Abstract. The main framework of **multivariate** extreme value theory is well- known in terms of probability, but inference and **model** choice remain an active research eld. Theoretically, an angular measure on the positive quadrant of the unit sphere can describe the dependence among very high values, but no parametric form can entirely capture it. The practitioner often makes an as- sertive choice and arbitrarily ts a specic parametric angular measure on the data. Another statistician could come up with another **model** and a completely dierent estimate. This leads to the problem of how to merge the two dierent tted angular measures. One natural way around this issue is to weigh them ac- cording to the marginal **model** likelihoods. This strategy, the so-called **Bayesian** **Model** **Averaging** (BMA), has been extensively studied in various context, but (to our knowledge) it has never been adapted to angular measures. The main goal of this article is to determine if the BMA approach can oer an added value when analyzing extreme values.

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25 Lee mas

We analyze trends of high values of tropospheric ozone over Mexico City based on data corresponding to the years 2001-2014. The data consists of monthly maxima ozone concentrations based on 29 monitoring stations. geographical zones. We assess time trends based on a statistical **model** that assumes that these observations follow an extreme value distribution, where the location parameter changes in time accordingly to a regression **model**. In addition, we use **Bayesian** methods to estimate simultaneously a zonal and an overall time-trend parameter along with the shape and scale parameters of the Generalized Extreme Value distribution. We compare our results to a **model** that is based on a normal distribution. Our analyses show some evidence of decaying ozone levels **for** the monthly maxima during the period of study.

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14 Lee mas

Pareto the probabilities are 0.208 and 0.033, respectively. It appears that, relative to the two-parameter Lorenz curves, the **Bayesian** procedure has substantially penalized the three-parameter curves **for** the additional uncertainty associated with one more unknown parameter. The generalized Pareto has a low posterior probability (0.033) despite the fact that the standard errors of γˆ and αˆ **for** the generalized Pareto **model**, and the differences in the log-likelihood function values, suggest that the hypotheses γ = 1 and α = 0 , that yield the Ortega and RGKO functions, respectively, are likely to be rejected. Since γ = 1 and α = 0 are on the boundary of the parameter space, we cannot say definitely that these hypotheses will be rejected; the sampling theory tests require special treatment (see, **for** example, Andrews 1998) that we do not pursue here. Nevertheless, the sampling evidence in favour of the 3-parameter generalized Pareto is much stronger than that from **Bayesian** inference.

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23 Lee mas

There have also been some attempts **for** combining both database information and ACMs. This is done by combining the model’s pre- dicted patterns with the information available in databases of ob- servations (e.g., rainfall) and predictions (gridded atmospheric pat- terns). Therefore, sub-grid detail in the prediction is gained by post- processing the outputs of ACMs using knowledge extracted from the databases (downscaling methods). One of the most popular down- scaling techniques is the method of analogs, which assumes that sim- ilar atmospheric patterns may lead to similar future outcomes [5]. Thus, predictions based on an atmospheric pattern can be derived from an “analog ensemble” extracted from the database. Different clustering techniques have been recently introduced to select this en- semble (see [6, 7] and references therein). However when dealing with **multivariate** time series, the analog technique assume different statistical independence relationships to simplify the **model**, neglect- ing important information among the variables in the database (most of them do not include spatial dependencies, and each station is pre- dicted separately).

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5 Lee mas

Besides the segmentation results, we presented a new application of a B-spline **model** **for** the bias estimation. Built upon two existing methods, we combined the orig- inal bias estimation methodology described previously [71] with the bias field **model** proposed in another study [70]. The B-spline **model** of Tustison et al. has been proven to behave accurately without a heavy computa- tional cost, and it was naturally embedded within the EM algorithm, as described in section 2.3. Visual as- sessment of results was documented. Our methodology improved the bias estimated with respect to FAST **for** all the channels. Moreover, **multivariate** segmentation per- formed robustly against the bias field. This is justified because the image channels share a unique distribution **model** that is used to estimate the bias more effectively, regardless of the modality of the channel. Even though we observed that the bias correction can have a slightly negative impact on final segmentation, we concluded that the explicit modeling of the bias field is interesting as a multichannel bias field estimation technique itself. Most of bias correction methodologies (e.g. [70]) have been well tested on T1w images, but their behavior has not been studied in depth with other MRI sequences. In addition, they do not exploit the advantages of the underlying distribution **model** shared among pulse se- quences. The fine tuning of the bias estimation strategy included in MBIS, and the demonstration of its expedi- ence **for** the bias correction of **multivariate** images is a promising line **for** forthcoming research.

