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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Josep Fortiana Gregori, [es] En este trabajo se explica el contexto histórico sobre diversos estudios que se han hecho tratando de encontrar una forma óptima para predecir el resultado de un partido de futbol. Explicaremos, definiremos y detallaremos también como calcular los modelos lineales generalizados. Finalmente trataremos de aplicar lo aprendido de cara a definir un modelo de regresión lineal de Poisson para predecir los resultados de una temporada de fútbol entera.

Treballs Finals de Grau d'Enginyeria Informàtica, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Mireia Ribera i Josep Vives i Santa Eulàlia, [en] IT engineers widely use statistics nowadays and, more often, Bayesian Statistics. That is because Big Data and other data mining techniques are the day’s order, which is needed to create the a priori beliefs required for this kind of Statistics. Commonly, degree studies in Mathematics centre on classic Statistics, which means Frequentist, but scarce knowledge about Bayesian Statistics concepts is addressed. So doing a better mathematical analysis of the Bayesian approach appears to be very useful. That reason has motivated the development of a comparison between these two types of Statistics, which you will find in this research project. First, a more theoretical and general approach is addressed, explaining aspects where they differ. Then, that comparison is analysed by selecting and using a few simple problems that can be described using statistical graphics. These graphics have been made accessible (in a way that screen readers can manage their information) using two different IT libraries. Then, a Users Test was designed and prepared, and a population sample of blind people performed it. Their analysis will clarify which library is better and will highlight the requirements for creating adapted graphics. The results obtained from the tests are then studied, proving that it’s possible to make digital graphics accessible in a pretty simple way. And that users can interact easily with them. Users have referred to a high degree of satisfaction with the adapted graphics.

Immunotherapy; PARP inhibitors; Pembrolizumab Immunoteràpia; Inhibidors de PARP; Pembrolizumab Inmunoterapia; Inhibidores de PARP; Pembrolizumab Metastatic triple-negative breast cancer (mTNBC) is a poor prognostic disease with limited treatments and uncertain therapeutic algorithms. We performed a systematic review and multiple Bayesian network meta-analyses according to treatment line to establish an optimal therapeutic sequencing strategy for this lethal disease. We included 125 first-line trials (37,812 patients) and 33 s/further-lines trials (11,321 patients). The primary endpoint was progression-free survival (PFS). Secondary endpoints included overall response rates (ORR), overall survival (OS) and safety, for first and further lines, separately. We also estimated separate treatment rankings for the first and subsequent lines according to each endpoint, based on (surface under the cumulative ranking curve) SUCRA values. No first-line treatment was associated with superior PFS and OS than paclitaxel ± bevacizumab. Platinum-based polychemotherapies were generally superior in terms of ORR, at the cost of higher toxicity.. PARP-inhibitors in germline-BRCA1/2-mutant patients, and immunotherapy + chemotherapy in PD-L1-positive mTNBC, performed similar to paclitaxel ± bevacizumab. In PD-L1-positive mTNBC, pembrolizumab + chemotherapy was better than atezolizumab + nab-paclitaxel in terms of OS according to SUCRA values. In second/further-lines, sacituzumab govitecan outperformed all other treatments on all endpoints, followed by PARP-inhibitors in germline-BRCA1/2-mutant tumors. Trastuzumab deruxtecan in HER2-low mTNBC performed similarly and was the best advanced-line treatment in terms of PFS and OS after sacituzumab govitecan, according to SUCRA values. Moreover, comparisons with sacituzumab govitecan, talazoparib and olaparib were not statistically significant. The most effective alternatives or candidates for subsequent lines were represented by nab-paclitaxel (in ORR), capecitabine (in PFS) and eribulin (in PFS and OS).

Decision-making based on machine learning systems, especially when this decision-making can affect human lives, is a subject of maximum interest in the Machine Learning community. It is, therefore, necessary to equip these systems with a means of estimating uncertainty in the predictions they emit in order to help practitioners make more informed decisions. In the present work, we introduce the topic of uncertainty estimation, and we analyze the peculiarities of such estimation when applied to classification systems. We analyze different methods that have been designed to provide classification systems based on deep learning with mechanisms for measuring the uncertainty of their predictions. We will take a look at how this uncertainty can be modeled and measured using different approaches, as well as practical considerations of different applications of uncertainty. Moreover, we review some of the properties that should be borne in mind when developing such metrics. All in all, the present survey aims at providing a pragmatic overview of the estimation of uncertainty in classification systems that can be very useful for both academic research and deep learning practitioners.

En este trabajo se ha realizado una breve introducción sobre la metodología Regresión de Proceso Gaussiano (GPR) y dos aplicaciones en el ámbito Actuarial. Por un lado, se ha realizado un ejercicio de interpolación sobre las tablas de mortalidad PASEM Unisex 2020, concluyendo que el GPR es una excelente herramienta de interpolación, y que nos permite una tarificación más ajustada en el ramo de Vida. Por otro lado, se ha integrado el GPR como medida de predicción de provisiones en los ramos de No-Vida, obteniendo unos resultados prometedores. Por último, se concluye que un GPR puede ser un instrumento útil, siempre y cuando, se realice una buena selección del Kernel y un correcto período de entrenamiento del modelo.

Treballs Finals de Grau en Estadística UB-UPC, Facultat d'Economia i Empresa (UB) i Facultat de Matemàtiques i Estadística (UPC), Curs: 2021-2022, Tutor: Xavier Puig Oriol, Aquest treball presenta una anàlisi espacial conjunta de la incidència de tres tipus de càncer, d’esòfag, d’estómac i de còlon, en les municipalitats de Tarragona durant el període 2000-2014, distingint per sexes. Aquest estudi el realitzarem amb models bayesians jeràrquics que permeten modelar el comportament espacial i proporcionen evidències de l’existència de diferències en el risc de patir càncer al llarg del territori. Primer estudiarem la incidència dels tres tipus de càncer de forma separada i després els analitzarem de manera conjunta. Els resultats mostren un patró territorial comú entre els càncers d’estómac i d’esòfag, coincidint amb l’anàlisi individual, tant per als homes com per les dones, distingint-lo de la incidència del càncer de còlon. L’anàlisi conjunta ho corrobora en el cas de les dones amb una major dependència de l'efecte espacial compartit, mostrant un efecte especial igualment distribuït en les tres malalties per al cas dels homes.

