Testing allele homogeneity: the problem of nested hypotheses

Background: The evaluation of associations between genotypes and diseases in a case-control framework plays an important role in genetic epidemiology. This paper focuses on the evaluation of the homogeneity of both genotypic and allelic frequencies. The traditional test that is used to check allelic homogeneity is known to be valid only under Hardy-Weinberg equilibrium, a property that may not hold in practice. Results: We first describe the flaws of the traditional (chi-squared) tests for both allelic and genotypic homogeneity. Besides the known problem of the allelic procedure, we show that whenever these tests are used, an incoherence may arise: sometimes the genotypic homogeneity hypothesis is not rejected, but the allelic hypothesis is. As we argue, this is logically impossible. Some methods that were recently proposed implicitly rely on the idea that this does not happen. In an attempt to correct this incoherence, we describe an alternative frequentist approach that is appropriate even when Hardy-Weinberg equilibrium does not hold. It is then shown that the problem remains and is intrinsic of frequentist procedures. Finally, we introduce the Full Bayesian Significance Test to test both hypotheses and prove that the incoherence cannot happen with these new tests. To illustrate this, all five tests are applied to real and simulated datasets. Using the celebrated power analysis, we show that the Bayesian method is comparable to the frequentist one and has the advantage of being coherent. Conclusions: Contrary to more traditional approaches, the Full Bayesian Significance Test for association studies provides a simple, coherent and powerful tool for detecting associations.

Phylogeny of Lundia (Bignoniaceae) based on ndhF and PepC sequences

The circumscription of genera belonging to tribe Bignonieae (Bignoniaceae) has traditionally been complex, with only a few genera having stable circumscriptions in the various classification systems proposed for the tribe. The genus Lundia, for instance, is well characterized by a series of morphological synapomorphies and its circumscription has remained quite stable throughout its history. Despite the stable circumscription of Lundia, the circumscription of species within the genus has remained problematic. This study aims to reconstruct the phylogeny of Lundia in order to refine species circumscriptions, gain a better understanding of relationships between taxa, and identify potential morphological synapomorphies for species and major clades. We sampled 26 accessions representing 13 species of Lundia, and 5 outgroups, and reconstructed the phylogeny of the genus using a chloroplast (ndhF) and a nuclear marker (PepC). Data derived from sequences of the individual loci were analyzed using parsimony and Bayesian inference, and the combined molecular dataset was analyzed with Bayesian methods. The monophyly of Lundia nitidula, a species with a particularly complex circumscription, was tested using Shimodaira-Hasegawa (SH) test and the approximately unbiased test for phylogenetic tree selection (AU test). In addition, 40 morphological characters were mapped onto the tree that resulted from the analysis of the combined molecular dataset in order to identify morphological synapomorphies of individual species and major clades. Lundia and most species currently recognized within the genus were strongly supported as monophyletic in all analyses. One species, Lundia nitidula, was not resolved as monophyletic, but the monophyly of this species was not rejected by the AU and SH tests. Lundia sect. Eriolundia is resolved as paraphyletic in all analyses, while Lundia sect. Eulundia is monophyletic and supported by the same morphological characters traditionally used to circumscribe this section. The phylogeny of Lundia contributed important information for a better circumscription of species and served as basis the taxonomic revision of the genus.

Phylogeographic Analysis of HIV-1 Subtype C Dissemination in Southern Brazil

The HIV-1 subtype C has spread efficiently in the southern states of Brazil (Rio Grande do Sul, Santa Catarina and Parana). Phylogeographic studies indicate that the subtype C epidemic in southern Brazil was initiated by the introduction of a single founder virus population at some time point between 1960 and 1980, but little is known about the spatial dynamics of viral spread. A total of 135 Brazilian HIV-1 subtype C pol sequences collected from 1992 to 2009 at the three southern state capitals (Porto Alegre, Florianopolis and Curitiba) were analyzed. Maximum-likelihood and Bayesian methods were used to explore the degree of phylogenetic mixing of subtype C sequences from different cities and to reconstruct the geographical pattern of viral spread in this country region. Phylogeographic analyses supported the monophyletic origin of the HIV-1 subtype C clade circulating in southern Brazil and placed the root of that clade in Curitiba (Parana state). This analysis further suggested that Florianopolis (Santa Catarina state) is an important staging post in the subtype C dissemination displaying high viral migration rates from and to the other cities, while viral flux between Curitiba and Porto Alegre (Rio Grande do Sul state) is very low. We found a positive correlation (r(2) = 0.64) between routine travel and viral migration rates among localities. Despite the intense viral movement, phylogenetic intermixing of subtype C sequences from different Brazilian cities is lower than expected by chance. Notably, a high proportion (67%) of subtype C sequences from Porto Alegre branched within a single local monophyletic sub-cluster. These results suggest that the HIV-1 subtype C epidemic in southern Brazil has been shaped by both frequent viral migration among states and in situ dissemination of local clades.

