Editors: Stefano Cabras and Michele Guindani

Transcription

1 B O O K of A B S T R A C T S Editors: Stefano Cabras and Michele Guindani

2 ISBN: ISBA 2016 World Meeting Cagliari, June 13-17, c 2016 CUEC Cooperativa Universitaria Editrice Cagliaritana via Is Mirrionis 1, Cagliari Tel. e Fax info@cuec.eu

3 Scientific Committee Michele Guindani (Chair) Christopher Hans Ramses Mena David Banks Cathy Chen Catherine Forbes Subhashis Ghoshal Katja Ickstadt Purushottam Laud Bhramar Mukherjee Fernando Quintana David Rossell Judith Rousseau Bruno Sansó Mahlet Tadesse Mike West University of Texas MD Anderson Cancer Center, USA Ohio State University,USA Universidad Nacional Autonoma de Mexico, UNAM, Mexico Duke University, USA Feng Chia University, Taiwan Monash University, Australia North Carolina State University, USA Technische Universitat Dortmund, Germany Medical College of Wisconsin, USA University of Michigan, USA Pontificia Universidad Catholica de Chile, Chile University of Warwick, UK Universite Paris Dauphine, France University of California Santa Cruz, USA Georgetown University, USA Duke University, USA

4 Local Organizing Committee Stefano Cabras (Chair) Antonio Lijoi Brunero Liseo Monica Musio Igor Pruenster Walter Racugno Laura Ventura Universitá di Cagliari, Italy and Universidad Carlos III de Madrid, Spain Universitá di Pavia,Italy La Sapienza Universitá di Roma, Italy Universitá di Cagliari, Italy Universitá di Torino and Collegio Carlo Alberto, Italy Universitá di Cagliari, Italy Universitá di Padova, Italy

5 Welcome message The Program Council of ISBA, the Scientific Committee and the Local Organizing Committee welcome you to the ISBA 2016 World Meeting! We would like to thank all the participants for their invaluable contributions to the scientific program, which confirm the significance of the World Meeting for the Bayesian community. We estimate that over 600 participants will be present at the ISBA 2016 World Meeting. We have a fantastic program which features 3 Foundational lectures, 4 Keynote lectures, 17 invited sessions, 53 contributed sessions, 10 short sessions, and close to 400 posters (the main event of these conferences and a great ISBA/Bayesian tradition). Following the format of the ISBA 2014 meeting in Cancun, many sessions have been directly organized or sponsored by the ISBA Sections. In addition to the traditional session to honor the finalists of the Savage Award, the program features the Bayesian Analysis session, organized by Marina Vannucci and Bruno Sanso, former and current editors in chief, respectively, of our flagship journal, Bayesian Analysis. A particular mention should be given to the session in honor of Kathryn Chaloner, to remember an outstanding leader in our profession and a devoted advocate for diversity and inclusion. On the occasion of the 30th anniversary of Bruno De Finetti s death, in 1985, ISBA is honoring his memory by instituting a Bruno de Finetti Lecture at the ISBA World Meeting As established by the ISBA Board of Directors, the Bruno de Finetti Lecture shall be delivered at the ISBA World Meetings by an outstanding scholar who has provided significant contributions to the advancement of Bayesian Statistics. The inaugural lecturer is Persi Diaconis (Stanford University), one of the icons of modern probability and statistics. In the first ISBA World Meeting without Susie Bayarri, ISBA is honoring her work for Bayesian Statistics and for ISBA. As established by the ISBA Board of Directors, the Susie Bayarri Lecture shall be delivered at the ISBA World Meetings by an outstanding young researcher under 35 years of age. The inaugural lecturer is James Scott (University of Texas at Austin), who has already provided important contributions in the areas of multiple testing, prior choice in hierarchical models and scalable Bayesian computation. We will also honor the new ISBA Fellows during the Welcome Reception on Monday, June 13th, and will celebrate the career and legacy of A.F.M. Smith and A.P. Dawid on Tuesday, June 14th with the bestowal of an Honorary Lifetime Membership. We are indebted to the generous support of our colleagues at Google, StataCorp, RStudio, the US National Science Foundation, the US Office of Naval Research, and of course ISBA itself (ISBA General, Lifetime Membership, and Pilar Iglesias Funds). Their support has allowed us to issue more than 120 travel grants to a very diverse group of junior researchers, including students, postdocs and

