Search results for: Bayesian nets

Authors: Alexandru-Ion Marinescu

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There exist a plethora of methods in the scientific literature which tackle the well-established task of credit score evaluation. In its most abstract form, a credit scoring algorithm takes as input several credit applicant properties, such as age, marital status, employment status, loan duration, etc. and must output a binary response variable (i.e. “GOOD” or “BAD”) stating whether the client is susceptible to payment return delays. Data imbalance is a common occurrence among financial institution databases, with the majority being classified as “GOOD” clients (clients that respect the loan return calendar) alongside a small percentage of “BAD” clients. But it is the “BAD” clients we are interested in since accurately predicting their behavior is crucial in preventing unwanted loss for loan providers. We add to this whole context the constraint that the algorithm must yield an actual, tractable mathematical formula, which is friendlier towards financial analysts. To this end, we have turned to genetic algorithms and genetic programming, aiming to evolve actual mathematical expressions using specially tailored mutation and crossover operators. As far as data representation is concerned, we employ a very flexible mechanism – LINQ expression trees, readily available in the C# programming language, enabling us to construct executable pieces of code at runtime. As the title implies, they model trees, with intermediate nodes being operators (addition, subtraction, multiplication, division) or mathematical functions (sin, cos, abs, round, etc.) and leaf nodes storing either constants or variables. There is a one-to-one correspondence between the client properties and the formula variables. The mutation and crossover operators work on a flattened version of the tree, obtained via a pre-order traversal. A consequence of our chosen technique is that we can identify and discard client properties which do not take part in the final score evaluation, effectively acting as a dimensionality reduction scheme. We compare ourselves with state of the art approaches, such as support vector machines, Bayesian networks, and extreme learning machines, to name a few. The data sets we benchmark against amount to a total of 8, of which we mention the well-known Australian credit and German credit data sets, and the performance indicators are the following: percentage correctly classified, area under curve, partial Gini index, H-measure, Brier score and Kolmogorov-Smirnov statistic, respectively. Finally, we obtain encouraging results, which, although placing us in the lower half of the hierarchy, drive us to further refine the algorithm.

Keywords: expression trees, financial credit scoring, genetic algorithm, genetic programming, symbolic evolution

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Authors: Yiqi Zhu, Jean Francois Trani, Rameez Ulhassan

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Extreme weather phenomena increased by 46% between 2007 and 2017 and have become more intense with the rise in global average temperatures. This increased intensity of climate variations often induces humanitarian crises and particularly affects vulnerable populations in low- and middle-income countries (LMICs). Expectant and lactating mothers are among the most vulnerable groups. Pakistan ranks 10th among the most affected countries by climate disasters. In 2022, monsoon floods submerged a third of the country, causing the loss of 1,500 lives. Approximately 650,000 expectant and lactating mothers faced systematic stress from climatic disasters. Our study used participatory methods to investigate the systematic impact of climatic disasters on maternal health. In March 2023, we conducted six Group Model Building (GMB) workshops with healthcare workers, fathers, and mothers separately in two of the most affected areas in Pakistan. This study was approved by the Islamic Relief Research Review Board. GMB workshops consist of three sessions. In the first session, participants discussed the factors that impact maternal health. After identifying the factors, they discussed the connections among them and explored the system structures that collectively impact maternal health. Based on the discussion, a causal loop diagram (CLD) was created. Finally, participants discussed action ideas that could improve the system to enhance maternal health. Based on our discussions and the causal loop diagram, we identified interconnected factors at the family, community, and policy levels. Mothers and children are directly impacted by three interrelated factors: food insecurity, unstable housing, and lack of income. These factors create a reinforcing cycle that negatively affects both mothers and newborns. After the flood, many mothers were unable to produce sufficient breastmilk due to their health status. Without breastmilk and sufficient food for complementary feeding, babies tend to get sick in damp and unhygienic environments resulting from temporary or unstable housing. When parents take care of sick children, they miss out on income-generating opportunities. At the community level, the lack of access to clean water and sanitation (WASH) and maternal healthcare further worsens the situation. Structural failures such as a lack of safety nets and programs associated with flood preparedness make families increasingly vulnerable with each disaster. Several families reported that they had not fully recovered from a flood that occurred ten years ago, and this latest disaster destroyed their lives again. Although over twenty non-profit organizations are working in these villages, few of them provide sustainable support. Therefore, participants called for systemic changes in response to the increasing frequency of climate disasters. The study reveals the systematic vulnerabilities of mothers and children after climatic disasters. The most vulnerable populations are often affected the most by climate change. Collaborative efforts are required to improve water and forest management, strengthen public infrastructure, increase access to WASH, and gradually build climate-resilient communities. Governments, non-governmental organizations, and the community should work together to develop and implement effective strategies to prevent, mitigate, and adapt to climate change and its impacts.