Phylodynamics and Dispersal of HRSV Entails Its Permanence in the General Population in between Yearly Outbreaks in Children

Background: Human respiratory syncytial virus (HRSV) is one of the major etiologic agents of respiratory tract infections among children worldwide. Methodology/Principal Findings: Here through a comprehensive analysis of the two major HRSV groups A and B (n = 1983) which comprise of several genotypes, we present a complex pattern of population dynamics of HRSV over a time period of 50 years (1956-2006). Circulation pattern of HRSV revealed a series of expansions and fluctuations of co-circulating lineages with a predominance of HRSVA. Positively selected amino acid substitutions of the G glycoprotein occurred upon population growth of GB3 with a 60-nucleotide insertion (GB3 Insert), while other genotypes acquired substitutions upon both population growth and decrease, thus possibly reflecting a role for immune selected epitopes in linkage to the traced substitution sites that may have important relevance for vaccine design. Analysis evidenced the co-circulation and predominance of distinct HRSV genotypes in Brazil and suggested a year-round presence of the virus. In Brazil, GA2 and GA5 were the main culprits of HRSV outbreaks until recently, when the GB3 Insert became highly prevalent. Using Bayesian methods, we determined the dispersal patterns of genotypes through several inferred migratory routes. Conclusions/Significance: Genotypes spread across continents and between neighboring areas. Crucially, genotypes also remained at any given region for extended periods, independent of seasonal outbreaks possibly maintained by re-infecting the general population.

Customer Evolution in Sales Channel Migration

This research has been triggered by an emergent trend in customer behavior: customers have rapidly expanded their channel experiences and preferences beyond traditional channels (such as stores) and they expect the company with which they do business to have a presence on all these channels. This evidence has produced an increasing interest in multichannel customer behavior and it has motivated several researchers to study the customers’ channel choices dynamics in multichannel environment. We study how the consumer decision process for channel choice and response to marketing communications evolves for a cohort of new customers. We assume a newly acquired customer’s decisions are described by a “trial” model, but the customer’s choice process evolves to a “post-trial” model as the customer learns his or her preferences and becomes familiar with the firm’s marketing efforts. The trial and post-trial decision processes are each described by different multinomial logit choice models, and the evolution from the trial to post-trial model is determined by a customer-level geometric distribution that captures the time it takes for the customer to make the transition. We utilize data for a major retailer who sells in three channels – retail store, the Internet, and via catalog. The model is estimated using Bayesian methods that allow for cross-customer heterogeneity. This allows us to have distinct parameters estimates for a trial and an after trial stages and to estimate the quickness of this transit at the individual level. The results show for example that the customer decision process indeed does evolve over time. Customers differ in the duration of the trial period and marketing has a different impact on channel choice in the trial and post-trial stages. Furthermore, we show that some people switch channel decision processes while others don’t and we found that several factors have an impact on the probability to switch decision process. Insights from this study can help managers tailor their marketing communication strategy as customers gain channel choice experience. Managers may also have insights on the timing of the direct marketing communications. They can predict the duration of the trial phase at individual level detecting the customers with a quick, long or even absent trial phase. They can even predict if the customer will change or not his decision process over time, and they can influence the switching process using specific marketing tools

Immune reconstitution inflammatory syndrome in patients starting antiretroviral therapy for HIV infection: a systematic review and meta-analysis

In patients with HIV-1 infection who are starting combination antiretroviral therapy (ART), the incidence of immune reconstitution inflammatory syndrome (IRIS) is not well defined. We did a meta-analysis to establish the incidence and lethality of the syndrome in patients with a range of previously diagnosed opportunistic infections, and examined the relation between occurrence and the degree of immunodeficiency. Systematic review identified 54 cohort studies of 13 103 patients starting ART, of whom 1699 developed IRIS. We calculated pooled cumulative incidences with 95% credibility intervals (CrI) by Bayesian methods and did a random-effects metaregression to analyse the relation between CD4 cell count and incidence of IRIS. In patients with previously diagnosed AIDS-defining illnesses, IRIS developed in 37.7% (95% CrI 26.6-49.4) of those with cytomegalovirus retinitis, 19.5% (6.7-44.8) of those with cryptococcal meningitis, 15.7% (9.7-24.5) of those with tuberculosis, 16.7% (2.3-50.7) of those with progressive multifocal leukoencephalopathy, and 6.4% (1.2-24.7) of those with Kaposi's sarcoma, and 12.2% (6.8-19.6) of those with herpes zoster. 16.1% (11.1-22.9) of unselected patients starting ART developed any type of IRIS. 4.5% (2.1-8.6) of patients with any type of IRIS died, 3.2% (0.7-9.2) of those with tuberculosis-associated IRIS died, and 20.8% (5.0-52.7) of those with cryptococcal meningitis died. Metaregression analyses showed that the risk of IRIS is associated with CD4 cell count at the start of ART, with a high risk in patients with fewer than 50 cells per microL. Occurrence of IRIS might therefore be reduced by initiation of ART before immunodeficiency becomes advanced.

