single nucleotide polymorphisms (SNPs) are the most frequent type of sequence variation between individuals, and represent a promising tool for finding genetic determinants of complex diseases and understanding the differences in drug response. In this regard, it is of particular interest to study the effect of non-synonymous SNPs in the context of biological networks such as cell signalling pathways. UniProt provides curated information about the functional and phenotypic effects of sequence variation, including SNPs, as well as on mutations of protein sequences. However, no strategy has been developed to integrate this information with biological networks, with the ultimate goal of studying the impact of the functional effect of SNPs in the structure and dynamics of biological networks. Results: First, we identified the different challenges posed by the integration of the phenotypic effect of sequence variants and mutations with biological networks. Second, we developed a strategy for the combination of data extracted from public resources, such as UniProt, NCBI dbSNP, Reactome and BioModels. We generated attribute files containing phenotypic and genotypic annotations to the nodes of biological networks, which can be imported into network visualization tools such as Cytoscape. These resources allow the mapping and visualization of mutations and natural variations of human proteins and their phenotypic effect on biological networks (e.g. signalling pathways, protein-protein interaction networks, dynamic models). Finally, an example on the use of the sequence variation data in the dynamics of a network model is presented. Conclusion: In this paper we present a general strategy for the integration of pathway and sequence variation data for visualization, analysis and modelling purposes, including the study of the functional impact of protein sequence variations on the dynamics of signalling pathways. This is of particular interest when the SNP or mutation is known to be associated to disease. We expect that this approach will help in the study of the functional impact of disease-associated SNPs on the behaviour of cell signalling pathways, which ultimately will lead to a better understanding of the mechanisms underlying complex diseases.

Wavelet analysis residual kriging vs. neural network residual kriging

This paper deals with the problem of spatial data mapping. A new method based on wavelet interpolation and geostatistical prediction (kriging) is proposed. The method - wavelet analysis residual kriging (WARK) - is developed in order to assess the problems rising for highly variable data in presence of spatial trends. In these cases stationary prediction models have very limited application. Wavelet analysis is used to model large-scale structures and kriging of the remaining residuals focuses on small-scale peculiarities. WARK is able to model spatial pattern which features multiscale structure. In the present work WARK is applied to the rainfall data and the results of validation are compared with the ones obtained from neural network residual kriging (NNRK). NNRK is also a residual-based method, which uses artificial neural network to model large-scale non-linear trends. The comparison of the results demonstrates the high quality performance of WARK in predicting hot spots, reproducing global statistical characteristics of the distribution and spatial correlation structure.

Network revenue management with product-specific no-shows

Revenue management practices often include overbooking capacity to account for customerswho make reservations but do not show up. In this paper, we consider the network revenuemanagement problem with no-shows and overbooking, where the show-up probabilities are specificto each product. No-show rates differ significantly by product (for instance, each itinerary andfare combination for an airline) as sale restrictions and the demand characteristics vary byproduct. However, models that consider no-show rates by each individual product are difficultto handle as the state-space in dynamic programming formulations (or the variable space inapproximations) increases significantly. In this paper, we propose a randomized linear program tojointly make the capacity control and overbooking decisions with product-specific no-shows. Weestablish that our formulation gives an upper bound on the optimal expected total profit andour upper bound is tighter than a deterministic linear programming upper bound that appearsin the existing literature. Furthermore, we show that our upper bound is asymptotically tightin a regime where the leg capacities and the expected demand is scaled linearly with the samerate. We also describe how the randomized linear program can be used to obtain a bid price controlpolicy. Computational experiments indicate that our approach is quite fast, able to scale to industrialproblems and can provide significant improvements over standard benchmarks.