Keywords: climatic disasters, maternal health, Pakistan, systematic impact, flood, disaster relief.

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Authors: Lydia Tan, Philippe Lemey, Lieselot Houspie, Marco Viveen, Darren Martin, Frank Coenjaerts

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Introduction: Human respiratory syncytial virus (hRSV) is the leading cause of severe respiratory tract infections in infants under the age of two. Genomic substitutions and related evolutionary dynamics of hRSV are of great influence on virus transmission behavior. The evolutionary patterns formed are due to a precarious interplay between the host immune response and RSV, thereby selecting the most viable and less immunogenic strains. Studying genomic profiles can teach us which genes and consequent proteins play an important role in RSV survival and transmission dynamics. Study design: In this study, genetic diversity and evolutionary rate analysis were conducted on 36 RSV subgroup B whole genome sequences and 37 subgroup A genome sequences. Clinical RSV isolates were obtained from nasopharyngeal aspirates and swabs of children between 2 weeks and 5 years old of age. These strains, collected during epidemic seasons from 2001 to 2011 in the Netherlands and Belgium by either conventional or 454-sequencing. Sequences were analyzed for genetic diversity, recombination events, synonymous/non-synonymous substitution ratios, epistasis, and translational consequences of mutations were mapped to known 3D protein structures. We used Bayesian statistical inference to estimate the rate of RSV genome evolution and the rate of variability across the genome. Results: The A and B profiles were described in detail and compared to each other. Overall, the majority of the whole RSV genome is highly conserved among all strains. The attachment protein G was the most variable protein and its gene had, similar to the non-coding regions in RSV, more elevated (two-fold) substitution rates than other genes. In addition, the G gene has been identified as the major target for diversifying selection. Overall, less gene and protein variability was found within RSV-B compared to RSV-A and most protein variation between the subgroups was found in the F, G, SH and M2-2 proteins. For the F protein mutations and correlated amino acid changes are largely located in the F2 ligand-binding domain. The small hydrophobic phosphoprotein and nucleoprotein are the most conserved proteins. The evolutionary rates were similar in both subgroups (A: 6.47E-04, B: 7.76E-04 substitution/site/yr), but estimates of the time to the most recent common ancestor were much lower for RSV-B (B: 19, A: 46.8 yrs), indicating that there is more turnover in this subgroup. Conclusion: This study provides a detailed description of whole RSV genome mutations, the effect on translation products and the first estimate of the RSV genome evolution tempo. The immunogenic G protein seems to require high substitution rates in order to select less immunogenic strains and other conserved proteins are most likely essential to preserve RSV viability. The resulting G gene variability makes its protein a less interesting target for RSV intervention methods. The more conserved RSV F protein with less antigenic epitope shedding is, therefore, more suitable for developing therapeutic strategies or vaccines.

Keywords: drug target selection, epidemiology, respiratory syncytial virus, RSV

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Authors: Jean-Philippe Amat, Timothée Vergne, Aymeric Hans, Bénédicte Ferry, Pascal Hendrikx, Jackie Tapprest, Barbara Dufour, Agnès Leblond

