Multiple testing in spatial epidemiology: a Bayesian approach

In this work we aim to propose a new approach for preliminary epidemiological studies on Standardized Mortality Ratios (SMR) collected in many spatial regions. A preliminary study on SMRs aims to formulate hypotheses to be investigated via individual epidemiological studies that avoid bias carried on by aggregated analyses. Starting from collecting disease counts and calculating expected disease counts by means of reference population disease rates, in each area an SMR is derived as the MLE under the Poisson assumption on each observation. Such estimators have high standard errors in small areas, i.e. where the expected count is low either because of the low population underlying the area or the rarity of the disease under study. Disease mapping models and other techniques for screening disease rates among the map aiming to detect anomalies and possible high-risk areas have been proposed in literature according to the classic and the Bayesian paradigm. Our proposal is approaching this issue by a decision-oriented method, which focus on multiple testing control, without however leaving the preliminary study perspective that an analysis on SMR indicators is asked to. We implement the control of the FDR, a quantity largely used to address multiple comparisons problems in the eld of microarray data analysis but which is not usually employed in disease mapping. Controlling the FDR means providing an estimate of the FDR for a set of rejected null hypotheses. The small areas issue arises diculties in applying traditional methods for FDR estimation, that are usually based only on the p-values knowledge (Benjamini and Hochberg, 1995; Storey, 2003). Tests evaluated by a traditional p-value provide weak power in small areas, where the expected number of disease cases is small. Moreover tests cannot be assumed as independent when spatial correlation between SMRs is expected, neither they are identical distributed when population underlying the map is heterogeneous. The Bayesian paradigm oers a way to overcome the inappropriateness of p-values based methods. Another peculiarity of the present work is to propose a hierarchical full Bayesian model for FDR estimation in testing many null hypothesis of absence of risk.We will use concepts of Bayesian models for disease mapping, referring in particular to the Besag York and Mollié model (1991) often used in practice for its exible prior assumption on the risks distribution across regions. The borrowing of strength between prior and likelihood typical of a hierarchical Bayesian model takes the advantage of evaluating a singular test (i.e. a test in a singular area) by means of all observations in the map under study, rather than just by means of the singular observation. This allows to improve the power test in small areas and addressing more appropriately the spatial correlation issue that suggests that relative risks are closer in spatially contiguous regions. The proposed model aims to estimate the FDR by means of the MCMC estimated posterior probabilities b i's of the null hypothesis (absence of risk) for each area. An estimate of the expected FDR conditional on data (\FDR) can be calculated in any set of b i's relative to areas declared at high-risk (where thenull hypothesis is rejected) by averaging the b i's themselves. The\FDR can be used to provide an easy decision rule for selecting high-risk areas, i.e. selecting as many as possible areas such that the\FDR is non-lower than a prexed value; we call them\FDR based decision (or selection) rules. The sensitivity and specicity of such rule depend on the accuracy of the FDR estimate, the over-estimation of FDR causing a loss of power and the under-estimation of FDR producing a loss of specicity. Moreover, our model has the interesting feature of still being able to provide an estimate of relative risk values as in the Besag York and Mollié model (1991). A simulation study to evaluate the model performance in FDR estimation accuracy, sensitivity and specificity of the decision rule, and goodness of estimation of relative risks, was set up. We chose a real map from which we generated several spatial scenarios whose counts of disease vary according to the spatial correlation degree, the size areas, the number of areas where the null hypothesis is true and the risk level in the latter areas. In summarizing simulation results we will always consider the FDR estimation in sets constituted by all b i's selected lower than a threshold t. We will show graphs of the\FDR and the true FDR (known by simulation) plotted against a threshold t to assess the FDR estimation. Varying the threshold we can learn which FDR values can be accurately estimated by the practitioner willing to apply the model (by the closeness between\FDR and true FDR). By plotting the calculated sensitivity and specicity (both known by simulation) vs the\FDR we can check the sensitivity and specicity of the corresponding\FDR based decision rules. For investigating the over-smoothing level of relative risk estimates we will compare box-plots of such estimates in high-risk areas (known by simulation), obtained by both our model and the classic Besag York Mollié model. All the summary tools are worked out for all simulated scenarios (in total 54 scenarios). Results show that FDR is well estimated (in the worst case we get an overestimation, hence a conservative FDR control) in small areas, low risk levels and spatially correlated risks scenarios, that are our primary aims. In such scenarios we have good estimates of the FDR for all values less or equal than 0.10. The sensitivity of\FDR based decision rules is generally low but specicity is high. In such scenario the use of\FDR = 0:05 or\FDR = 0:10 based selection rule can be suggested. In cases where the number of true alternative hypotheses (number of true high-risk areas) is small, also FDR = 0:15 values are well estimated, and \FDR = 0:15 based decision rules gains power maintaining an high specicity. On the other hand, in non-small areas and non-small risk level scenarios the FDR is under-estimated unless for very small values of it (much lower than 0.05); this resulting in a loss of specicity of a\FDR = 0:05 based decision rule. In such scenario\FDR = 0:05 or, even worse,\FDR = 0:1 based decision rules cannot be suggested because the true FDR is actually much higher. As regards the relative risk estimation, our model achieves almost the same results of the classic Besag York Molliè model. For this reason, our model is interesting for its ability to perform both the estimation of relative risk values and the FDR control, except for non-small areas and large risk level scenarios. A case of study is nally presented to show how the method can be used in epidemiology.