A randomized concave programming method for choice network revenue management

Models incorporating more realistic models of customer behavior, as customers choosing froman offer set, have recently become popular in assortment optimization and revenue management.The dynamic program for these models is intractable and approximated by a deterministiclinear program called the CDLP which has an exponential number of columns. However, whenthe segment consideration sets overlap, the CDLP is difficult to solve. Column generationhas been proposed but finding an entering column has been shown to be NP-hard. In thispaper we propose a new approach called SDCP to solving CDLP based on segments and theirconsideration sets. SDCP is a relaxation of CDLP and hence forms a looser upper bound onthe dynamic program but coincides with CDLP for the case of non-overlapping segments. Ifthe number of elements in a consideration set for a segment is not very large (SDCP) can beapplied to any discrete-choice model of consumer behavior. We tighten the SDCP bound by(i) simulations, called the randomized concave programming (RCP) method, and (ii) by addingcuts to a recent compact formulation of the problem for a latent multinomial-choice model ofdemand (SBLP+). This latter approach turns out to be very effective, essentially obtainingCDLP value, and excellent revenue performance in simulations, even for overlapping segments.By formulating the problem as a separation problem, we give insight into why CDLP is easyfor the MNL with non-overlapping considerations sets and why generalizations of MNL posedifficulties. We perform numerical simulations to determine the revenue performance of all themethods on reference data sets in the literature.

Dietary folates and cancer risk in a network of case-control studies.

Background Folate deficiency leads to DNA damage and inadequate repair, caused by a decreased synthesis of thymidylate and purines. We analyzed the relationship between dietary folate intake and the risk of several cancers. Patients and methods The study is based on a network of case-control studies conducted in Italy and Switzerland in 1991-2009. The odds ratios (ORs) for dietary folate intake were estimated by multiple logistic regression models, adjusted for major identified confounding factors. Results For a few cancer sites, we found a significant inverse relation, with ORs for an increment of 100 μg/day of dietary folate of 0.65 for oropharyngeal (1467 cases), 0.58 for esophageal (505 cases), 0.83 for colorectal (2390 cases), 0.72 for pancreatic (326 cases), 0.67 for laryngeal (851 cases) and 0.87 for breast (3034 cases) cancers. The risk estimates were below unity, although not significantly, for cancers of the endometrium (OR = 0.87, 454 cases), ovary (OR = 0.86, 1031 cases), prostate (OR = 0.91, 1468 cases) and kidney (OR = 0.88, 767 cases), and was 1.00 for stomach cancer (230 cases). No material heterogeneity was found in strata of sex, age, smoking and alcohol drinking. Conclusions Our data support a real inverse association of dietary folate intake with the risk of several common cancers.

A tractable consideration set structure for network revenue management

Models incorporating more realistic models of customer behavior, as customers choosing from an offerset, have recently become popular in assortment optimization and revenue management. The dynamicprogram for these models is intractable and approximated by a deterministic linear program called theCDLP which has an exponential number of columns. When there are products that are being consideredfor purchase by more than one customer segment, CDLP is difficult to solve since column generationis known to be NP-hard. However, recent research indicates that a formulation based on segments withcuts imposing consistency (SDCP+) is tractable and approximates the CDLP value very closely. In thispaper we investigate the structure of the consideration sets that make the two formulations exactly equal.We show that if the segment consideration sets follow a tree structure, CDLP = SDCP+. We give acounterexample to show that cycles can induce a gap between the CDLP and the SDCP+ relaxation.We derive two classes of valid inequalities called flow and synchronization inequalities to further improve(SDCP+), based on cycles in the consideration set structure. We give a numeric study showing theperformance of these cycle-based cuts.

Diabetes mellitus and cancer risk in a network of case-control studies.