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The surveillance of infectious diseases is necessary to describe their occurrence and help the planning, implementation and evaluation of risk mitigation activities. However, the exact number of detected cases may remain unknown whether surveillance is based on serological tests because identifying seroconversion may be difficult. Moreover, incomplete detection of cases or outbreaks is a recurrent issue in the field of disease surveillance. This study addresses these two issues. Using a viral animal disease as an example (equine viral arteritis), the goals were to establish suitable rules for identifying seroconversion in order to estimate the number of cases and outbreaks detected by a surveillance system in France between 2006 and 2013, and to assess the sensitivity of this system by estimating the total number of outbreaks that occurred during this period (including unreported outbreaks) using a capture-recapture model. Data from horses which exhibited at least one positive result in serology using viral neutralization test between 2006 and 2013 were used for analysis (n=1,645). Data consisted of the annual antibody titers and the location of the subjects (towns). A consensus among multidisciplinary experts (specialists in the disease and its laboratory diagnosis, epidemiologists) was reached to consider seroconversion as a change in antibody titer from negative to at least 32 or as a three-fold or greater increase. The number of seroconversions was counted for each town and modeled using a unilist zero-truncated binomial (ZTB) capture-recapture model with R software. The binomial denominator was the number of horses tested in each infected town. Using the defined rules, 239 cases located in 177 towns (outbreaks) were identified from 2006 to 2013. Subsequently, the sensitivity of the surveillance system was estimated as the ratio of the number of detected outbreaks to the total number of outbreaks that occurred (including unreported outbreaks) estimated using the ZTB model. The total number of outbreaks was estimated at 215 (95% credible interval CrI95%: 195-249) and the surveillance sensitivity at 82% (CrI95%: 71-91). The rules proposed for identifying seroconversion may serve future research. Such rules, adjusted to the local environment, could conceivably be applied in other countries with surveillance programs dedicated to this disease. More generally, defining ad hoc algorithms for interpreting the antibody titer could be useful regarding other human and animal diseases and zoonosis when there is a lack of accurate information in the literature about the serological response in naturally infected subjects. This study shows how capture-recapture methods may help to estimate the sensitivity of an imperfect surveillance system and to valorize surveillance data. The sensitivity of the surveillance system of equine viral arteritis is relatively high and supports its relevance to prevent the disease spreading.

Keywords: Bayesian inference, capture-recapture, epidemiology, equine viral arteritis, infectious disease, seroconversion, surveillance

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Authors: Samia Elfekih, Wee Tek Tay, Karl Gordon, Paul De Barro

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Invasive species represent an increasing threat to food biosecurity, causing significant economic losses in agricultural systems. An example is the sweet potato whitefly, Bemisia tabaci, which is a complex of morphologically indistinguishable species causing average annual global damage estimated at US$2.4 billion. The Bemisia complex represents an interesting model for evolutionary studies because of their extensive distribution and potential for invasiveness and population expansion. Within this complex, two species, Middle East-Asia Minor 1 (MEAM1) and Mediterranean (MED) have invaded well beyond their home ranges whereas others, such as Indian Ocean (IO) and Australia (AUS), have not. In order to understand why some Bemisia species have become invasive, genome-wide sequence scans were used to estimate population dynamics over time and relate these to climate. The Bayesian Skyline Plot (BSP) method as implemented in BEAST was used to infer the historical effective population size. In order to overcome sampling bias, the populations were combined based on geographical origin. The datasets used for this particular analysis are genome-wide SNPs (single nucleotide polymorphisms) called separately in each of the following groups: Sub-Saharan Africa (Burkina Faso), Europe (Spain, France, Greece and Croatia), USA (Arizona), Mediterranean-Middle East (Israel, Italy), Middle East-Central Asia (Turkmenistan, Iran) and Reunion Island. The non-invasive ‘AUS’ species endemic to Australia was used as an outgroup. The main findings of this study show that the BSP for the Sub-Saharan African MED population is different from that observed in MED populations from the Mediterranean Basin, suggesting evolution under a different set of environmental conditions. For MED, the effective size of the African (Burkina Faso) population showed a rapid expansion ≈250,000-310,000 years ago (YA), preceded by a period of slower growth. The European MED populations (i.e., Spain, France, Croatia, and Greece) showed a single burst of expansion at ≈160,000-200,000 YA. The MEAM1 populations from Israel and Italy and the ones from Iran and Turkmenistan are similar as they both show the earlier expansion at ≈250,000-300,000 YA. The single IO population lacked the latter expansion but had the earlier one. This pattern is shared with the Sub-Saharan African (Burkina Faso) MED, suggesting IO also faced a similar history of environmental change, which seems plausible given their relatively close geographical distributions. In conclusion, populations within the invasive species MED and MEAM1 exhibited signatures of population expansion lacking in non-invasive species (IO and AUS) during the Pleistocene, a geological epoch marked by repeated climatic oscillations with cycles of glacial and interglacial periods. These expansions strongly suggested the potential of some Bemisia species’ genomes to affect their adaptability and invasiveness.