Mortality from road traffic accidents in Switzerland: longitudinal and spatial analyses

Road traffic accidents (RTA) are an important cause of premature death. We examined socio-demographic and geographical determinants of RTA mortality in Switzerland by linking 2000 census data to RTA mortality records 2000-2005 (ICD-10 codes V00-V99). Data from 5.5 million residents aged 18-94 years, 1744 study areas, and 1620 RTA deaths were analyzed, including 978 deaths (60.4%) in motor vehicle occupants, 254 (15.7%) in motorcyclists, 107 (6.6%) in cyclists, and 259 (16.0%) in pedestrians. Weibull survival models and Bayesian methods were used to calculate hazard ratios (HR), and standardized mortality ratios (SMR) across study areas. Adjusted HR comparing women with men ranged from 0.04 (95% CI 0.02-0.07) in motorcyclists to 0.43 (95% CI 0.32-0.56) in pedestrians. There was a u-shaped relationship with age in motor vehicle occupants and motorcyclists. In cyclists and pedestrians, mortality increased after age 55 years. Mortality was higher in individuals with primary education (HR 1.53; 95% CI 1.29-1.81), and higher in single (HR 1.24; 95% CI 1.05-1.46), widowed (HR 1.31; 95% CI 1.05-1.65) and divorced individuals (HR 1.62; 95% CI 1.33-1.97), compared to persons with tertiary education or married persons. The association with education was particularly strong for pedestrians (HR 1.87; 95% CI 1.20-2.91). RTA mortality increased with decreasing population density of study areas for motor vehicle occupants (test for trend p<0.0001) and motorcyclists (p=0.0021) but not for cyclists (p=0.39) or pedestrians (p=0.29). SMR standardized for socio-demographic and geographical variables ranged from 82 to 190. Prevention efforts should aim to reduce inequities across socio-demographic and educational groups, and across geographical areas, with interventions targeted at high-risk groups and areas, and different traffic users, including pedestrians.

Patterns of morphological changes and hybridization between sympatric whitefish morphs (Coregonus spp.) in a Swiss lake: a role for eutrophication?

Whitefish, genus Coregonus, show exceptional levels of phenotypic diversity with sympatric morphs occurring in numerous postglacial lakes in the northern hemisphere. Here, we studied the effects of human-induced eutrophication on sympatric whitefish morphs in the Swiss lake, Lake Thun. In particular, we addressed the questions whether eutrophication (i) induced hybridization between two ecologically divergent summer-spawning morphs through a loss of environmental heterogeneity, and (ii) induced rapid adaptive morphological changes through changes in the food web structure. Genetic analysis based on 11 microsatellite loci of 282 spawners revealed that the pelagic and the benthic morph represent highly distinct gene pools occurring at different relative proportions on all seven known spawning sites. Gill raker counts, a highly heritable trait, showed nearly discrete distributions for the two morphs. Multilocus genotypes characteristic of the pelagic morph had more gill rakers than genotypes characteristic of benthic morph. Using Bayesian methods, we found indications of recent but limited introgressive hybridization. Comparisons with historical gill raker data yielded median evolutionary rates of 0.24 haldanes and median selection intensities of 0.27 for this trait in both morphs for 1948-2004 suggesting rapid evolution through directional selection at this trait. However, phenotypic plasticity as an alternative explanation for this phenotypic change cannot be discarded. We hypothesize that both the temporal shifts in mean gill raker counts and the recent hybridization reflect responses to changes in the trophic state of the lake induced by pollution in the 1960s, which created novel selection pressures with respect to feeding niches and spawning site preferences.

Simulation study of joint transition and Weibull survival model with shared parameters

This study investigates a theoretical model where a longitudinal process, that is a stationary Markov-Chain, and a Weibull survival process share a bivariate random effect. Furthermore, a Quality-of-Life adjusted survival is calculated as the weighted sum of survival time. Theoretical values of population mean adjusted survival of the described model are computed numerically. The parameters of the bivariate random effect do significantly affect theoretical values of population mean. Maximum-Likelihood and Bayesian methods are applied on simulated data to estimate the model parameters. Based on the parameter estimates, predicated population mean adjusted survival can then be calculated numerically and compared with the theoretical values. Bayesian method and Maximum-Likelihood method provide parameter estimations and population mean prediction with comparable accuracy; however Bayesian method suffers from poor convergence due to autocorrelation and inter-variable correlation. ^

Video analysis based vehicle detection and tracking using an MCMC sampling framework