Physical and mineralogical changes of Hungarian monumental stones exposed to different conditions: stone-testing in-situ and under laboratory conditions

The Székesfehérvár Ruin Garden is a unique assemblage of monuments belonging to the cultural heritage of Hungary due to its important role in the Middle Ages as the coronation and burial church of the Kings of the Hungarian Christian Kingdom. It has been nominated for “National Monument” and as a consequence, its protection in the present and future is required. Moreover, it was reconstructed and expanded several times throughout Hungarian history. By a quick overview of the current state of the monument, the presence of several lithotypes can be found among the remained building and decorative stones. Therefore, the research related to the materials is crucial not only for the conservation of that specific monument but also for other historic structures in Central Europe. The current research is divided in three main parts: i) description of lithologies and their provenance, ii) physical properties testing of historic material and iii) durability tests of analogous stones obtained from active quarries. The survey of the National Monument of Székesfehérvár, focuses on the historical importance and the architecture of the monument, the different construction periods, the identification of the different building stones and their distribution in the remaining parts of the monument and it also included provenance analyses. The second one was the in situ and laboratory testing of physical properties of historic material. As a final phase samples were taken from local quarries with similar physical and mineralogical characteristics to the ones used in the monument. The three studied lithologies are: fine oolitic limestone, a coarse oolitic limestone and a red compact limestone. These stones were used for rock mechanical and durability tests under laboratory conditions. The following techniques were used: a) in-situ: Schmidt Hammer Values, moisture content measurements, DRMS, mapping (construction ages, lithotypes, weathering forms) b) laboratory: petrographic analysis, XRD, determination of real density by means of helium pycnometer and bulk density by means of mercury pycnometer, pore size distribution by mercury intrusion porosimetry and by nitrogen adsorption, water absorption, determination of open porosity, DRMS, frost resistance, ultrasonic pulse velocity test, uniaxial compressive strength test and dynamic modulus of elasticity. The results show that initial uniaxial compressive strength is not necessarily a clear indicator of the stone durability. Bedding and other lithological heterogeneities can influence the strength and durability of individual specimens. In addition, long-term behaviour is influenced by exposure conditions, fabric and, especially, the pore size distribution of each sample. Therefore, a statistic evaluation of the results is highly recommended and they should be evaluated in combination with other investigations on internal structure and micro-scale heterogeneities of the material, such as petrographic observation, ultrasound pulse velocity and porosimetry. Laboratory tests used to estimate the durability of natural stone may give a good guidance to its short-term performance but they should not be taken as an ultimate indication of the long-term behaviour of the stone. The interdisciplinary study of the results confirms that stones in the monument show deterioration in terms of mineralogy, fabric and physical properties in comparison with quarried stones. Moreover stone-testing proves compatibility between quarried and historical stones. Good correlation is observed between the non-destructive-techniques and laboratory tests results which allow us to minimize sampling and assessing the condition of the materials. Concluding, this research can contribute to the diagnostic knowledge for further studies that are needed in order to evaluate the effect of recent and future protective measures.