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22 Lee mas

10 Lee mas

Diebold et al (2006), find strong evidence of macroeconomic effects on the future yield curve and somewhat weaker evidence of yield curve effects on future macroeconomic developments. Although bi-directional causality is likely present, effects in a research done by Ang and Piazzesi (2003) seem relatively more important than those previously presented by Estrella and Hardouvelis (1991), Estrella and Mishkin (1998), and Stock and Watson (2000). Shmueli (2010) states that endogeneity does not pose an estimation bias when dealing with predictive modeling, since the focus is on association rather than causation and the prospective context, there is no need to delve into the exact role of each variable in terms of an underlying causal structure. On the contrary, criteria **for** choosing predictors are quality of the association between the predictors and the response, data quality, and availability of the predictors at the time of prediction, known as ex-ante availability.

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27 Lee mas

We propose a **Bayesian** nonparametric hierarchical **model** that includes a cluster analysis, aimed at identifying profiles or hospital behaviors that may affect the out- come at patient level. In particular, we introduce a **multivariate** multiple regression **model**, where the response has three mixed-type components. The components are, respectively: (1) the door to balloon time (DB), i.e. the time between the admission to the hospital and the PTCA; (2) the in-hospital survival; and (3) the survival after 60 days from admission. The first response (continuous) is essential in quantifying the efficiency of health providers, since it plays a key role in the success of the ther- apy; the second is the basic treatment success indicator, while the third concerns a 60-days period, during which the treatment effectiveness, in terms of survival and quality of life, can be truly evaluated. Note that the last two responses are binary, so that, as a whole, the **multivariate** response is of mixed type. It is worth noting that the information on patients’ survival after 60 days is obtained from the linkage between STEMI archive and a further administrative database concerning patient-specific vital statistics such as date of birth and death **for** general causes. The linkage between the different data sources was carried out by Lombardia Informatica S.p.A, the agency managing regional datawarehouses. We do not have direct access to the data sources so as to construct different outcomes of potential interest. Moreover we work with a singly imputed data set and we could not identify data preprocessing tools used by the Lombardia Informatica S.p.A. agency, in particular the technique used to impute the missing data. The modeling of multiple outcomes from data collected in STEMI Archive was previously discussed in Ieva et al. (2014), under a semiparametric fre- quentist bivariate probit **model**. Their aim was to analyze the relationship among in-hospital mortality and a treatment effectiveness outcome in the presence of con- founders, that is, variables that are associated with both covariates and response. This is a problem that poses serious limitations to covariate adjustment since the use of classical techniques may yield biased and inconsistent estimates. In this context, Ieva et al. (2014) proposed the use of a semiparametric recursive bivariate probit **model**, as an effective way to estimate the effect that a binary regressor has on a binary outcome in the presence of nonlinear confounder response relationships. In contrast, we focus on a joint **model** **for** the grouped outcomes. As discussed below, our aim is to find relevant groups of hospitals in terms of patient-specific characteristics, which may assist in further planning and policy making.

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25 Lee mas

Some NMF methods such as Lee and Seung [2001] rely on optimisation-based techniques, where a cost func- tion between the observed matrix R and the predicted matrix F G T is minimised, like the mean squared error or I-divergence, using multiplicative updates. Alter- natively, probabilistic models formulate the problem of NMF by treating the entries in F , G as unobserved or latent variables, and the entries in R as observed dat- apoints. **Bayesian** approaches furthermore place prior distributions over the latent variables. The problem then involves finding the distribution over F , G after observing R, p(F , G |R). This **Bayesian** approach has several benefits: it is less prone to overfitting, espe- cially on small or sparse datasets; a distribution over the factors is obtained, rather than just a point esti- mate; it allows **for** flexible and elegant models (such as automatic **model** selection using Automatic Relevance Determination); and missing entries are easily handled (we simply do not include them in the observed data, through the Ω set introduced earlier). However, find- ing this posterior distribution can be very inefficient. Schmidt et al. [2009] introduced a **Bayesian** **model** **for** non-negative matrix factorisation, by using Exponen- tial priors and a Gaussian likelihood. **For** the precision τ of the likelihood they used a Gamma distribution with shape α > 0 and rate β > 0. The full set of parameters **for** this **model** is denoted θ = {F , G, τ}.