Keywords: whitefly, RADseq, invasive species, SNP, climate change

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Authors: Vitor M. Vilas Boas, Cleison D. Silva, Gustavo S. Mafra, Alexandre Trofino Neto

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Motor imagery (MI) based brain-computer interfaces (BCI) uses event-related (de)synchronization (ERS/ ERD), typically recorded using electroencephalography (EEG), to translate brain electrical activity into control commands. To mitigate undesirable artifacts and noise measurements on EEG signals, methods based on band-pass filters defined by a specific frequency band (i.e., 8 – 30Hz), such as the Infinity Impulse Response (IIR) filters, are typically used. Spatial techniques, such as Common Spatial Patterns (CSP), are also used to estimate the variations of the filtered signal and extract features that define the imagined motion. The CSP effectiveness depends on the subject's discriminative frequency, and approaches based on the decomposition of the band of interest into sub-bands with smaller frequency ranges (SBCSP) have been suggested to EEG signals classification. However, despite providing good results, the SBCSP approach generally increases the computational cost of the filtering step in IM-based BCI systems. This paper proposes the use of the Fast Fourier Transform (FFT) algorithm in the IM-based BCI filtering stage that implements SBCSP. The goal is to apply the FFT algorithm to reduce the computational cost of the processing step of these systems and to make them more efficient without compromising classification accuracy. The proposal is based on the representation of EEG signals in a matrix of coefficients resulting from the frequency decomposition performed by the FFT, which is then submitted to the SBCSP process. The structure of the SBCSP contemplates dividing the band of interest, initially defined between 0 and 40Hz, into a set of 33 sub-bands spanning specific frequency bands which are processed in parallel each by a CSP filter and an LDA classifier. A Bayesian meta-classifier is then used to represent the LDA outputs of each sub-band as scores and organize them into a single vector, and then used as a training vector of an SVM global classifier. Initially, the public EEG data set IIa of the BCI Competition IV is used to validate the approach. The first contribution of the proposed method is that, in addition to being more compact, because it has a 68% smaller dimension than the original signal, the resulting FFT matrix maintains the signal information relevant to class discrimination. In addition, the results showed an average reduction of 31.6% in the computational cost in relation to the application of filtering methods based on IIR filters, suggesting FFT efficiency when applied in the filtering step. Finally, the frequency decomposition approach improves the overall system classification rate significantly compared to the commonly used filtering, going from 73.7% using IIR to 84.2% using FFT. The accuracy improvement above 10% and the computational cost reduction denote the potential of FFT in EEG signal filtering applied to the context of IM-based BCI implementing SBCSP. Tests with other data sets are currently being performed to reinforce such conclusions.

Keywords: brain-computer interfaces, fast Fourier transform algorithm, motor imagery, sub-band common spatial patterns

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Authors: Vikas Kumar, Kailash Chandra, Kaomud Tyagi

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The insect order Thysanoptera includes small insects commonly called thrips. As insect vectors, only thrips are capable of Tospoviruses transmission (genus Tospovirus, family Bunyaviridae) affecting various crops. Currently, fifteen species of subfamily Thripinae (Thripidae) have been reported as vectors for tospoviruses. Frankliniella schultzei, which is reported as act as a vector for at least five tospovirses, have been suspected to be a species complex with more than one species. It is one of the historical unresolved issues where, two species namely, F. schultzei Trybom and F. sulphurea Schmutz were erected from South Africa and Srilanaka respectively. These two species were considered to be valid until 1968 when sulphurea was treated as colour morph (pale form) and synonymised under schultzei (dark form) However, these two have been considered as valid species by some of the thrips workers. Parallel studies have indicated that brown form of schultzei is a vector for tospoviruses while yellow form is a non-vector. However, recent studies have shown that yellow populations have also been documented as vectors. In view of all these facts, it is highly important to have a clear understanding whether these colour forms represent true species or merely different populations with different vector carrying capacities and whether there is some hidden diversity in 'Frankliniella schultzei species complex'. In this study, we aim to study the 'Frankliniella schultzei species complex' with molecular spectacles with DNA data from India and Australia and Africa. A total of fifty-five specimens was collected from diverse locations in India and Australia. We generated molecular data using partial fragments of mitochondrial cytochrome c oxidase I gene (mtCOI) and 28S rRNA gene. For COI dataset, there were seventy-four sequences, out of which data on fifty-five was generated in the current study and others were retrieved from NCBI. All the four different tree construction methods: neighbor-joining, maximum parsimony, maximum likelihood and Bayesian analysis, yielded the same tree topology and produced five cryptic species with high genetic divergence. For, rDNA, there were forty-five sequences, out of which data on thirty-nine was generated in the current study and others were retrieved from NCBI. The four tree building methods yielded four cryptic species with high bootstrap support value/posterior probability. Here we could not retrieve one cryptic species from South Africa as we could not generate data on rDNA from South Africa and sequence for rDNA from African region were not available in the database. The results of multiple species delimitation methods (barcode index numbers, automatic barcode gap discovery, general mixed Yule-coalescent, and Poisson-tree-processes) also supported the phylogenetic data and produced 5 and 4 Molecular Operational Taxonomic Units (MOTUs) for mtCOI and 28S dataset respectively. These results of our study indicate the likelihood that F. sulphurea may be a valid species, however, more morphological and molecular data is required on specimens from type localities of these two species and comparison with type specimens.