Competence: intelligence in sheep's clothing? Culture, representations, and cognitive performance

The first aim of this thesis was to contribute to the understanding of how cultural capital (Bourdieu, 1983/1986) affects students achievements and performances. We specifically claimed that the effect of cultural capital is at least partly explained by the positioning students take towards the principles they use to attribute competence and intelligence. The testing of these hypothesis have been framed within the social representations theory, specifically in the formulation of the Lemanic school approach (Doise, 1986).

Earthquake forecasting and seismic hazard analysis: some insights on the testing phase and the modeling

This thesis is divided in three chapters. In the first chapter we analyse the results of the world forecasting experiment run by the Collaboratory for the Study of Earthquake Predictability (CSEP). We take the opportunity of this experiment to contribute to the definition of a more robust and reliable statistical procedure to evaluate earthquake forecasting models. We first present the models and the target earthquakes to be forecast. Then we explain the consistency and comparison tests that are used in CSEP experiments to evaluate the performance of the models. Introducing a methodology to create ensemble forecasting models, we show that models, when properly combined, are almost always better performing that any single model. In the second chapter we discuss in depth one of the basic features of PSHA: the declustering of the seismicity rates. We first introduce the Cornell-McGuire method for PSHA and we present the different motivations that stand behind the need of declustering seismic catalogs. Using a theorem of the modern probability (Le Cam's theorem) we show that the declustering is not necessary to obtain a Poissonian behaviour of the exceedances that is usually considered fundamental to transform exceedance rates in exceedance probabilities in the PSHA framework. We present a method to correct PSHA for declustering, building a more realistic PSHA. In the last chapter we explore the methods that are commonly used to take into account the epistemic uncertainty in PSHA. The most widely used method is the logic tree that stands at the basis of the most advanced seismic hazard maps. We illustrate the probabilistic structure of the logic tree, and then we show that this structure is not adequate to describe the epistemic uncertainty. We then propose a new probabilistic framework based on the ensemble modelling that properly accounts for epistemic uncertainties in PSHA.

Towards Centrifugal Compressor Stages Virtual Testing

Flow features inside centrifugal compressor stages are very complicated to simulate with numerical tools due to the highly complex geometry and varying gas conditions all across the machine. For this reason, a big effort is currently being made to increase the fidelity of the numerical models during the design and validation phases. Computational Fluid Dynamics (CFD) plays an increasing role in the assessment of the performance prediction of centrifugal compressor stages. Historically, CFD was considered reliable for performance prediction on a qualitatively level, whereas tests were necessary to predict compressors performance on a quantitatively basis. In fact "standard" CFD with only the flow-path and blades included into the computational domain is known to be weak in capturing efficiency level and operating range accurately due to the under-estimation of losses and the lack of secondary flows modeling. This research project aims to fill the gap in accuracy between "standard" CFD and tests data by including a high fidelity reproduction of the gas domain and the use of advanced numerical models and tools introduced in the author's OEM in-house CFD code. In other words, this thesis describes a methodology by which virtual tests can be conducted on single stages and multistage centrifugal compressors in a similar fashion to a typical rig test that guarantee end users to operate machines with a confidence level not achievable before. Furthermore, the new "high fidelity" approach allowed understanding flow phenomena not fully captured before, increasing aerodynamicists capability and confidence in designing high efficiency and high reliable centrifugal compressor stages.