Treballs Finals de Grau en Estadística UB-UPC, Facultat d'Economia i Empresa (UB) i Facultat de Matemàtiques i Estadística (UPC), Curs: 2021-2022, Tutor: Lourdes Rodero De Lamo, Companies are often interested in assessing the future profitability of their customers. This is especially challenging for clients that the company recently acquired, given the small amount of information available. In this thesis, we investigate a different way of approaching this problem, using the Pareto/NBD and Gamma/Gamma models. These allow us to establish statistical descriptions of the purchase rates, the length of the relation with a client and the average value of their purchases. In the end with these models we will create a binary classifier that, given the purchase history of a group of clients acquired at a certain time will tell us which are expected to be profitable in the future, which will present extremely high specificity and acceptable sensibility.

A sequence of short-lived agents must choose which action to take under a fixed, but unknown, state of the world. Prior to the realization of the state, the long-lived principal designs and commits to a dynamic information policy to persuade agents toward his most preferred action. The principal's persuasion power is potentially limited by the existence of conditionally independent and identically distributed private signals for the agents as well as their ability to observe the history of past actions. I characterize the problem for the principal in terms of a dynamic belief manipulation mechanism and analyze its implications for social learning. For a class of private information structure - the log-concave class, I derive conditions under which the principal should encourage some social learning and when he should induce herd behavior from the start (single disclosure). I also show that social learning is less valuable to a more patient principal: as his discount factor converges to one, the value of any optimal policy converges to the value of the single disclosure policy.

Treballs Finals del Màster de Ciències Actuarials i Financeres, Facultat d'Economia i Empresa, Universitat de Barcelona, Curs: 2021-2022, Tutor: Salvador Torra Porras, En este trabajo se ha realizado una breve introducción sobre que es una Regresión de Proceso Gaussiano (GPR) y dos aplicaciones que pueden integrarse en el ámbito de las Ciencias Actuariales. Por un lado, se ha realizado un ejercicio de interpolación sobre las tablas de mortalidad PASEM Unisex 2020, concluyendo que el GPR es una fuerte herramienta de interpolación y permite una tarificación más ajustada en el ramo de Vida. Por otro lado, se ha integrado el GPR como medida de predicción de provisiones en los ramos de No-Vida, obteniendo unos datos de salida prometedores. Por último, se concluye que un GPR puede ser un instrumento útil, siempre y cuando, se realice una buena selección del Kernel y un correcto período de entrenamiento del modelo.

Background Community-acquired pneumonia (CAP) is one of the leading causes of morbidity and mortality in the USA. Our objective was to assess the predictive value on critical illness and disposition of a sequential Bayesian Model that integrates Lactate and procalcitonin (PCT) for pneumonia. Methods Sensitivity and specificity of lactate and PCT attained from pooled meta-analysis data. Likelihood ratios calculated and inserted in Bayesian/ Fagan nomogram to calculate posttest probabilities. Bayesian Diagnostic Gains (BDG) were analyzed comparing pre and post-test probability. To assess the value of integrating both PCT and Lactate in Severity of Illness Prediction we built a model that combined CURB65 with PCT as the Pre-Test markers and later integrated the Lactate Likelihood Ratio Values to generate a combined CURB 65 + Procalcitonin + Lactate Sequential value. Results The BDG model integrated a CUBR65 Scores combined with Procalcitonin (LR+ and LR-) for Pre-Test Probability Intermediate and High with Lactate Positive Likelihood Ratios. This generated for the PCT LR+ Post-test Probability (POSITIVE TEST) Posterior probability: 93% (95% CI [91,96%]) and Post Test Probability (NEGATIVE TEST) of: 17% (95% CI [15–20%]) for the Intermediate subgroup and 97% for the high risk sub-group POSITIVE TEST: Post-Test probability:97% (95% CI [95,98%]) NEGATIVE TEST: Post-test probability: 33% (95% CI [31,36%]) . ANOVA analysis for CURB 65 (alone) vs CURB 65 and PCT (LR+) vs CURB 65 and PCT (LR+) and Lactate showed a statistically significant difference (P value = 0.013). Conclusions The sequential combination of CURB 65 plus PCT with Lactate yielded statistically significant results, demonstrating a greater predictive value for severity of illness thus ICU level care.