This article presents a probabilistic method for vehicle detection and tracking through the analysis of monocular images obtained from a vehicle-mounted camera. The method is designed to address the main shortcomings of traditional particle filtering approaches, namely Bayesian methods based on importance sampling, for use in traffic environments. These methods do not scale well when the dimensionality of the feature space grows, which creates significant limitations when tracking multiple objects. Alternatively, the proposed method is based on a Markov chain Monte Carlo (MCMC) approach, which allows efficient sampling of the feature space. The method involves important contributions in both the motion and the observation models of the tracker. Indeed, as opposed to particle filter-based tracking methods in the literature, which typically resort to observation models based on appearance or template matching, in this study a likelihood model that combines appearance analysis with information from motion parallax is introduced. Regarding the motion model, a new interaction treatment is defined based on Markov random fields (MRF) that allows for the handling of possible inter-dependencies in vehicle trajectories. As for vehicle detection, the method relies on a supervised classification stage using support vector machines (SVM). The contribution in this field is twofold. First, a new descriptor based on the analysis of gradient orientations in concentric rectangles is dened. This descriptor involves a much smaller feature space compared to traditional descriptors, which are too costly for real-time applications. Second, a new vehicle image database is generated to train the SVM and made public. The proposed vehicle detection and tracking method is proven to outperform existing methods and to successfully handle challenging situations in the test sequences.

Contribución al estudio de las metodologías de cálculo realista con incertidumbre (BEPU), dentro del análisis determinista de seguridad de plantas nucleares