Keywords: DNA barcoding, species complex, thrips, species delimitation

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Authors: Hsiang-Yu Yuan, Marc Baguelin, Kin O. Kwok, Nimalan Arinaminpathy, Edwin Leeuwen, Steven Riley

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Traditional syndromic surveillance for influenza has substantial public health value in characterizing epidemics. Because the relationship between syndromic incidence and the true infection events can vary from one population to another and from one year to another, recent studies rely on combining serological test results with syndromic data from traditional surveillance into epidemic models to make inference on epidemiological processes of influenza. However, despite the widespread availability of serological data, epidemic models have thus far not explicitly represented antibody titre levels and their correspondence with immunity. Most studies use dichotomized data with a threshold (Typically, a titre of 1:40 was used) to define individuals as likely recently infected and likely immune and further estimate the cumulative incidence. Underestimation of Influenza attack rate could be resulted from the dichotomized data. In order to improve the use of serosurveillance data, here, a refinement of the concept of the stratified immunity within an epidemic model for influenza transmission was proposed, such that all individual antibody titre levels were enumerated explicitly and mapped onto a variable scale of susceptibility in different age groups. Haemagglutination inhibition titres from 523 individuals and 465 individuals during pre- and post-pandemic phase of the 2009 pandemic in Hong Kong were collected. The model was fitted to serological data in age-structured population using Bayesian framework and was able to reproduce key features of the epidemics. The effects of age-specific antibody boosting and protection were explored in greater detail. RB was defined to be the effective reproductive number in the presence of stratified immunity and its temporal dynamics was compared to the traditional epidemic model using use dichotomized seropositivity data. Deviance Information Criterion (DIC) was used to measure the fitness of the model to serological data with different mechanisms of the serological response. The results demonstrated that the differential antibody response with age was present (ΔDIC = -7.0). The age-specific mixing patterns with children specific transmissibility, rather than pre-existing immunity, was most likely to explain the high serological attack rates in children and low serological attack rates in elderly (ΔDIC = -38.5). Our results suggested that the disease dynamics and herd immunity of a population could be described more accurately for influenza when the distribution of immunity was explicitly represented, rather than relying only on the dichotomous states 'susceptible' and 'immune' defined by the threshold titre (1:40) (ΔDIC = -11.5). During the outbreak, RB declined slowly from 1.22[1.16-1.28] in the first four months after 1st May. RB dropped rapidly below to 1 during September and October, which was consistent to the observed epidemic peak time in the late September. One of the most important challenges for infectious disease control is to monitor disease transmissibility in real time with statistics such as the effective reproduction number. Once early estimates of antibody boosting and protection are obtained, disease dynamics can be reconstructed, which are valuable for infectious disease prevention and control.

Keywords: effective reproductive number, epidemic model, influenza epidemic dynamics, stratified immunity

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Authors: T. C. C. Soo, S. Bhassu