[eng] Arguably, one of the stimuli that move human the most is music. What physically consists in an array of sounds organized in time and frequency, is capable of evoking a rich palette of emotions, thoughts and behaviors in the listener. Despite the complexity of these psychological phenomena, however, music is also capable of evoking one of the most basic psychophysiological reactions to stimuli in humans: pleasure. Thus, a relevant question is how music, an arbitrary concatenation of sounds, ends up translated into this unique affective experience. As with many other aspects of human behavior, studying the brain function underlying this psychological phenomenon offers an insightful view on this intriguing inquiry. As of today, decades of research have been devoted to elucidate the neuropsychological mechanisms through which music-evoked pleasantness takes place. From psychological models of emotion and affect to evidence-based neuroscientific theories, the question of how music becomes pleasurable has been addressed from many different disciplines, approaches and methodologies. As a result, the brain architecture and mechanics underlying music evoked pleasantness have begun to be understood to great detail. Perhaps the most important breakthrough has been to verify that music engages the brain reward system, validating the idea that musical stimuli are indeed a source of hedonic impact. Nevertheless, along the brain reward system work a number of cortical areas responsible for the perceptual processing of musical stimuli. Altogether, this anatomical and functional interplay conforms an extensive network that actively contributes to the pleasurable experience of listening to music. Furthermore, other brain areas have been observed to be involved in these networks depending on the level of familiarity with the music stimuli, a factor that has been replicated to be intimately associated with music reward processing. As such, these networks utilize precise neural dynamics in order to transfer the information back and forth between the areas involved. A candidate mechanism for this information transfer are neural oscillations. By synchronizing to the same inputs, neuronal populations can pass information and process it efficiently to fulfill a task or demand. The neural oscillations associated with music-evoked pleasantness are just beginning to be understood. However, a common oscillatory signature of musical plea­ sure does appear consistently in the literature: theta oscillations. Nonetheless, whether the different areas engaged in music reward processing are indeed synchronized by these rhythms is yet to be determined. One goal of this thesis is to study whether theta rhythms indeed synchronize relevant brain nodes during pleasant music listening. In order to answer this question, in study 1 we acquired EEG signals from a cohort of participants while they listened and rated a number of musical excerpts. After analysis of the EEG data jointly with the self-reports, we observed that right frontal and temporal signals were more synchronized by theta rhythms the more pleasant music was found. These results converge with previous literature pinpointing right fronto-temporal connectivity to be actively involved in the process of assigning value to music, as well as with literature identifying theta rhythms as a correlate of music-evoked pleasantness and related constructs. Following this line of research, another goal of this thesis is to test whether the nodes synchronized by theta rhythms during pleasant music listening are indeed related to the music processing brain networks consistently replicated in the neuroimaging literature. For this purpose, in study 2 we acquired simultaneous fMRI-EEG recordings with a similar paradigm to that of study l. After replicating previous results identifying a fronto-temporal music-related brain network in our fMRI data, we studied the activity of this network in relation to theta synchronization as measured with EEG and reported pleasantness. We observed that theta synchronization between frontal and temporal signals was positively related to music-related brain function when music was reported to be liked the most, providing empirical evidence for the link between the two phenomena. Yet another intriguing question is whether liking for familiar music synchronizes similar or different brain nodes by theta rhythms. Familiar music has been observed to be liked more than unfamiliar music, suggesting qualitative and/or quantitative differences in its processing. lndeed, previous research has revealed that in addition to music processing areas, familiar music engages the parietal cortex. In study 3 we familiarized a cohort of participants with some music stimuli and had them rate the excerpts 24h later along a new set of stimuli while their EEG was recorded . We found that the right fronto-temporal theta connectivity profile found in the previous studies was only associated with liking for novel music. lnstead, temporo-parietal theta connectivity was more engaged when liking familiar music. These results go in line with previous research and pose the first attempt to our knowledge to study the familiarity effect on musical liking from an oscillatory dynamics perspective. Therefore, the research conducted in this thesis adds up to the state of the art in the neuroscience of music-evoked pleasantness. We provide novel evidence for the role of theta oscillations in synchronizing relevant brain nodes during pleasant music listening, as well as the different cortical nodes these rhythms synchronize depending on the familiarity level with music. Particularly, fronto-temporal theta rhythms were identified to be associated with music-evoked pleasantness overall, and with liking for novel music specifically. We also provide evidence that in the particular case of familiar music, liking is supported by theta temporo-parietal synchronization. Last but not least, our results also link empirically the fronto-temporal brain networks underlying music perception as measured with fMRI with theta oscillations associated with music-evoked pleasantness as measured with EEG. Altogether, the results presented in this thesis contribute to the understanding of the brain networks involved in pleasant and familiar music listening, insofar they corroborate theta rhythms as a means of synchronization dynamics, opening up new windows for future research, [spa] Podría decirse que uno de los estímulos que más conmueven al ser humano es la música. Lo que físicamente consiste en una serie de sonidos organizados en tiempo y frecuencia, es capaz de evocar una rica amalgama de emociones, pensamientos y comportamientos en el oyente. Sin embargo, a pesar de la complejidad de estos fenómenos psicológicos, la música también es capaz de evocar una de las reacciones psicofisiológicas más básicas que los estímulos pueden despertar en los seres humanos: placer. Por tanto, una cuestión relevante es cómo la música, una concatenación arbitraria de sonidos, acaba traduciéndose en esta experiencia afectiva única. Como ocurre con muchos otros aspectos del comportamiento humano, estudiar la función cerebral asociada a este fenómeno psicológico ofrece un punto de vista esclarecedor sobre esta intrigante cuestión. A día de hoy, se han dedicado décadas de investigación para dilucidar los mecanismos neuropsicológicos a través de los cuales se produce el placer evocado por la música. Desde modelos psicológicos de emoción y afecto hasta teorías neurocientíficas basadas en evidencia empírica, la cuestión de cómo la música se vuelve placentera se ha abordado desde muchas disciplinas, enfoques y metodologías diferentes. Como resultado, la arquitectura del cerebro y la mecánica subyacente a el placer a la música han comenzado a entenderse con gran detalle. Quizás el avance más importante ha sido verificar que la música activa el sistema de recompensa del cerebro, validando la idea de que los estímulos musicales son en efecto una fuente de impacto hedónico. Sin embargo, junto al sistema de recompensa cerebral funcionan una serie de áreas corticales responsables del procesamiento perceptual de los estímulos musicales. En conjunto, esta interacción anatómica y funcional conforma una red extensa que contribuye activamente a la experiencia de escuchar música placentera. Además, se ha observado que otras áreas del cerebro están involucradas en estas redes dependiendo del nivel de familiaridad con los estímulos musicales, un factor íntimamente asociado con el procesamiento de la recompensa musical, como así se ha replicado en la literatura . Como tal, estas redes utilizan dinámicas neuronales concretas para transferir la información entre las áreas involucradas. Un mecanismo candidato para explicar esta transferencia de información son las oscilaciones neuronales. Al sincronizarse con los mismos inputs, las poblaciones neuronales pueden comunicar información y procesarla de manera eficiente para cumplir con una tarea o demanda. Las oscilaciones neuronales asociadas al placer musical apenas han comenzado a entenderse. No obstante, hay un correlato oscilatorio del placer musical que aparece consistentemente en la literatura: las oscilaciones theta. Sin embargo, aún no se ha determinado si las diferentes áreas involucradas en el procesamiento de recompensas musicales están realmente sincronizadas a través de estos ritmos. Uno de los objetivos de esta tesis es estudiar si los ritmos theta realmente sincronizan los nodos cerebrales relevantes durante la escucha de música placentera. Para contestar esta pregunta, en el primer estudio adquirimos señales de EEG en un grupo de participantes mientras escuchaban y evaluaban una serie de fragmentos musicales. Después del análisis de los datos de EEG junto a las evaluaciones de placer, observamos que las señales frontales y temporales derechas estaban más sincronizadas a través de ritmos theta cuanto más placentera resultaba la música. Estos resultados convergen con literatura previa que señala que las redes fronto-temporales derechas participan activamente en el proceso de valoración musical, así como con literatura que identifica los ritmos theta como un correlato del placer evocado por la música y constructos relacionados. Siguiendo esta línea de investigación, otro objetivo de esta tesis es probar si los nodos sincronizados por ritmos theta durante la escucha de música placentera están real­ mente relacionados con las redes cerebrales de procesamiento musical normalmente halladas en la literatura de neuroimagen. Para ello, en el estudio 2 adquirimos registros simultáneos de fMRI-EEG en un paradigma similar. Después de replicar resultados anteriores identificando una red cerebral fronto-temporal relacionada con la música en nuestros datos de resonancia magnética funcional, estudiamos la actividad de esta red en relación con la sincronización theta medida con EEG, y el placer evocado. Observamos que la sincronización theta entre las señales frontales y temporales se relaciona positivamente con la función cerebral relacionada con la música cuando se reporta que ésta gusta más, proporcionando evidencia empírica del vínculo entre estos dos fenómenos. Otra cuestión importante es si el placer evocado por la música familiar sincroniza los mismos o diferentes nodos cerebrales por ritmos theta. Se ha observado que la música familiar gusta más que la música desconocida, lo que sugiere diferencias cualitativas y/o cuantitativas en su procesamiento. De hecho, investigaciones anteriores han revelado que, además de las áreas de procesamiento musical, la música familiar activa la corteza parietal. En el estudio 3 familiarizamos a un grupo participantes con algunos estímulos musicales y les pedimos que evaluaran los mismos fragmentos 24 horas después junto a un nuevo conjunto de estímulos mientras se registraba su EEG. Encontramos que la conectividad theta fronto-temporal derecha encontrada en los estudios anteriores solo se encontró asociada al placer evocado por música novel. En cambio, un perfil de conectividad theta temporo-parietal se encontró más asociado al placer cuando éste fue evocado por música familiar. Estos resultados están en línea con investigaciones previas y suponen el primer intento, a nuestro entender, en estudiar el efecto de familiaridad en el placer musical desde una perspectiva de dinámicas oscilatorias. Por todo esto, la investigación realizada en esta tesis contribuye a la vanguardia en la neurociencia del placer musical. Proporcionamos evidencia novedosa sobre el papel de las oscilaciones theta en la sincronización de los nodos cerebrales relevantes durante la escucha de música agradable, así como los diferentes nodos corticales que estos ritmos sincronizan según el nivel de familiaridad con la música. Particularmente, se identificó que los ritmos theta fronto-temporales están asociados con el placer evocado por la música en general, y específicamente con el placer evocado por la música nueva. También proporcionamos evidencia que en el caso particular de la música familiar, el placer está asociado con sincronización theta temporo-parietal. Por último, aunque no menos importante, nuestros resultados también vinculan empíricamente las redes cerebrales fronto-temporales relacionadas que subyacen a la percepción de la música (medidas con fMRI) con oscilaciones theta asociadas al placer musical (medidas con EEG). En conjunto, los resultados presentados en esta tesis contribuyen a la comprensión de las redes cerebrales involucradas en la escucha de música placentera y familiar, en la medida en que corroboran los ritmos theta como medio de comunicación neuronal, abriendo nuevas oportunidades para futuras investigaciones.