El análisis determinista de seguridad (DSA) es el procedimiento que sirve para diseñar sistemas, estructuras y componentes relacionados con la seguridad en las plantas nucleares. El DSA se basa en simulaciones computacionales de una serie de hipotéticos accidentes representativos de la instalación, llamados escenarios base de diseño (DBS). Los organismos reguladores señalan una serie de magnitudes de seguridad que deben calcularse en las simulaciones, y establecen unos criterios reguladores de aceptación (CRA), que son restricciones que deben cumplir los valores de esas magnitudes. Las metodologías para realizar los DSA pueden ser de 2 tipos: conservadoras o realistas. Las metodologías conservadoras utilizan modelos predictivos e hipótesis marcadamente pesimistas, y, por ello, relativamente simples. No necesitan incluir un análisis de incertidumbre de sus resultados. Las metodologías realistas se basan en hipótesis y modelos predictivos realistas, generalmente mecanicistas, y se suplementan con un análisis de incertidumbre de sus principales resultados. Se les denomina también metodologías BEPU (“Best Estimate Plus Uncertainty”). En ellas, la incertidumbre se representa, básicamente, de manera probabilista. Para metodologías conservadores, los CRA son, simplemente, restricciones sobre valores calculados de las magnitudes de seguridad, que deben quedar confinados en una “región de aceptación” de su recorrido. Para metodologías BEPU, el CRA no puede ser tan sencillo, porque las magnitudes de seguridad son ahora variables inciertas. En la tesis se desarrolla la manera de introducción de la incertidumbre en los CRA. Básicamente, se mantiene el confinamiento a la misma región de aceptación, establecida por el regulador. Pero no se exige el cumplimiento estricto sino un alto nivel de certidumbre. En el formalismo adoptado, se entiende por ello un “alto nivel de probabilidad”, y ésta corresponde a la incertidumbre de cálculo de las magnitudes de seguridad. Tal incertidumbre puede considerarse como originada en los inputs al modelo de cálculo, y propagada a través de dicho modelo. Los inputs inciertos incluyen las condiciones iniciales y de frontera al cálculo, y los parámetros empíricos de modelo, que se utilizan para incorporar la incertidumbre debida a la imperfección del modelo. Se exige, por tanto, el cumplimiento del CRA con una probabilidad no menor a un valor P0 cercano a 1 y definido por el regulador (nivel de probabilidad o cobertura). Sin embargo, la de cálculo de la magnitud no es la única incertidumbre existente. Aunque un modelo (sus ecuaciones básicas) se conozca a la perfección, la aplicación input-output que produce se conoce de manera imperfecta (salvo que el modelo sea muy simple). La incertidumbre debida la ignorancia sobre la acción del modelo se denomina epistémica; también se puede decir que es incertidumbre respecto a la propagación. La consecuencia es que la probabilidad de cumplimiento del CRA no se puede conocer a la perfección; es una magnitud incierta. Y así se justifica otro término usado aquí para esta incertidumbre epistémica: metaincertidumbre. Los CRA deben incorporar los dos tipos de incertidumbre: la de cálculo de la magnitud de seguridad (aquí llamada aleatoria) y la de cálculo de la probabilidad (llamada epistémica o metaincertidumbre). Ambas incertidumbres pueden introducirse de dos maneras: separadas o combinadas. En ambos casos, el CRA se convierte en un criterio probabilista. Si se separan incertidumbres, se utiliza una probabilidad de segundo orden; si se combinan, se utiliza una probabilidad única. Si se emplea la probabilidad de segundo orden, es necesario que el regulador imponga un segundo nivel de cumplimiento, referido a la incertidumbre epistémica. Se denomina nivel regulador de confianza, y debe ser un número cercano a 1. Al par formado por los dos niveles reguladores (de probabilidad y de confianza) se le llama nivel regulador de tolerancia. En la Tesis se razona que la mejor manera de construir el CRA BEPU es separando las incertidumbres, por dos motivos. Primero, los expertos defienden el tratamiento por separado de incertidumbre aleatoria y epistémica. Segundo, el CRA separado es (salvo en casos excepcionales) más conservador que el CRA combinado. El CRA BEPU no es otra cosa que una hipótesis sobre una distribución de probabilidad, y su comprobación se realiza de forma estadística. En la tesis, los métodos estadísticos para comprobar el CRA BEPU en 3 categorías, según estén basados en construcción de regiones de tolerancia, en estimaciones de cuantiles o en estimaciones de probabilidades (ya sea de cumplimiento, ya sea de excedencia de límites reguladores). Según denominación propuesta recientemente, las dos primeras categorías corresponden a los métodos Q, y la tercera, a los métodos P. El propósito de la clasificación no es hacer un inventario de los distintos métodos en cada categoría, que son muy numerosos y variados, sino de relacionar las distintas categorías y citar los métodos más utilizados y los mejor considerados desde el punto de vista regulador. Se hace mención especial del método más utilizado hasta el momento: el método no paramétrico de Wilks, junto con su extensión, hecha por Wald, al caso multidimensional. Se decribe su método P homólogo, el intervalo de Clopper-Pearson, típicamente ignorado en el ámbito BEPU. En este contexto, se menciona el problema del coste computacional del análisis de incertidumbre. Los métodos de Wilks, Wald y Clopper-Pearson requieren que la muestra aleatortia utilizada tenga un tamaño mínimo, tanto mayor cuanto mayor el nivel de tolerancia exigido. El tamaño de muestra es un indicador del coste computacional, porque cada elemento muestral es un valor de la magnitud de seguridad, que requiere un cálculo con modelos predictivos. Se hace especial énfasis en el coste computacional cuando la magnitud de seguridad es multidimensional; es decir, cuando el CRA es un criterio múltiple. Se demuestra que, cuando las distintas componentes de la magnitud se obtienen de un mismo cálculo, el carácter multidimensional no introduce ningún coste computacional adicional. Se prueba así la falsedad de una creencia habitual en el ámbito BEPU: que el problema multidimensional sólo es atacable desde la extensión de Wald, que tiene un coste de computación creciente con la dimensión del problema. En el caso (que se da a veces) en que cada componente de la magnitud se calcula independientemente de los demás, la influencia de la dimensión en el coste no se puede evitar. Las primeras metodologías BEPU hacían la propagación de incertidumbres a través de un modelo sustitutivo (metamodelo o emulador) del modelo predictivo o código. El objetivo del metamodelo no es su capacidad predictiva, muy inferior a la del modelo original, sino reemplazar a éste exclusivamente en la propagación de incertidumbres. Para ello, el metamodelo se debe construir con los