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Unlike the common presence of both innate and adaptive immunity in vertebrates, crustaceans, in particular, shrimps, have been discovered to possess only innate immunity. This further emphasizes the importance of innate immunity within shrimps in pathogenic resistance. Under the study of pathogenic immune challenge, different shrimp species actually exhibit varying degrees of immune resistance towards the same pathogen. Furthermore, even within the same shrimp species, different batches of challenged shrimps can have different strengths of immune defence. Several important pathways are activated within shrimps during pathogenic infection. One of them is JAK-STAT pathway that is activated during bacterial, viral and fungal infections by which STAT(Signal Transducer and Activator of Transcription) gene is the core element of the pathway. Based on theory of Central Dogma, the genomic information is transmitted in the order of DNA, RNA and protein. This study is focused in uncovering the important evolutionary patterns present within the DNA (non-coding region) and RNA (coding region). The three shrimp species involved are Macrobrachium rosenbergii, Penaeus monodon and Litopenaeus vannamei which all possess commercial significance. The shrimp species were challenged with a famous penaeid shrimp virus called white spot syndrome virus (WSSV) which can cause serious lethality. Tissue samples were collected during time intervals of 0h, 3h, 6h, 12h, 24h, 36h and 48h. The DNA and RNA samples were then extracted using conventional kits from the hepatopancreas tissue samples. PCR technique together with designed STAT gene conserved primers were utilized for identification of the STAT coding sequences using RNA-converted cDNA samples and subsequent characterization using various bioinformatics approaches including Ramachandran plot, ProtParam and SWISS-MODEL. The varying levels of immune STAT gene activation for the three shrimp species during WSSV infection were confirmed using qRT-PCR technique. For one sample, three biological replicates with three technical replicates each were used for qRT-PCR. On the other hand, DNA samples were important for uncovering the structural variations within the genomic region of STAT gene which would greatly assist in understanding the STAT protein functional variations. The partially-overlapping primers technique was used for the genomic region sequencing. The evolutionary inferences and event predictions were then conducted through the Bayesian Inference method using all the acquired coding and non-coding sequences. This was supplemented by the construction of conventional phylogenetic trees using Maximum likelihood method. The results showed that adaptive evolution caused STAT gene sequence mutations between different shrimp species which led to evolutionary divergence event. Subsequently, the divergent sites were correlated to the differing expressions of STAT gene. Ultimately, this study assists in knowing the shrimp species innate immune variability and selection of disease resistant shrimps for breeding purpose. The deeper understanding of STAT gene evolution from the perspective of both purifying and adaptive approaches not only can provide better immunological insight among shrimp species, but also can be used as a good reference for immunological studies in humans or other model organisms.

Keywords: gene evolution, JAK-STAT pathway, immunology, STAT gene

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Authors: André Python

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To this day, terrorism persists as a worldwide threat, exemplified by the recent deadly attacks in January 2015 in Paris and the ongoing massacres perpetrated by ISIS in Iraq and Syria. In response to this threat, states deploy various counterterrorism measures, the cost of which could be reduced through effective preventive measures. In order to increase the efficiency of preventive measures, policy-makers may benefit from accurate predictive models that are able to capture the complex spatial dynamics of terrorism occurring at a local scale. Despite empirical research carried out at country-level that has confirmed theories explaining the diffusion processes of terrorism across space and time, scholars have failed to assess diffusion’s theories on a local scale. Moreover, since scholars have not made the most of recent statistical modelling approaches, they have been unable to build up predictive models accurate in both space and time. In an effort to address these shortcomings, this research suggests a novel approach to systematically assess the theories of terrorism’s diffusion on a local scale and provide a predictive model of the local spatial dynamics of terrorism worldwide. With a focus on the lethal terrorist events that occurred after 9/11, this paper addresses the following question: why and how does lethal terrorism diffuse in space and time? Based on geolocalised data on worldwide terrorist attacks and covariates gathered from 2002 to 2013, a binomial spatio-temporal point process is used to model the probability of terrorist attacks on a sphere (the world), the surface of which is discretised in the form of Delaunay triangles and refined in areas of specific interest. Within a Bayesian framework, the model is fitted through an integrated nested Laplace approximation - a recent fitting approach that computes fast and accurate estimates of posterior marginals. Hence, for each location in the world, the model provides a probability of encountering a lethal terrorist attack and measures of volatility, which inform on the model’s predictability. Diffusion processes are visualised through interactive maps that highlight space-time variations in the probability and volatility of encountering a lethal attack from 2002 to 2013. Based on the previous twelve years of observation, the location and lethality of terrorist events in 2014 are statistically accurately predicted. Throughout the global scope of this research, local diffusion processes such as escalation and relocation are systematically examined: the former process describes an expansion from high concentration areas of lethal terrorist events (hotspots) to neighbouring areas, while the latter is characterised by changes in the location of hotspots. By controlling for the effect of geographical, economical and demographic variables, the results of the model suggest that the diffusion processes of lethal terrorism are jointly driven by contagious and non-contagious factors that operate on a local scale – as predicted by theories of diffusion. Moreover, by providing a quantitative measure of predictability, the model prevents policy-makers from making decisions based on highly uncertain predictions. Ultimately, this research may provide important complementary tools to enhance the efficiency of policies that aim to prevent and combat terrorism.

Keywords: diffusion process, terrorism, spatial dynamics, spatio-temporal modeling

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