PDF superior Bayesian Model Averaging for multivariate extremes

Bayesian Model Averaging for multivariate extremes

Bayesian Model Averaging for multivariate extremes

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

A study of trends for Mexico City ozone extremes: 2001-2014

A study of trends for Mexico City ozone extremes: 2001-2014

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

Averaging Lorenz Curves

Averaging Lorenz Curves

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

Bayesian networks for probabilistic weather prediction

Bayesian networks for probabilistic weather prediction

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

MBIS: Multivariate Bayesian Image Segmentation Tool

MBIS: Multivariate Bayesian Image Segmentation Tool

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

Bayesian analysis for a fractional population growth model

Bayesian analysis for a fractional population growth model

For multivariate distributions, we can apply the single variable slice sampling for each 𝜃 𝑖 , 𝑖 = 1, . . . , 𝑝, in turn. An example of JAGS implementation is given in Appendix. 3.2. Bayesian Model Comparison. In this section, our interest is to make a comparison between two different models. In one, the dynamic system changes in an ordinary way and in the other it changes anomalously, that is, with an entire derivative and with a fractional derivative, respectively. As soon as we obtain experimental data from a dynamical phenomenon, the uncertainty becomes present. Moreover, the mechanism that governs the evolution law is unknown at some level. So, the challenge here is to know which model best fits and best describes the data.
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10 Lee mas

Prediction of Federal Funds Target Rate: a dynamic logistic Bayesian Model averaging approach

Prediction of Federal Funds Target Rate: a dynamic logistic Bayesian Model averaging approach

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

A semiparametric Bayesian joint model for multiple mixed type outcomes: an application to acute myocardial infarction

A semiparametric Bayesian joint model for multiple mixed type outcomes: an application to acute myocardial infarction

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

Bayesian Hybrid Matrix Factorisation for Data Integration

Bayesian Hybrid Matrix Factorisation for Data Integration

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

Bayesian Reliability Analysis for Hardware/Software Systems

Bayesian Reliability Analysis for Hardware/Software Systems

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

Bayesian parameter estimation for discrete data spectra

Bayesian parameter estimation for discrete data spectra

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

An Objective Bayesian Criterion to Determine Model Prior Probabilities

An Objective Bayesian Criterion to Determine Model Prior Probabilities

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

BAYESIAN ESTIMATION OF A SUBJECT-SPECIFIC MODEL OF VOICE PRODUCTION FOR THE CLINICAL ASSESSMENT OF VOCAL FUNCTION

BAYESIAN ESTIMATION OF A SUBJECT-SPECIFIC MODEL OF VOICE PRODUCTION FOR THE CLINICAL ASSESSMENT OF VOCAL FUNCTION

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

Inductive transfer for learning Bayesian networks

Inductive transfer for learning Bayesian networks

For many machine learning applications, it is assumed that a sufficiently large dataset is available from which a reliable model can be induced. In some domains, however, it is dif- ficult to gather enough data, for instance, in manufacturing some products that are rarely produced or in medicine where there are some rare diseases. Experts, when confronted with a problem in a novel task, use their experience from related tasks to solve the problem. Recently, there has been an increasing interest in the machine learning community for us- ing data from related tasks, in particular when the available data is scarce (Thrun 1996; Caruana 1997; Baxter 1997; Silver et al. 2008), an approach known as transfer learning. In many domains it is common to have uncertainty and Bayesian networks have proved to be an adequate and powerful technique to deal with it; however, there is limited previous work on transfer learning for Bayesian networks (BNs). Previous work considers learning simul- taneously multiples tasks by combining data (Niculescu-Mizil and Caruana 2007) or expert knowledge (Richardson and Domingos 2003). Although our work is related to these meth- ods, the main focus is different; we are interested on learning a model for a task with limited data, taking advantage of data from related tasks. Another important difference is that our method is based on independence tests, while previous approaches are based on search and score techniques. The learning methods based on independence tests tend to degrade more severely when there is not enough data, so in this case transfer learning has a greater impact. In this paper we propose a transfer learning method for Bayesian networks that induces a model for a target task, from data from this task and from other related auxiliary tasks. The method includes both, structure and parameter learning. The structure learning method is based on the PC algorithm (Spirtes et al. 1993), and it combines the dependency measures obtained from data in the target task, with those obtained from data in the auxiliary tasks. We propose a combination function that takes into account the reliability and consistency between these measures.
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29 Lee mas

Decision boundary for discrete Bayesian network classifiers

Decision boundary for discrete Bayesian network classifiers

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

Transfer learning for temporal nodes bayesian networks

Transfer learning for temporal nodes bayesian networks

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

Chapter V   Multivariate Analysis for Business, 2019, 3 doc

Chapter V Multivariate Analysis for Business, 2019, 3 doc

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

Bayesian meta-analysis models for heterogeneous genomics data

Bayesian meta-analysis models for heterogeneous genomics data

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

A Macroeconometric Model for Serbia

A Macroeconometric Model for Serbia

model simulations and forecasts, this short-term interest rate which is determined by the National Bank of Serbia might either be exogenous or endogenous. In the first case, the forecaster has to determine the expected future path of monetary policy and hence of the NBS interest rate. In this case, the model equation determining the NBS interest rate has to be switched off in forecasts. For the case of a model-based monetary policy path, the model contains a Taylor rule (Taylor 1993) type equation determining the short-term interest rate, i.e. the NBS interest rate. In this equation, the NBS interest rate for open market operations depends positively on the inflation rate and on the output gap in Serbia. This approach implies that the National Bank of Serbia follows both inflation and an output target. In this case, monetary policy becomes more restrictive, i.e. the interest rate is raised if inflation rises and/or actual output exceeds potential output. In the latter case, i.e. if resources are fully or even over- employed, inflationary pressure arises since employees’ associations have more power to claim higher wage increases, and as machines run at full capacity, costs for maintenance and repairs rise. In a term structure equation, the long-term interest rate depends on the short-term interest rate. The nominal effective exchange rate of the Serbian dinar is determined by important bilateral exchange rates. Since the countries of the euro area are Serbia’s most important trading partners, the nominal effective exchange rate of the Serbian dinar is mainly determined by the exchange rate vis-à-vis the euro. When including both the euro and the US dollar, the latter has to wrong sign. Hence, only the euro is considered as determinant of the nominal effective exchange rate of the dinar in the Serbia model. The real effective
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22 Lee mas

Multi-facet determination for clustering with Bayesian networks

Multi-facet determination for clustering with Bayesian networks

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

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