parámetros de input que más contribuyan a la incertidumbre del resultado, y eso requiere un análisis de importancia o de sensibilidad previo. Por su simplicidad, el modelo sustitutivo apenas supone coste computacional, y puede estudiarse exhaustivamente, por ejemplo mediante muestras aleatorias. En consecuencia, la incertidumbre epistémica o metaincertidumbre desaparece, y el criterio BEPU para metamodelos se convierte en una probabilidad simple. En un resumen rápido, el regulador aceptará con más facilidad los métodos estadísticos que menos hipótesis necesiten; los exactos más que los aproximados; los no paramétricos más que los paramétricos, y los frecuentistas más que los bayesianos. El criterio BEPU se basa en una probabilidad de segundo orden. La probabilidad de que las magnitudes de seguridad estén en la región de aceptación no sólo puede asimilarse a una probabilidad de éxito o un grado de cumplimiento del CRA. También tiene una interpretación métrica: representa una distancia (dentro del recorrido de las magnitudes) desde la magnitud calculada hasta los límites reguladores de aceptación. Esta interpretación da pie a una definición que propone esta tesis: la de margen de seguridad probabilista. Dada una magnitud de seguridad escalar con un límite superior de aceptación, se define el margen de seguridad (MS) entre dos valores A y B de la misma como la probabilidad de que A sea menor que B, obtenida a partir de las incertidumbres de A y B. La definición probabilista de MS tiene varias ventajas: es adimensional, puede combinarse de acuerdo con las leyes de la probabilidad y es fácilmente generalizable a varias dimensiones. Además, no cumple la propiedad simétrica. El término margen de seguridad puede aplicarse a distintas situaciones: distancia de una magnitud calculada a un límite regulador (margen de licencia); distancia del valor real de la magnitud a su valor calculado (margen analítico); distancia desde un límite regulador hasta el valor umbral de daño a una barrera (margen de barrera). Esta idea de representar distancias (en el recorrido de magnitudes de seguridad) mediante probabilidades puede aplicarse al estudio del conservadurismo. El margen analítico puede interpretarse como el grado de conservadurismo (GC) de la metodología de cálculo. Utilizando la probabilidad, se puede cuantificar el conservadurismo de límites de tolerancia de una magnitud, y se pueden establecer indicadores de conservadurismo que sirvan para comparar diferentes métodos de construcción de límites y regiones de tolerancia. Un tópico que nunca se abordado de manera rigurosa es el de la validación de metodologías BEPU. Como cualquier otro instrumento de cálculo, una metodología, antes de poder aplicarse a análisis de licencia, tiene que validarse, mediante la comparación entre sus predicciones y valores reales de las magnitudes de seguridad. Tal comparación sólo puede hacerse en escenarios de accidente para los que existan valores medidos de las magnitudes de seguridad, y eso ocurre, básicamente en instalaciones experimentales. El objetivo último del establecimiento de los CRA consiste en verificar que se cumplen para los valores reales de las magnitudes de seguridad, y no sólo para sus valores calculados. En la tesis se demuestra que una condición suficiente para este objetivo último es la conjunción del cumplimiento de 2 criterios: el CRA BEPU de licencia y un criterio análogo, pero aplicado a validación. Y el criterio de validación debe demostrarse en escenarios experimentales y extrapolarse a plantas nucleares. El criterio de licencia exige un valor mínimo (P0) del margen probabilista de licencia; el criterio de validación exige un valor mínimo del margen analítico (el GC). Esos niveles mínimos son básicamente complementarios; cuanto mayor uno, menor el otro. La práctica reguladora actual impone un valor alto al margen de licencia, y eso supone que el GC exigido es pequeño. Adoptar valores menores para P0 supone menor exigencia sobre el cumplimiento del CRA, y, en cambio, más exigencia sobre el GC de la metodología. Y es importante destacar que cuanto mayor sea el valor mínimo del margen (de licencia o analítico) mayor es el coste computacional para demostrarlo. Así que los esfuerzos computacionales también son complementarios: si uno de los niveles es alto (lo que aumenta la exigencia en el cumplimiento del criterio) aumenta el coste computacional. Si se adopta un valor medio de P0, el GC exigido también es medio, con lo que la metodología no tiene que ser muy conservadora, y el coste computacional total (licencia más validación) puede optimizarse. ABSTRACT Deterministic Safety Analysis (DSA) is the procedure used in the design of safety-related systems, structures and components of nuclear power plants (NPPs). DSA is based on computational simulations of a set of hypothetical accidents of the plant, named Design Basis Scenarios (DBS). Nuclear regulatory authorities require the calculation of a set of safety magnitudes, and define the regulatory acceptance criteria (RAC) that must be fulfilled by them. Methodologies for performing DSA van be categorized as conservative or realistic. Conservative methodologies make use of pessimistic model and assumptions, and are relatively simple. They do not need an uncertainty analysis of their results. Realistic methodologies are based on realistic (usually mechanistic) predictive models and assumptions, and need to be supplemented with uncertainty analyses of their results. They are also termed BEPU (“Best Estimate Plus Uncertainty”) methodologies, and are typically based on a probabilistic representation of the uncertainty. For conservative methodologies, the RAC are simply the restriction of calculated values of safety magnitudes to “acceptance regions” defined on their range. For BEPU methodologies, the RAC cannot be so simple, because the safety magnitudes are now uncertain. In the present Thesis, the inclusion of uncertainty in RAC is studied. Basically, the restriction to the acceptance region must be fulfilled “with a high certainty level”. Specifically, a high probability of fulfillment is required. The calculation uncertainty of the magnitudes is considered as propagated from inputs through the predictive model. Uncertain inputs include model empirical parameters, which store the uncertainty due to the model imperfection. The fulfillment of the RAC is required with a probability not less than a value P0 close to 1 and defined by the regulator (probability or coverage level). Calculation uncertainty is not the only one involved. Even if a model (i.e. the basic equations) is perfectly known, the input-output mapping produced by the model is imperfectly known (unless the model is very simple). This ignorance is called epistemic uncertainty, and it is associated to the process of propagation). In fact, it is propagated to the probability of fulfilling the RAC. Another term used on the