6 6 junior faculty. We are also indebted to the generous support of Collegio Carlo Alberto (Torino, Italy), Universidad Carlos III (Madrid, Spain), and University of Cagliari (Italy), which have helped with the logistic organization of both the conference and the short courses. Finally, we would have not been able to put this conference together without all the hard work of the Scientific Committee, the ISBA Executive Board, experienced past ISBA officers, and the Local Organizing Committee. Many thanks to all of you! We hope you enjoy the conference. Welcome to Sardinia! Cagliari, June 13, 2016 Michele Guindani Christopher Hans Clair Alston-Knox and Stefano Cabras

7 Contents 7

8 8 CONTENTS

9 FL1 - Foundational Lecture 1 Graphical modelling and Bayesian structural learning Peter Green, University of Technology, Sydney (UTS), Australia and University of Bristol, UK (Graphical models and Bayesian structural learning), mapjg@bristol.ac.uk (LSC:1222) ABSTRACT. Conditional independence is key to understanding the structure of multivariate distributions and multivariate data. Graphical modelling provides a rigorous formalism for encoding, visualising and reasoning with conditional independence assumptions, and thus provides tools for assessing structure in data and delivering inferences in graphical form - this is the goal of structural learning. In this lecture I will review the role of graphical representations of conditional independence in modelling and inference for multivariate data, and their interpretation as a description of structure in the modelled system. I will go on to discuss the state of the art in Bayesian approaches to structural learning: how can we formulate priors, what can we hope to infer (and on what scale and to what degree of approximation), and how should such inferences be interpreted? Decomposable graphs, trees, forests and directed acyclic graphs will all be considered. Keywords: Conditional independence. 9

10 10 FL1 - Foundational Lecture 1

11 FL2 - Foundational Lecture 2 A subjective tour through foundations and modern trends Sonia Petrone, Universita Bocconi (Italy), sonia.petrone@unibocconi.it (LSC:1223) ABSTRACT. This lecture will be a tutorial-tour starting from a brief reminder of the origin of subjective probability and risk, focusing on notions of exchangeability and touching a (personal choice of) problems and current trends. A general question underlies the tour: In the data science era, do we still care about subjective foundations, or about foundations at all? I am sure we do, and the talk aims at discussing some reasons and implications. Keywords:. 11

12 12 FL2 - Foundational Lecture 2

13 FL3 - Foundational Lecture 3 Trying to be a public (Bayesian) statistician David Spiegelhalter, University of Cambridge (United Kingdom), d.spiegelhalter@statslab.cam.ac.uk (LSC:1224) ABSTRACT. Statisticians have special insights into way numbers and evidence are used, but they don t tend to have much of a public role. In my job I am supposed to improve the way that statistics and risk are discussed in the media and society. This is not an easy task, and I will summarise lessons learned from both positive and negative experiences from radio, TV, print and online, covering topics such as climate change, terrorism, polls, sky-diving, and sex. You can share the panic at being asked unanswerable questions live on radio, and the joys of doing well in Winter Wipeout due to careful study of the statistics. And although I would never mention the B-word in public, a Bayesian perspective turns out to be very valuable. I will end by a rousing call to statisticians to raise their public profile. Keywords: B-word. 13

14 14 FL3 - Foundational Lecture 3

15 DL - De Finetti Lecture Building Apriori Knowledge Into Conclusions Drawn From Simulations Persi Diaconis, Stanford University (United States), diaconis@math.stanford.edu (LSC:1264) ABSTRACT. Simulations rule much of Bayesian(and nonbayesian) practice. If you look at what most of do with the output of a simulation, it s surprisingly naive; use the mean +-2 s.d..what happened to Bayes (or modern statistics)? I have found classes of problems, e.g. estimating normalizing constants by sequential importance sampling, where reasonable use of prior information helps: the importance weights can be usefully (and sometimes provably) modeled as mixtures of log normals and this helps. This is joint work with Marc Coram.. Keywords:. 15