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10 Lee mas

Stemming from work by Goel and Soenjoto (1981), there has been interest in HW/SW systems reliability. Many papers have used general Continuous Time Markov Chains (CTMCs) models **for** such purpose, including Welke et al. (1995), who incorporate a Nonhomogenous Poisson Process (NHPP) software reliability **model** into a CTMC hardware reliability **model**. Pukite and Pukite (1998) and Xie et al. (2004) describe simpler models **for** HW/SW reliability. Recently, more sophisticated models have been developed, which take into account dependencies or dynamic or functional aspects, through stochastic Petri nets, see e.g. Lollini et al. (2009); Dynamic Reliability Block Diagrams (DRBDs), see e.g. Distefano and Puliafito (2009); or modified Reliability Block Diagrams (RBDs), see e.g. Levitin (2007).

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27 Lee mas

Discrete spectra are ubiquitous in physics; **for** example nuclear physics, laser physics and experimental high energy physics measure integer counts in the form of particles in depen- dence of angle, wavelength, energy etc. **Bayesian** parameter estimation (tting a function with free parameters to the data) is a sophisticated framework which can handle cases of sparse data as well as input of pertinent background information into the data analysis in the form of a prior probability. **Bayesian** comparison of competing models and functions takes into account all possible parameter values rather than just the best t values. We rst review the general statistical basis of data analysis, focusing in particular on the Poisson, Negative Binomial and associated distributions. After introducing the conceptual shift and basic relations of the **Bayesian** approach, we show how these distributions can be combined with arbitrary **model** functions and data counts to yield two general discrete likelihoods. While we keep an eye on the asymptotic behaviour as useful analytical checks, we then in- troduce and review the theoretical basis **for** Markov Chain Monte Carlo numerical methods and show how these are applied in practice in the Metropolis-Hastings and Nested Sampling algorithms. We proceed to apply these to a number of simple situations based on simulation of a background plus two or three Gaussian peaks with both Poisson and Negative Binomial likelihoods, and discuss how to select models based on numerical outputs.

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92 Lee mas

Having identified this approach to assign the mass to each **model** on the basis of worth, we see it takes into consideration the “position” of each **model** with respect to the others. The quantification of the worth comes from a result in Berk (1966) which says that, if the **model** is misspecified, the posterior distribution asymptotically tends to accumulate at the nearest **model** in terms of the Kullback–Leibler divergence (Kullback & Leibler, 1951). Therefore, if we were to remove **model** M j from the set of possible models, and it is the true one, the loss we would incur

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28 Lee mas

The body-cover **model** (BCM) is a numerical **model** of the vocal folds (VF) broadly used **for** the study of voice production and VF behavior. 44 The BCM however, makes several assump- tions that hampers its ability to describe vocal hyperfunction (VH). The **model** was modified to include a posterior glottal opening (PGO) and a triangular glottal shape through the concept of arytenoid rotation and displacement. These modifications produced an improved description of collision forces, allowed **for** membranous and cartilaginous incomplete glottal closure, and improved the **model** representation of the onset condition, which is the VF posturing prior to phonation. This enhanced **model** is referred to as triangular body-cover **model** (TBCM). In addition to the anatomical modifications, several numerical improvements were made. A state space vocal tract propagation method was implemented to reduce the computational time used to propagate sound waves, a truncated Taylor series (TTS) was implemented to solve the equa- tions of motion of the system, and a smooth flow solution was implemented to avoid numerical errors. 96 The ability of the proposed **model** to represent VH was investigated in detail. By

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162 Lee mas

29 Lee mas

In this paper we try to generalize the above results within a unified framework. To do this we compute polynomial threshold functions **for** **Bayesian** network (BN) binary classifiers in order to express their decision boundaries. This research is restricted to BN classifiers where the binary class variable, C, has no parents and where the predictors are categorical. As usual, our results extend to non-binary classifiers considering an ensemble of binary classifiers. Polynomial threshold functions are a way to describe the decision boundary of a discrete classifier and are a generalization of the results of Minsky (1961) and Peot (1996). In absence of V -structures in the BN we prove that the obtained families of polynomial representing the induced decision functions form linear spaces that are representations of the inner product spaces. We are able to compute the dimensions of those linear spaces and thus of the inner product space extending the results of Nakamura et al. (2005) and Yang and Wu (2012).