Thesis for this epistemic uncertainty is metauncertainty. The RAC must include the two types of uncertainty: one for the calculation of the magnitude (aleatory uncertainty); the other one, for the calculation of the probability (epistemic uncertainty). The two uncertainties can be taken into account in a separate fashion, or can be combined. In any case the RAC becomes a probabilistic criterion. If uncertainties are separated, a second-order probability is used; of both are combined, a single probability is used. On the first case, the regulator must define a level of fulfillment for the epistemic uncertainty, termed regulatory confidence level, as a value close to 1. The pair of regulatory levels (probability and confidence) is termed the regulatory tolerance level. The Thesis concludes that the adequate way of setting the BEPU RAC is by separating the uncertainties. There are two reasons to do so: experts recommend the separation of aleatory and epistemic uncertainty; and the separated RAC is in general more conservative than the joint RAC. The BEPU RAC is a hypothesis on a probability distribution, and must be statistically tested. The Thesis classifies the statistical methods to verify the RAC fulfillment in 3 categories: methods based on tolerance regions, in quantile estimators and on probability (of success or failure) estimators. The former two have been termed Q-methods, whereas those in the third category are termed P-methods. The purpose of our categorization is not to make an exhaustive survey of the very numerous existing methods. Rather, the goal is to relate the three categories and examine the most used methods from a regulatory standpoint. Special mention deserves the most used method, due to Wilks, and its extension to multidimensional variables (due to Wald). The counterpart P-method of Wilks’ is Clopper-Pearson interval, typically ignored in the BEPU realm. The problem of the computational cost of an uncertainty analysis is tackled. Wilks’, Wald’s and Clopper-Pearson methods require a minimum sample size, which is a growing function of the tolerance level. The sample size is an indicator of the computational cost, because each element of the sample must be calculated with the predictive models (codes). When the RAC is a multiple criteria, the safety magnitude becomes multidimensional. When all its components are output of the same calculation, the multidimensional character does not introduce additional computational cost. In this way, an extended idea in the BEPU realm, stating that the multi-D problem can only be tackled with the Wald extension, is proven to be false. When the components of the magnitude are independently calculated, the influence of the problem dimension on the cost cannot be avoided. The former BEPU methodologies performed the uncertainty propagation through a surrogate model of the code, also termed emulator or metamodel. The goal of a metamodel is not the predictive capability, clearly worse to the original code, but the capacity to propagate uncertainties with a lower computational cost. The emulator must contain the input parameters contributing the most to the output uncertainty, and this requires a previous importance analysis. The surrogate model is practically inexpensive to run, so that it can be exhaustively analyzed through Monte Carlo. Therefore, the epistemic uncertainty due to sampling will be reduced to almost zero, and the BEPU RAC for metamodels includes a simple probability. The regulatory authority will tend to accept the use of statistical methods which need a minimum of assumptions: exact, nonparametric and frequentist methods rather than approximate, parametric and bayesian methods, respectively. The BEPU RAC is based on a second-order probability. The probability of the safety magnitudes being inside the acceptance region is a success probability and can be interpreted as a fulfillment degree if the RAC. Furthermore, it has a metric interpretation, as a distance (in the range of magnitudes) from calculated values of the magnitudes to acceptance regulatory limits. A probabilistic definition of safety margin (SM) is proposed in the thesis. The same from a value A to other value B of a safety magnitude is defined as the probability that A is less severe than B, obtained from the uncertainties if A and B. The probabilistic definition of SM has several advantages: it is nondimensional, ranges in the interval (0,1) and can be easily generalized to multiple dimensions. Furthermore, probabilistic SM are combined according to the probability laws. And a basic property: probabilistic SM are not symmetric. There are several types of SM: distance from a calculated value to a regulatory limit (licensing margin); or from the real value to the calculated value of a magnitude (analytical margin); or from the regulatory limit to the damage threshold (barrier margin). These representations of distances (in the magnitudes’ range) as probabilities can be applied to the quantification of conservativeness. Analytical margins can be interpreted as the degree of conservativeness (DG) of the computational methodology. Conservativeness indicators are established in the Thesis, useful in the comparison of different methods of constructing tolerance limits and regions. There is a topic which has not been rigorously tackled to the date: the validation of BEPU methodologies. Before being applied in licensing, methodologies must be validated, on the basis of comparisons of their predictions ad real values of the safety magnitudes. Real data are obtained, basically, in experimental facilities. The ultimate goal of establishing RAC is to verify that real values (aside from calculated values) fulfill them. In the Thesis it is proved that a sufficient condition for this goal is the conjunction of 2 criteria: the BEPU RAC and an analogous criterion for validation. And this las criterion must be proved in experimental scenarios and extrapolated to NPPs. The licensing RAC requires a minimum value (P0) of the probabilistic licensing margin; the validation criterion requires a minimum value of the analytical margin (i.e., of the DG). These minimum values are basically complementary; the higher one of them, the lower the other one. The regulatory practice sets a high value on the licensing margin, so that the required DG is low. The possible adoption of lower values for P0 would imply weaker exigence on the RCA fulfillment and, on the other hand, higher exigence on the conservativeness of the methodology. It is important to highlight that a higher minimum value of the licensing or analytical margin requires a higher computational cost. Therefore, the computational efforts are also complementary. If medium levels are adopted, the required DG is also medium, and the methodology does not need to be very conservative. The total computational effort (licensing plus validation) could be optimized.