Diabetes has been associated to the risk of a few cancer sites, though quantification of this association in various populations remains open to discussion. We analyzed the relation between diabetes and the risk of various cancers in an integrated series of case-control studies conducted in Italy and Switzerland between 1991 and 2009. The studies included 1,468 oral and pharyngeal, 505 esophageal, 230 gastric, 2,390 colorectal, 185 liver, 326 pancreatic, 852 laryngeal, 3,034 breast, 607 endometrial, 1,031 ovarian, 1,294 prostate, and 767 renal cell cancer cases and 12,060 hospital controls. The multivariate odds ratios (OR) for subjects with diabetes as compared to those without-adjusted for major identified confounding factors for the cancers considered through logistic regression models-were significantly elevated for cancers of the oral cavity/pharynx (OR = 1.58), esophagus (OR = 2.52), colorectum (OR = 1.23), liver (OR = 3.52), pancreas (OR = 3.32), postmenopausal breast (OR = 1.76), and endometrium (OR = 1.70). For cancers of the oral cavity, esophagus, colorectum, liver, and postmenopausal breast, the excess risk persisted over 10 yr since diagnosis of diabetes. Our data confirm and further quantify the association of diabetes with colorectal, liver, pancreatic, postmenopausal breast, and endometrial cancer and suggest forthe first time that diabetes may also increase the risk of oral/pharyngeal and esophageal cancer. [Table: see text] [Table: see text].

Aggregate fluctuations and the network structure of intersectoral trade

This paper analyzes the flow of intermediate inputs across sectors by adopting a network perspective on sectoral interactions. I apply these tools to show how fluctuationsin aggregate economic activity can be obtained from independent shocks to individualsectors. First, I characterize the network structure of input trade in the U.S. On thedemand side, a typical sector relies on a small number of key inputs and sectors arehomogeneous in this respect. However, in their role as input-suppliers sectors do differ:many specialized input suppliers coexist alongside general purpose sectors functioningas hubs to the economy. I then develop a model of intersectoral linkages that can reproduce these connectivity features. In a standard multisector setup, I use this modelto provide analytical expressions linking aggregate volatility to the network structureof input trade. I show that the presence of sectoral hubs - by coupling productiondecisions across sectors - leads to fluctuations in aggregates.

On bounds for network revenue management

The Network Revenue Management problem can be formulated as a stochastic dynamic programming problem (DP or the\optimal" solution V *) whose exact solution is computationally intractable. Consequently, a number of heuristics have been proposed in the literature, the most popular of which are the deterministic linear programming (DLP) model, and a simulation based method, the randomized linear programming (RLP) model. Both methods give upper bounds on the optimal solution value (DLP and PHLP respectively). These bounds are used to provide control values that can be used in practice to make accept/deny decisions for booking requests. Recently Adelman [1] and Topaloglu [18] have proposed alternate upper bounds, the affine relaxation (AR) bound and the Lagrangian relaxation (LR) bound respectively, and showed that their bounds are tighter than the DLP bound. Tight bounds are of great interest as it appears from empirical studies and practical experience that models that give tighter bounds also lead to better controls (better in the sense that they lead to more revenue). In this paper we give tightened versions of three bounds, calling themsAR (strong Affine Relaxation), sLR (strong Lagrangian Relaxation) and sPHLP (strong Perfect Hindsight LP), and show relations between them. Speciffically, we show that the sPHLP bound is tighter than sLR bound and sAR bound is tighter than the LR bound. The techniques for deriving the sLR and sPHLP bounds can potentially be applied to other instances of weakly-coupled dynamic programming.

An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer-set, andthe firm decides the best subset to offer at any given moment to maximize expected revenue. The resultingdynamic program for the firm is intractable and approximated by a deterministic linear programcalled the CDLP which has an exponential number of columns. However, under the choice-set paradigmwhen the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has beenproposed but finding an entering column has been shown to be NP-hard. In this paper, starting with aconcave program formulation based on segment-level consideration sets called SDCP, we add a class ofconstraints called product constraints, that project onto subsets of intersections. In addition we proposea natural direct tightening of the SDCP called ?SDCP, and compare the performance of both methodson the benchmark data sets in the literature. Both the product constraints and the ?SDCP method arevery simple and easy to implement and are applicable to the case of overlapping segment considerationsets. In our computational testing on the benchmark data sets in the literature, SDCP with productconstraints achieves the CDLP value at a fraction of the CPU time taken by column generation and webelieve is a very promising approach for quickly approximating CDLP when segment consideration setsoverlap and the consideration sets themselves are relatively small.