Treballs finals del Màster de Fonaments de Ciència de Dades, Facultat de matemàtiques, Universitat de Barcelona. Curs: 2020-2021. Tutor: Jerónimo Hernández González, [en] Embryo selection is a critical step in assisted reproduction (ART): a good selection criteria is expected to increase the probability of inducing pregnancy. In the past, machine learning methods have been used to predict implantation and to rank the most promising embryos. Here, we study the use of a probabilistic graphical model that assumes independence between embryos’ individual features and cycles characteristics. It also accounts for a third source of uncertainty attributed to unknown factors. We present an empirical validation and analysis of the behavior of the model within real data. The dataset describes 604 consecutive ART cycles carried out at Hospital Donostia (Spain), where embryo selection was performed following the Spanish Association for Reproduction Biology Studies (ASEBIR) protocol, based on morphological features. The performance of our model is evaluated with different metrics and the predicted probability densities are examined to obtain significant insights about the process. We assemble an experimental setup consisting of alternative and simpler methods as a basic reference point to compare against. They are built in an incre- mental way in order to test different aspects of our probabilistic graphical model. We show the benefits of using an EM algorithm and the importance of the cycles characteristics. Special attention is given to the relation between the models and the ASEBIR protocol. We validate our model by showing that its predictions show correlation with the ASEBIR score when the score is not provided as a feature. However, once the selection based on this protocol has taken place, our model is unable to separate implanted and failed embryos when only embryo individual features are used. From here, we can infer that ASEBIR score provides a good summary of morphological features.

Population aging in most industrialized societies has led to a dramatic increase in emergency medical demand among the elderly. In the context of private health care, an optimal allocation of the medical resources for seniors is commonly done by forecasting their life spans. Accounting for each subject's particularities is therefore indispensable, so the available data must be processed at an individual level. We use a large and unique dataset of insured parties aged 65 and older to appropriately relate the emergency care usage with mortality risk. Longitudinal and time-to-event processes are jointly modeled, and their underlying relationship can therefore be assessed. Such an application, however, requires some special features to also be considered. First, longitudinal demand for emergency services exhibits a nonnegative integer response with an excess of zeros due to the very nature of the data. These subject-specific responses are handled by a zero-inflated version of the hierarchical negative binomial model. Second, event times must account for the left truncation derived from the fact that policyholders must reach the age of 65 before they may begin to be observed. Consequently, a delayed entry bias arises for those individuals entering the study after this age threshold. Third, and as the main challenge of our analysis, the association parameter between both processes is expected to be age-dependent, with an unspecified association structure. This is well-approximated through a flexible functional specification provided by penalized B-splines. The parameter estimation of the joint model is derived under a Bayesian scheme.

Increasing retirement ages in an automatic or scheduled way with increasing life expectancy at retirement is a popular pension policy response to continuous longevity improvements. The question addressed here is: to what extent is simply adopting this approach likely to fulfill the overall goals of policy? To shed some light on the answer, we examine the policies of four countries that have recently introduced automatic indexation of pension ages to life expectancy–The Netherlands, Denmark, Portugal and Slovakia. To this end, we forecast an alternative period and cohort life expectancy measures using a Bayesian Model Ensemble of heterogeneous stochastic mortality models comprised of parametric models, principal component methods, and smoothing approaches. The approach involves both the selection of the model confidence set and the determination of optimal weights. Model-averaged Bayesian credible prediction intervals are derived accounting for various stochastic process, model, and parameter risks. The results show that: (i) retirement ages are forecasted to increase substantially in the coming decades, particularly if a constant period in retirement is targeted, (ii) retirement age policy outcomes may substantially deviate from the policy goal(s) depending on the design adopted and its implementation, and (iii) the choice of a cohort over period life expectancy measure matters. In addition, the distributional issues arising with the increasing socio-economic gap in life expectancy remain largely unaddressed.

When actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce different regression models in order to relax the independence assumption, including zero-inflated models to account for excess of zeros and overdispersion. These models have been largely ignored to multivariate Poisson date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.

© 2020 by the authors., Importance sampling is a Monte Carlo method where samples are obtained from an alternative proposal distribution. This can be used to focus the sampling process in the relevant parts of space, thus reducing the variance. Selecting the proposal that leads to the minimum variance can be formulated as an optimization problem and solved, for instance, by the use of a variational approach. Variational inference selects, from a given family, the distribution which minimizes the divergence to the distribution of interest. The Rényi projection of order 2 leads to the importance sampling estimator of minimum variance, but its computation is very costly. In this study with discrete distributions that factorize over probabilistic graphical models, we propose and evaluate an approximate projection method onto fully factored distributions. As a result of our evaluation it becomes apparent that a proposal distribution mixing the information projection with the approximate Rényi projection of order 2 could be interesting from a practical perspective., This research was partially funded by the CI-SUSTAIN project (PID2019-104156GB-I00) of the Spanish Ministry of Science and Innovation, the CROWD4SDG (872944) and the Humane-AI-Net (952026) projects, both of the EU Horizon 2020 programme. J.H.-G. carried out a large part of this work while at IIIA-CSIC with a Juan de la Cierva-Incorporación grant from the Spanish Ministry of Science and Innovation.

This document is a research in the field of quantitative genetics that looks to provide a math- ematical approach to the evolution of traits by looking at how inheritance and environmental effects impact these. An overview of current software options is given first, then we will docu- ment our attempt at developing an R script that does what current programs can do but both for free and in R, which is not an available option at the moment. The software developed should be able to, given a dataset, find the variance/covariance components of the random effects asso- ciated to a set of individuals. Late into the research the library proves to be unable to fit models with multiple predictors.

La metodología observacional, a lo largo de las cuatro últimas décadas, se ha consolidado como método científico, y progresivamente se han ido incorporando desarrollos procedimentales que la han dotado de una gran rigurosidad, sin menoscabo de la flexibilidad que le es inherente. En el marco actual de los mixed methods, el aspecto crucial por antonomasia es la integración de elementos cualitativos y cuantitativos, cuestión nada fácil, y sobre la cual se han pronunciado numerosos investigadores relevantes. En este trabajo, de carácter procedimental, se hace una propuesta acerca de la metodología observacional, considerada como mixed method en sí misma, que requieren el desarrollo de fórmulas de integración (quantitizing) entre elementos cualitativos y cuantitativos, y se recomienda la incorporación del análisis bayesiano a los estudios mixed methods, utilizando el investigador su propia experiencia y conocimiento como punto de partida. La vía propuesta de quantitizing toma como punto de partida la realización de una observación sistemática en la cual se obtienen registros descriptivos (fase QUAL); a partir del marco teórico y pericia empírica se construye un instrumento de observación, con una estructura definida, que posibilita la sistematización del registro basándose en el parámetro orden o secuencia, y posibilitará que el registro adopte el formato de una matriz de códigos, y ésta se podrá analizar mediante técnicas cuantitativas (fase QUAN); los resultados se interpretarán retornando al problema inicial de estudio (fase QUAL). La estrategia que conlleva esta forma de realizar el quantitizing es innovadora, y no tiene límites de aplicabilidad. The observational methodology has consolidated as scientific method along four last decades, and during this period has developed the procedure, with the addition of new advances concerning it. This progress implies the maintenance of two characteristic features: rigor and flexibility, that are essential in this methodology. In the current framework of mixed methods, the core is the integration ways between qualitative and quantitative elements, that is not easy, and prestigious researchers have written about this issue. In this work, focused in procedural aspects, we do a proposal about observational methodology considered itself as mixed method, that imply integration ways (quantitizing) between qualitative and quantitative elements; also, we recommend to set up the bayesian approach to mixed methods studies, that is based on the subjective perspective of probability, and for this the researcher uses his/her own experience and knowledge as a starting point. The proposal of quantitizing begins with a systematic observation, and implies qualitative records (QUAL step); from theoretical framework and empirical expertise it is necessary to build an observation instrument with a specific structure that allows for systematizing the record from order or sequence parameter, and following a matrix codes format, that we will analyze quantitatively (QUAN step); the results will interpret coming back to initial problem (QUAL step). The strategy that implies this quantitizing way is innovative, and it has not applying limits.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Josep Fortiana Gregori, [en] The goal of this article is to generate cancer risk maps for the region of Tarragona. We use Bayesian hierachical models adapted to the spatial correlation inherent the data. In the report we explain some elements of Bayesian Statistics to set a foundation for the models we apply, we discuss computational techniques and visualize on maps the results we obtained.

(1) Background: Mild cognitive impairment (MCI) is a diagnostic label in which stability is typically low. The aim of this study was to examine temporal changes in the diagnosis of MCI subtypes by using an overlapping-time strategy, (2) Methods: The study included 435 participants aged over 50 years with subjective cognitive complaints and who completed at least one follow-up evaluation. The probability of transition was estimated using Bayesian odds ratios, (3) Results: Within the different time intervals, the controls with subjective cognitive complaints represented the largest proportion of participants, followed by sda-MCI at baseline and in the first five intervals of the follow-up, but not in the last eight intervals. The odds ratios indicated higher odds of conversion to dementia in sda-MCI and mda-MCI groups relative to na-MCI (e.g., interval 9&ndash, 15 months&mdash, sda-MCI OR = 9 and mda-MCI OR = 3.36, interval 27&ndash, 33&mdash, sda-MCI OR = 16 and mda-MCI = 5.06, interval 42&ndash, 48&mdash, sda-MCI OR = 8.16 and mda-MCI = 3.45, interval 45&ndash, 51&mdash, sda-MCI OR = 3.31 and mda-MCI = 1), (4) Conclusions: Notable patterns of instability consistent with the current literature were observed. The limitations of a prospective approach in the study of MCI transitions are discussed.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Josep Vives i Santa Eulàlia, [en] This work presents the transformation of Harsanyi, that help us to transform a game with incomplete information into a game with information complete but imperfect, and the basic results related to games with incomplete information. After a long introduction with examples, this report studies Bayesian games in depth and presents the notion of equilibrium in these cases.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: David Márquez Carreras, [en] Bayesian statistics is that statistic that is based on the Bayes theorem, therefore, in the information we have before observe the data. As a result, we have the a priori distribution and a posteriori distribution, which we make inference. In this work we will study the process of estimation from Bayesian inference and simulation methods of a posteriori distribution. In addition, we will see this knowledge applied to practical examples.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Olga Julià de Ferran, [en] Bayesian statistics, based on Bayes' Theorem, arise when we expand classical inference to contexts where a more subjective interpretation of probability is needed. In this paper we define the basic concepts that are necessary to make bayesian inference. We are gonna focus on single-parameter models, as we will see: the binomial model, the normal model with known variance, the exponencial model and the Poisson model. We define concepts such as conjugate laws, informative and noninformative priors and other aspects that are useful for a bayesian analysis. Finally, one can nd two examples, both made using the statistic programming language R, where we apply most of the introduced concepts and techniques.