16 16 DL - De Finetti Lecture

17 KL2 - Keynote Lecture 2 Massively Scalable Gaussian Process Models for High-Dimensional Spatial-Temporal Datasets Sudipto Banerjee, University of California Los Angeles (United States), sudipto@ucla.edu (LSC:1269) ABSTRACT. With the growing capabilities of Geographic Information Systems (GIS) and userfriendly software, statisticians today routinely encounter geographically referenced data containing observations from a large number of spatial locations and time points. Over the last decade, hierarchical spatial-temporal process models have become widely deployed statistical tools for researchers to better understanding the complex nature of spatial and temporal variability. However, fitting hierarchical spatial-temporal models often involves expensive matrix computations with complexity increasing in cubic order for the number of spatial locations and temporal points. This renders such models unfeasible for large data sets. In this talk, I will present two approaches for constructing well-defined spatial-temporal stochastic processes that accrue substantial computational savings. Both these processes can be used as priors for spatial-temporal random fields. The first approach constructs a low-rank process operating on a lower-dimensional subspace. The second approach constructs a Nearest-Neighbor Gaussian Process (NNGP) that can be exploited as a dimension-reducing prior embedded within a rich and flexible hierarchical modeling framework to deliver exact Bayesian inference. Both these approaches lead to Markov chain Monte Carlo algorithms with floating point operations (flops) that are linear in the number of spatial locations (per iteration). We compare these methods and demonstrate its use in inferring on the spatial-temporal distribution of ambient air pollution in continental Europe using spatial-temporal regression models with chemistry transport models. Keywords:. 17

18 18 KL2 - Keynote Lecture 2

19 KL1 - Keynote Lecture 1 Bayesian Model Choice: Past, Present, Future Merlise Clyde, Duke University (United States), clyde@stat.duke.edu (LSC:1267) ABSTRACT. Bayesian model selection or model averaging requires the specification of prior distributions for the parameters defined for each candidate model; in variable selection this task becomes quickly daunting, particularly in the large p small n paradigm, as the number of models grows rapidly with the number of predictors. Because of the difficulty of subjective prior specification, there have been a number of attempts to define conventional or objective prior distributions for Bayesian model selection ranging from Zellner s g-prior or mixtures of g-priors to generalized ridge prior distributions. In addition to prior distributions on model specific parameters, prior probabilities on models play a key role in the large p paradigm. While many distributions have been shown to have desirable properties, there has been no uniform consensus as to which are the most successful. We discuss various criteria that have been deemed essential for model selection priors in the context of linear and generalized linear models and extensions. We highlight recent advances in theory and computation, and close with open questions. Keywords: Bayesian model selection. 19

20 20 KL1 - Keynote Lecture 1

21 BL - Bayarri Lecture Empirical Bayes and penalized likelihood James Scott, University of Texas at Austin (United States), james.scott@mccombs.utexas.edu Joint with: Oscar Padilla, Wesley Tansey. (LSC:1265) ABSTRACT. The core idea of empirical Bayes is to learn a prior distribution by pooling information across similar contexts, rather than to assume that the prior is known. As a philosophy of applied statistics, empirical Bayes has much to recommend it: it offers frequentists the allure of nearly full Bayes efficiency, and Bayesians some helpful computational simplifications. Classically, empirical Bayes involves marginal maximum likelihood: either parametric inference for low-dimensional hyperparameters, in the tradition of Efron and Morris; or nonparametric inference for an unknown distribution, in the tradition of Robbins. But regardless of flavor, the empirical Bayes philosophy is resolutely pragmatic: its adherents focus on what works for data analysis, rather than on what is provable. This talk will argue for the continued centrality of empirical-bayes thinking in modern statistical practice. Somewhat paradoxically, I will do so by highlighting three examples - deconvolution, large-scale multiple testing, and spatial density smoothing where classic empirical Bayes by marginal maximum likelihood either fails entirely, or has some obviously undesirable features. However, in each case, I will demonstrate the success of a blended approach that incorporates ideas from full Bayesian analysis, nonparametric empirical Bayes, and frequentist methods based on penalized likelihood and convex optimization. Drawing both on new theory and some evidence from practical applications, I will argue that this modern empirical-bayes approach provides a pragmatic alternative that addresses some shortcomings of both full Bayes analysis and pure frequentist methods. Keywords: Empirical bayes; Multiple testing. 21