Why I Am Not a Likelihoodist

Frequentist statistical methods continue to predominate in many areas of science despite prominent calls for "statistical reform." They do so in part because their main rivals, Bayesian methods, appeal to prior probability distributions that arguably lack an objective justification in typical cases. Some methodologists find a third approach called likelihoodism attractive because it avoids important objections to frequentism without appealing to prior probabilities. However, likelihoodist methods do not provide guidance for belief or action, but only assessments of data as evidence. I argue that there is no good way to use those assessments to guide beliefs or actions without appealing to prior probabilities, and that as a result likelihoodism is not a viable alternative to frequentism and Bayesianism for statistical reform efforts in science.

Precautionary principles: a jurisdiction-free framework for decision-making under risk

Fundamental principles of precaution are legal maxims that ask for preventive actions, perhaps as contingent interim measures while relevant information about causality and harm remains unavailable, to minimize the societal impact of potentially severe or irreversible outcomes. Such principles do not explain how to make choices or how to identify what is protective when incomplete and inconsistent scientific evidence of causation characterizes the potential hazards. Rather, they entrust lower jurisdictions, such as agencies or authorities, to make current decisions while recognizing that future information can contradict the scientific basis that supported the initial decision. After reviewing and synthesizing national and international legal aspects of precautionary principles, this paper addresses the key question: How can society manage potentially severe, irreversible or serious environmental outcomes when variability, uncertainty, and limited causal knowledge characterize their decision-making? A decision-analytic solution is outlined that focuses on risky decisions and accounts for prior states of information and scientific beliefs that can be updated as subsequent information becomes available. As a practical and established approach to causal reasoning and decision-making under risk, inherent to precautionary decision-making, these (Bayesian) methods help decision-makers and stakeholders because they formally account for probabilistic outcomes, new information, and are consistent and replicable. Rational choice of an action from among various alternatives-defined as a choice that makes preferred consequences more likely-requires accounting for costs, benefits and the change in risks associated with each candidate action. Decisions under any form of the precautionary principle reviewed must account for the contingent nature of scientific information, creating a link to the decision-analytic principle of expected value of information (VOI), to show the relevance of new information, relative to the initial ( and smaller) set of data on which the decision was based. We exemplify this seemingly simple situation using risk management of BSE. As an integral aspect of causal analysis under risk, the methods developed in this paper permit the addition of non-linear, hormetic dose-response models to the current set of regulatory defaults such as the linear, non-threshold models. This increase in the number of defaults is an important improvement because most of the variants of the precautionary principle require cost-benefit balancing. Specifically, increasing the set of causal defaults accounts for beneficial effects at very low doses. We also show and conclude that quantitative risk assessment dominates qualitative risk assessment, supporting the extension of the set of default causal models.

Single patient (n-of-1) trials with binary treatment preference

The use of a fully parametric Bayesian method for analysing single patient trials based on the notion of treatment 'preference' is described. This Bayesian hierarchical modelling approach allows for full parameter uncertainty, use of prior information and the modelling of individual and patient sub-group structures. It provides updated probabilistic results for individual patients, and groups of patients with the same medical condition, as they are sequentially enrolled into individualized trials using the same medication alternatives. Two clinically interpretable criteria for determining a patient's response are detailed and illustrated using data from a previously published paper under two different prior information scenarios. Copyright (C) 2005 John Wiley & Sons, Ltd.

Minimum description length, regularisation and multi-modal data

Conventional feed forward Neural Networks have used the sum-of-squares cost function for training. A new cost function is presented here with a description length interpretation based on Rissanen's Minimum Description Length principle. It is a heuristic that has a rough interpretation as the number of data points fit by the model. Not concerned with finding optimal descriptions, the cost function prefers to form minimum descriptions in a naive way for computational convenience. The cost function is called the Naive Description Length cost function. Finding minimum description models will be shown to be closely related to the identification of clusters in the data. As a consequence the minimum of this cost function approximates the most probable mode of the data rather than the sum-of-squares cost function that approximates the mean. The new cost function is shown to provide information about the structure of the data. This is done by inspecting the dependence of the error to the amount of regularisation. This structure provides a method of selecting regularisation parameters as an alternative or supplement to Bayesian methods. The new cost function is tested on a number of multi-valued problems such as a simple inverse kinematics problem. It is also tested on a number of classification and regression problems. The mode-seeking property of this cost function is shown to improve prediction in time series problems. Description length principles are used in a similar fashion to derive a regulariser to control network complexity.