We present the estimation of a likelihood map for the location of the source of a chemical plume dispersed under atmospheric turbulence under uniform wind conditions. The main contribution of this work is to extend previous proposals based on Bayesian inference with binary detections to the use of concentration information while at the same time being robust against the presence of background chemical noise. For that, the algorithm builds a background model with robust statistics measurements to assess the posterior probability that a given chemical concentration reading comes from the background or from a source emitting at a distance with a specific release rate. In addition, our algorithm allows multiple mobile gas sensors to be used. Ten realistic simulations and ten real data experiments are used for evaluation purposes. For the simulations, we have supposed that sensors are mounted on cars which do not have among its main tasks navigating toward the source. To collect the real dataset, a special arena with induced wind is built, and an autonomous vehicle equipped with several sensors, including a photo ionization detector (PID) for sensing chemical concentration, is used. Simulation results show that our algorithm, provides a better estimation of the source location even for a low background level that benefits the performance of binary version. The improvement is clear for the synthetic data while for real data the estimation is only slightly better, probably because our exploration arena is not able to provide uniform wind conditions. Finally, an estimation of the computational cost of the algorithmic proposal is presented. The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No. 217925: LOTUS: Localization of Threat Substances in an Urban Society. This work was partially funded by the Spanish MINECO program, under grants TEC2011-26143 (SMART-IMS), TEC2014-59229-R (SIGVOL), and BES-2015-071698 (SEVERO-OCHOA). The Signal and Information Processing for Sensor Systems group is a consolidated Grup de Recerca de la Generalitat de Catalunya and has support from the Departament d’Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya (expedient 2014-SGR-1445). This work has received support from the Comissionat per a Universitats i Recerca del DIUE de la Generalitat de Catalunya and the European Social Fund (ESF). Additional financial support has been provided by the Institut de Bioenginyeria de Catalunya (IBEC). IBEC is a member of the CERCA Programme/Generalitat de Catalunya.

The evolutionary nature of cancer relates directly to a renewed focus on the voluminous NGS (next generation sequencing) data, aiming at the identification of explanatory models of how the (epi)genomic events are choreographed in cancer initiation and development. However, despite the increasing availability of multiple additional -omics data, this quest has been frustrated by various theoretical and technical hurdles, mostly related to the dramatic heterogeneity and temporality of the disease. In this paper, we build on our recent works on selectivity relation among driver mutations in cancer progression and investigate their applicability to the modeling problem - both at the population and individual levels. On one hand, we devise an optimal, versatile and modular pipeline to extract ensemble-level progression models from cross sectional sequenced cancer genomes. The pipeline combines state-of-the-art techniques for sample stratification, driver selection, identification of fitness-equivalent exclusive alterations and progression model inference. We demonstrate this pipeline's ability to reproduce much of the current knowledge on colorectal cancer progression, as well as to suggest novel experimentally verifiable hypotheses. On the other hand, we prove that our framework can be applied, mutatis mutandis, in reconstructing the evolutionary history of cancer clones in single patients, as illustrated by an example with multiple biopsy data from clear cell renal carcinomas.

Presenting natural frequencies facilitates Bayesian inferences relative to using percentages. Nevertheless, many people, including highly educated and skilled reasoners, still fail to provide Bayesian responses to these computationally simple problems. We show that the complexity of relational reasoning (e.g., the structural mapping between the presented and requested relations) can help explain the remaining difficulties. With a non-Bayesian inference that required identical arithmetic but afforded a more direct structural mapping, performance was universally high. Furthermore, reducing the relational demands of the task through questions that directed reasoners to use the presented statistics, as compared with questions that prompted the representation of a second, similar sample, also significantly improved reasoning. Distinct error patterns were also observed between these presented- and similar-sample scenarios, which suggested differences in relational-reasoning strategies. On the other hand, while higher numeracy was associated with better Bayesian reasoning, higher-numerate reasoners were not immune to the relational complexity of the task. Together, these findings validate the relational-reasoning view of Bayesian problem solving and highlight the importance of considering not only the presented task structure, but also the complexity of the structural alignment between the presented and requested relations.

In this paper we present a new method for Joint Feature Selection and Classifier Learning using a sparse Bayesian approach. These tasks are performed by optimizing a global loss function that includes a term associated with the empirical loss and another one representing a feature selection and regularization constraint on the parameters. To minimize this function we use a recently proposed technique, the Boosted Lasso algorithm, that follows the regularization path of the empirical risk associated with our loss function. We develop the algorithm for a well known non-parametrical classification method, the relevance vector machine, and perform experiments using a synthetic data set and three databases from the UCI Machine Learning Repository. The results show that our method is able to select the relevant features, increasing in some cases the classification accuracy when feature selection is performed.

It has been shown that the accuracy of mammographic abnormality detection methods is strongly dependent on the breast tissue characteristics, where a dense breast drastically reduces detection sensitivity. In addition, breast tissue density is widely accepted to be an important risk indicator for the development of breast cancer. Here, we describe the development of an automatic breast tissue classification methodology, which can be summarized in a number of distinct steps: 1) the segmentation of the breast area into fatty versus dense mammographic tissue; 2) the extraction of morphological and texture features from the segmented breast areas; and 3) the use of a Bayesian combination of a number of classifiers. The evaluation, based on a large number of cases from two different mammographic data sets, shows a strong correlation ( and 0.67 for the two data sets) between automatic and expert-based Breast Imaging Reporting and Data System mammographic density assessment.

Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian inferences relative to normalized formats (e.g., probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on 'transparent' Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e., transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct vs. incorrect reasoners depart, and how individual differences might influence this time point.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2015, Director: Josep Fortiana Gregori, The present project consists of the study and analysis of several Statistical Classification methods oriented towards their application to real estate dealing contracts data with the aim of detecting cases of fiscal fraud where the declared transaction value is below a statutory price level.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2015, Director: Jesús Cerquides Bueno i Marc Pujol González, Modern companies have recognized machine learning techniques as a key instrument to gain competitive edges in their businesses, from better client profiling to optimization and streamlining of their resources and operations. Among the many approaches and problems defined un- der the machine learning umbrella, we focus on Probabilistic Graphical Models (PGM). PGM is a generic framework that allows analysts to harness collected statistics and make predictions using them. Nonetheless, the computation of such predictions is a known NP-hard problem, and hence presents a significant challenge. Therefore, the PGM community has mainly focused on the development of either useful relaxations that can be solved with a lower computational complexity or approximate algorithms that still provide good solutions. Meanwhile, the relentless technological advances of our era have brought us to an interesting situation. On the one hand, the sheer amount of collected data that can be analyzed and exploited is ever-increasing. On the other hand, the advent of cloud computing provides vast amounts of inexpensive computation capabilities. However, exploiting these resources is not an easy endeavor because they are distributed along many networked machines. Fortunately, the community response against these challenges has been the development of generic distributed computation platforms such as Hadoop or Spark. These platforms free the developers from dealing with the distribution challenges, allowing them to focus on the implementation of their algorithms instead. Against this background, the main goal of this project is to build a bridge between these worlds by implementing a core PGM algorithm in one of such distributed systems. The selected algorithm is Belief Propagation (BP), an approximate inference algorithm that has good complexity characteristics and has proven to provide good solutions in practice. Additionally, BP is based on a message-passing model, and hence stands as a perfect candidate for a distributed implementation. Furthermore, the implementation is done under Apache Spark, because it is designed specifically to support message-passing algorithms. Nonetheless, despite the invaluable foundation provided by the platform, Spark leaves many considerations left to the criteria of the developer. Therefore, in this project we present the challenges that arose during such implementation, and how they can be overcome. The end result of this project is hence a BP implementation that can run in a distributed manner between as many systems as supported by Spark. Moreover, the implementation is both unit-tested and checked against a centralized open-source library. This opens up the possibility for anyone to make predictions based on large PGM models built spanning gigabytes of information.

The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions and erroneous probability judgments. Specifically, decision makers commonly develop a wrong intuition that final probabilities are equally distributed, together with a preference for their first choice. Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning. However, modest improvements in probability judgments have been observed after guided explanations. To explain these dissociations, the present review focuses on two types of causes producing the observed biases: Emotional-based choice biases and cognitive limitations in understanding probabilistic information. Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities. We conclude that repeated practice and/or high incentives can be effective for overcoming choice biases, but promoting an adequate partitioning of possibilities seems to be necessary for overcoming cognitive illusions and improving Bayesian reasoning.

In this paper, we characterize two power indices introduced in [1] using two different modifications of the monotonicity property first stated by [2]. The sets of properties are easily comparable among them and with previous characterizations of other power indices., A. A. Pinto acknowledges the financial support of LIAAD INESC TEC through program PEst,USP-UP project, Faculty of Sciences, University of Porto, Calouste Gulbenkian Foundation,FEDER, POCI 2010 and COMPETE Programmes, PTDC/MAT/121107/2010 and Fundação para a Ciência e a Tecnologia (FCT). J. M. Alonso-Meijide and M. Álvarez-Mozos acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness through Projects ECO2008-03484-C02-02/ECO and MTM2011-27731-C03-03 and of Xunta de Galicia through Project INCITE09-207-064-PR.

Background Socioeconomic inequalities are increasingly recognised as an important public health issue, although their role in the leading causes of mortality in urban areas in Europe has not been fully evaluated. In this study, we used data from the INEQCITIES study to analyse inequalities in cause-specific mortality in 15 European cities at the beginning of the 21st century. Methods A cross-sectional ecological study was carried out to analyse 9 of the leading specific causes of death in small areas from 15 European cities. Using a hierarchical Bayesian spatial model, we estimated smoothed Standardized Mortality Ratios, relative risks and 95% credible intervals for cause-specific mortality in relation to a socioeconomic deprivation index, separately for men and women. Results We detected spatial socioeconomic inequalities for most causes of mortality studied, although these inequalities differed markedly between cities, being more pronounced in Northern and Central-Eastern Europe. In the majority of cities, most of these causes of death were positively associated with deprivation among men, with the exception of prostatic cancer. Among women, diabetes, ischaemic heart disease, chronic liver diseases and respiratory diseases were also positively associated with deprivation in most cities. Lung cancer mortality was positively associated with deprivation in Northern European cities and in Kosice, but this association was non-existent or even negative in Southern European cities. Finally, breast cancer risk was inversely associated with deprivation in three Southern European cities. Conclusions The results confirm the existence of socioeconomic inequalities in many of the main causes of mortality, and reveal variations in their magnitude between different European cities, Background Socioeconomic inequalities are increasingly recognised as an important public health issue, although their role in the leading causes of mortality in urban areas in Europe has not been fully evaluated. In this study, we used data from the INEQ-CITIES study to analyse inequalities in cause-specific mortality in 15 European cities at the beginning of the 21st century. Methods A cross-sectional ecological study was carried out to analyse 9 of the leading specific causes of death in small areas from 15 European cities. Using a hierarchical Bayesian spatial model, we estimated smoothed Standardized Mortality Ratios, relative risks and 95% credible intervals for cause-specific mortality in relation to a socioeconomic deprivation index, separately for men and women. Results We detected spatial socioeconomic inequalities for most causes of mortality studied, although these inequalities differed markedly between cities, being more pronounced in Northern and Central-Eastern Europe. In the majority of cities, most of these causes of death were positively associated with deprivation among men, with the exception of prostatic cancer. Among women, diabetes, ischaemic heart disease, chronic liver diseases and respiratory diseases were also positively associated with deprivation in most cities. Lung cancer mortality was positively associated with deprivation in Northern European cities and in Kosice, but this association was non-existent or even negative in Southern European cities. Finally, breast cancer risk was inversely associated with deprivation in three Southern European cities. Conclusions The results confirm the existence of socioeconomic inequalities in many of the main causes of mortality, and reveal variations in their magnitude between different European cities.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2014, Director: Antoni Benseny i Olga Julià de Ferran, The motivation for this work comes from looking for the best place to locate a Mathematics Academy for university students in Barcelona. Each of the degrees in every faculty has a mark scale which is based on certain parameters. The following parameters are taken from the net: - The number of academies which offer courses for the degree. - The number of mathematics subjects of the degree. - Average number of students enrolled for each subject. - Average number of students who fail each subject. It would be necessary to carry out many surveys of the students to obtain the following pa- rameters: - Average number of times the students need to do the subject to pass. - Average number of students who go to academies. - Degree of knowledge of the existence of other academies. - Degree of need for an mathematics academy. To avoid carrying out such an extensive number of studies, Bayesian Statistics are used to estimate the parameters properly. Bayesian methods make it possible to incorporate scientific hypothesis in the analysis(by means of prior distribution). Statistical inference about a quantity of interest is described as the modification of the uncertainty about its value in the light of evidence, and Bayes’ theorem precisely specifies how this modification should be made. Using the degree’s mark scheme and the distance between the center’s location and each place in Barcelona, a grade or mark is assigned to each location. It is done by several mathematical models which use geographical and cartesian coordinates. In models in cartesian coordinates Newton’s method is used to determine a suitable location for the academy. The work includes a didactic programming of a subject from the degree which gets the most marks. It shows how the academy will help the students to understand the subject and to become great at studying maths.