22 22 BL - Bayarri Lecture

23 KL3 - Keynote Lecture 3 Bayesian modeling approaches for brain images and signals Raquel Prado, University of California Santa Cruz (United States), raquel@soe.ucsc.edu (LSC:1266) ABSTRACT. I discuss some recent modeling approaches for detecting brain activation and connectivity from brain images and signals such as functional magnetic resonance imaging (fmri) and electroencephalograms (EEGs). I begin by considering a Bayesian model for multi-subject fmri data from multiple regions of interest. This model allows for simultaneous inference of connectivity networks and hemodynamic response functions that are region, task, and subject-specific, while taking into account variations across subjects and experimental conditions. Next, I present computationally feasible Bayesian approaches for detecting activation from complex-valued fmri data at the voxel-specific level. I illustrate these approaches through the analysis of various data sets, including experimentally realistic synthetic data, multi-subject and multi-task human fmri, as well as human complex-valued fmri. Finally, I discuss a frequency-domain Bayesian hierarchical approach for spectral analysis of multiple related time series with application to EEG data. Keywords: Eeg signal. 23

24 24 KL3 - Keynote Lecture 3

25 KL4 - Keynote Lecture 4 Bayesian analysis of complex discrete data David Dunson, Duke University (United States), dunson@duke.edu (LSC:1268) ABSTRACT. I provide an overview of some recent developments in Bayesian analysis of highdimensional discrete data, with a particular focus on nonparametric approaches for characterizing deep interactions and structure in tables, graphs and sequences. Keywords:. 25

26 26 KL4 - Keynote Lecture 4

27 121 - High-dimensional Statistics On the computational complexity of high-dimensional Bayesian variable selection Michael Jordan, University of California, Berkeley (United States), jordan@cs.berkeley.edu Joint with: Yun Yang, Martin Wainwright. (LSC:1000) ABSTRACT. We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency under relatively mild conditions on the design matrix. We then demonstrate that the statistical criterion of posterior concentration need not imply the computational desideratum of rapid mixing of the MCMC algorithm. By introducing a truncated sparsity prior for variable selection, we provide a set of conditions that guarantee both variable-selection consistency and rapid mixing of a particular Metropolis-Hastings algorithm. The mixing time is linear in the number of covariates up to a logarithmic factor. Our proof controls the spectral gap of the Markov chain by constructing a canonical path ensemble that is inspired by the steps taken by greedy algorithms for variable selection. Keywords: Convergence of mcmc; High-dimensional statistics; Lasso; Spectral gap. Singular Clustering Isabella Verdinelli, Carnegie Mellon University (United States), isabella@stat.cmu.edu Joint with: Chistopher Genovese, Marco Perone-pacifico, Larry Wasserman. (LSC:1001) ABSTRACT. Clustering and manifold identification techniques are useful procedures for reducing the dimensionality of a complex data set in large dimensions and for summarizing the most meaningful features of a point cloud. In this talk we unify these ideas. I will present methods for finding low dimensional clusters in noisy point clouds in large dimensional spaces. These clusters are high density sets of arbitrary shape, hidden in the point cloud but they have zero Lebesgue measure with respect 27

28 High-dimensional Statistics the ambient space. We call them singular clusters. I will present methods and theory for singular clustering. Keywords: Clustering; Dimension reduction. The Role Assumptions in High Dimensional Inference Larry Wasserman, Carnegie Mellon University (United States), larrywasserman.cool@gmail.com (LSC:1002) ABSTRACT. Many statistical procedures for high dimensional inference depend on strong assumptions. Typically, these assumptions are untestable and the resulting inferences are fragile. I will review the role of these assumption and then I ll discuss some procedures that use much weaker assumptions. Finally, I ll show that these methods can be used as diagnostics for Bayesian inference. Keywords: High-dimensional inference.