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25 Lee mas

While eorts have been made to compensate **for** lack of training information, most of these focus solely on one aspect of the **model** i.e., the structure or the parameters. Luis et al. propose a transfer learning strategy to learn both components of a **Bayesian** network [LSM10]. To learn the structure they proposed the PC-TL algorithm, which is an extension of the PC algorithm **for** transferring knowledge between tasks. A general outline of the algorithm is provided in Algorithm 4.1. PC-TL follows the same procedure as the PC algorithm; however it changes how the independence tests are evaluated. In the PC algorithm, an independence test evaluates whether two variables are independent given another variable, or an other set of variables. If two variables are determined to be independent, no arc will exist between them in the **Bayesian** network. In PC-TL the independence measure is a linear weighted combination of the independence tests performed on the target data with the independence tests performed on the most similar auxiliary task. The combined independence measure is given by the following function:

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128 Lee mas

In the “Christian Kid” example, we are trying to predict the probability that a customer will respond to an e-mail ad and buy a children’s magazine called “Christian Kid.” We have run an experiment and collected 673 observations where a customer was shown the Christian Kid ad. **For** each of these observations, we have recorded whether or not the customer buys together with a set of explanatory X-variables. Since the dependent Y variable is binary, logistic regression is appropriate.

19 Lee mas

are useful diagnostic markers **for** cancer prediction and prognosis (Kiechle et al., 2001; Lockwood et al., 2005). Therefore, studying the genomic causes and their as- sociation with phenotypic alterations is emergent in cancer biology. The underlying mechanism of CNV related genomic instability amongst tumors includes defects in maintenance/manipulation of genome stability, telomere erosion, chromosome break- age, cell cycle defects and failures in DNA repairs (Albertson, 2003). Consequential copy number aberrations of the above mentioned malfunctions will further change the dosage of key tumor-inducing and tumor-suppressing genes, which thereby af- fect DNA replication, DNA damage/repair, mitosis, centrosome, telomere, mRNA transcription and proliferation of neoplastic cells. In addition, microenvironmental stresses play a role in exerting strong selective pressure on cancer cells with amplifica- tion/deletion of particular regions of the chromosome (Lucas et al., 2010). Recently, high-throughput technologies have mapped genome-wide DNA copy number varia- tions at high resolution, and discovered multiple new genes in cancer. However, there is enormous diversity in each individual’s tumor, which harbors only a few driver mu- tations (copy number alterations playing a critical role in tumor development). In addition, CNV regions are particularly large containing many genes, most of which are indistinguishable from the passenger mutations (copy number segments affect- ing widespread chromosomal instability in many advanced human tumors) (Akavia et al., 2010). Thus analysis based on CNV data alone will leave the functional impor- tance and physiological impact of genetic alteration ineluctable on the tumor. Gene expression has been readily available **for** profiling many tumors, therefore, how to incorporate it with CNV data to identify key drivers becomes an important problem to uncover cancer mechanism.

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137 Lee mas

22 Lee mas

Learning from these approaches to the MPC paradigm, we propose a novel method that is able to recover alternative clustering solutions based on a facet determination process. Similar to the works of [12, 13, 17, 38, 42], we address the generation of alternative clusterings in an iterative manner where relevant but distinct partitions are retrieved. In contrast to these methods, our approach is not based on data transformations or orthogonal subspaces, it extends the idea of unsupervised feature selection by determining several meaningful subsets of attributes that are alternate to each other, known as facets. Our work follows the ideas presented in [11], [34] and [41] about systematically identifying several data perspectives, clustering the data along each one and presenting the results to the domain experts **for** their selection. However, even though we all follow this concept while using probabilistic graphical models, our methods differ in the identification of these facets and their posterior partition construction.

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14 Lee mas