We develop a climate-economy model with active learning. We consider three ways of active learning: improved observations, adding observations from the past and improved theory from climate research. From the model, we find that the decision maker invests a significant amount of money in climate research. Expenditures to increase the rate of learning are far greater than the current level of expenditure on climate research, as it helps in taking improved decisions. The optimal carbon tax for the active learning model is nontrivially lower than that for the uncertainty model and the passive learning model.

It has been suggested that recent cosmological and flavor-oscillation data favor the existence of additional neutrino species beyond the three predicted by the Standard Model of particle physics. We apply Bayesian model selection to determine whether there is indeed any evidence from current cosmological datasets for the standard cosmological model to be extended to include additional neutrino flavors. The datasets employed include cosmic microwave background temperature, polarization and lensing power spectra, and measurements of the baryon acoustic oscillation scale and the Hubble constant. We also consider other extensions to the standard neutrino model, such as massive neutrinos, and possible degeneracies with other cosmological parameters. The Bayesian evidence indicates that current cosmological data do not require any non-standard neutrino properties., Comment: 17 pages, 7 figures. v3: replaced with version published in JCAP (typo fixes, including Figure 1 units)

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to 7{\sigma} for fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter., Comment: Matches accepted verion to JCAP; conclusions unchaged, extra references added

There are not “universal methods” to determine diet composition of predators. Most traditional methods are biased because of their reliance on differential digestibility and the recovery of hard items. By relying on assimilated food, stable isotope and Bayesian mixing models (SIMMs) resolve many biases of traditional methods. SIMMs can incorporate prior information (i.e. proportional diet composition) that may improve the precision in the estimated dietary composition. However few studies have assessed the performance of traditional methods and SIMMs with and without informative priors to study the predators’ diets. Here we compare the diet compositions of the South American fur seal and sea lions obtained by scats analysis and by SIMMs-UP (uninformative priors) and assess whether informative priors (SIMMs-IP) from the scat analysis improved the estimated diet composition compared to SIMMs-UP. According to the SIMM-UP, while pelagic species dominated the fur seal’s diet the sea lion’s did not have a clear dominance of any prey. In contrast, SIMM-IP’s diets compositions were dominated by the same preys as in scat analyses. When prior information influenced SIMMs’ estimates, incorporating informative priors improved the precision in the estimated diet composition at the risk of inducing biases in the estimates. If preys isotopic data allow discriminating preys’ contributions to diets, informative priors should lead to more precise but unbiased estimated diet composition. Just as estimates of diet composition obtained from traditional methods are critically interpreted because of their biases, care must be exercised when interpreting diet composition obtained by SIMMs-IP. The best approach to obtain a near-complete view of predators’ diet composition should involve the simultaneous consideration of different sources of partial evidence (traditional methods, SIMM-UP and SIMM-IP) in the light of natural history of the predator species so as to reliably ascertain and weight the information yielded by each method.

La toma de decisiones referentes al diseño o en sistemas de alerta requieren el estudio de las acciones externas (frecuentemente meteorológicas), la descripción probabilista del sistema (vulnerabilidad, susceptibilidad) y los costes asociados a los efectos que se producen. Se hace especial referencia a los estudios de peligrosidad de fenómenos como vientos, oleaje, precipitación, etc. A partir de datos observados se estiman las probabilidades de ocurrencia de sucesos extremales y otros parámetros de la peligrosidad (periodos de retorno). Los métodos estadísticos utilizados son preferentemente bayesiano, los cuales permiten el control de la incertidumbre de las estimas. Se incluye el estudio de tendencias climáticas o la adquisición de datos de diferente procedencia.

The purpose of the study is to apply Bayesian inference in order to estimate the uncertainty in model parameters and predictions for environmental models. The analysis was based on a global optimization routine that finds good initial values for an adaptive Markov chains Monte Carlo (MCMC) algorithm that finally computes the posterior parameter distribution. A revised activated sludge model was used in order to perform a comparison between Bayesian and linear theory methods. It was observed that the linear theory method systematically underestimates the confidence intervals of the estimated model parameters because the multivariate normality assumption is violated and practical unidentifiability for some parameters occurs.

The paper discusses maintenance challenges of organisations with a huge number of devices and proposes the use of probabilistic models to assist monitoring and maintenance planning. The proposal assumes connectivity of instruments to report relevant features for monitoring. Also, the existence of enough historical registers with diagnosed breakdowns is required to make probabilistic models reliable and useful for predictive maintenance strategies based on them. Regular Markov models based on estimated failure and repair rates are proposed to calculate the availability of the instruments and Dynamic Bayesian Networks are proposed to model cause-effect relationships to trigger predictive maintenance services based on the influence between observed features and previously documented diagnostics.

A Point-Over-Threshold approach using a reparameterization of the Generalized Pareto Distribution (GPD) has been used to assess changes in the daily rainfall Barcelona series (1854–2006). A Bayesian approach, considering the suitable scale and physical features of the phenomenon, has been used to look for these alterations. Two different models have been assessed: existence of abrupt changes in the new GPD parameters due to modifications of the observatory locations and trends in these GPD parameters, pointing to a climate change scenario.

When actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce different regression models in order to relax the independence assumption, including zero-inflated models to account for excess of zeros and overdispersion. These models have been largely ignored to multivariate Poisson date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.