29 122 - Bayesian approaches to modeling complex phenomena in health applications Measuring the effects of time-varying medication adherence on health outcomes through latent states Mark Glickman, Harvard University (United States), glickman@fas.harvard.edu (LSC:1003) ABSTRACT. One of the most significant barriers to disease management is patients non-adherence to their prescription medication. Quantifying the impact of medication non-adherence can be difficult because a patient s adherence may be changing over time. With the availability of detailed adherence data derived from electronic pill-top monitors, it is now possible to measure the effects of time-varying adherence on health outcomes. We present a Bayesian modeling framework for patient outcomes from electronic monitored medication adherence data. The model assumes two ideal states for each patient; one in which a patient is perfectly adherent to a medication, and the other in which a patient in perfectly non-adherent. The mean outcome process varies dynamically between these two extremes as a function of the time-varying medication process. The framework permits the inclusion of baseline health characteristics, allows for missing adherence data, and can account for different medications, dosages and regimens. We demonstrate the modeling approach to a cohort of patients diagnosed with hypertension who were prescribed anti-hypertensive medication placed in electronic monitoring devices.. Keywords: Dynamic model; Hypertension; Latent class. 29

30 Bayesian approaches to modeling complex phenomena in health applications Bayesian modeling of between-and within-subject variances using mixed effects location scale models for intensive longitudinal data Donald Hedeker, University of Chicago (United States), hedeker@uchicago.edu (LSC:1004) ABSTRACT. For longitudinal data, mixed models include random subject effects to indicate how subjects influence their responses over the repeated assessments. The error variance and the variance of the random effects are usually considered to be homogeneous. These variance terms characterize the within-subjects (error variance) and between-subjects (random-effects variance) variation in the data. In studies using Ecological Momentary Assessment (EMA) or other types of intensive longitudinal data collection, up to thirty or forty observations are often obtained for each subject, and interest frequently centers around changes in the variances, both within-and between-subjects. In this presentation, we focus on an adolescent smoking study using EMA, where interest is on characterizing changes in mood variation associated with smoking. We describe, using Bayesian modeling, how covariates can influence the mood variances, and also describe an extension of the standard mixed model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to have influence on the mean, or location, and variability, or (square of the) scale, of their mood responses. Additionally, we allow the location and scale random effects to be correlated. These mixed-effects location scale models have useful applications in many research areas where interest centers on the joint modeling of the mean and variance structure. Keywords: Ecological momentary assessment. Bayesian nonparametric sensitivity analysis for measuring the impact of unobserved confounding Jennifer Hill, New York University (United States), jennifer.hill@nyu.edu Joint with: Vincent Dorie, Nicole Carnegie, Masataka Harada. (LSC:1005) ABSTRACT. A major obstacle to developing evidenced-based policy is the difficulty in implementing randomized experiments to answer all causal questions of interest. When using a non-experimental study, it is critical to assess how much the results could be affected by unmeasured confounding. We present a set of graphical and numeric tools to explore the sensitivity of causal estimates to the presence of an unmeasured confounder. We characterize the confounder through two parameters that describe the relationships between 1) the confounder and the treatment assignment and 2) the confounder and the outcome variable. Our approach has two primary advantages over similar

31 approaches that are currently implemented in standard software. First, it can be applied to both continuous and binary treatment variables. Second, our method for binary treatment variables allows the researcher to specify three possible estimands (average treatment effect, effect of the treatment on the treated, effect of the treatment on the controls). These options are all implemented in an R package called treatsens. We demonstrate the efficacy of the method through simulations. We illustrate its potential usefulness in practice in the context of two policy applications. Keywords: Bayesian nonparametrics; Causal inference. 31

32 Bayesian approaches to modeling complex phenomena in health applications

33 123 - On asymptotics for complex models A general framework for Bayes structured linear models Chao Gao, Yale University (United States), chao.gao@yale.edu Joint with: Aad Van Der Vaart And Harrison Zhou. (LSC:1006) ABSTRACT. A unified approach will be given to both Bayes high dimensional statistics and Bayes nonparametrics in a general framework of structured linear models. With the proposed two-step model selection prior, a general theorem of posterior contraction will be presented under an abstract setting. The main theorem can be used to derive new results on optimal posterior contraction under many complex model settings including stochastic block model, graphon estimation and dictionary learning. It can also be used to re-derive optimal posterior contraction for problems such as sparse linear regression and nonparametric aggregation, which improve upon previous Bayes results for these problems. The key of the success lies in the proposed two-step prior distribution. The prior on the parameters is an elliptical Laplace distribution that is capable to model signals with large magnitude, and the prior on the models involves an important correction factor that compensates the effect of the normalizing constant of the elliptical Laplace distribution. Keywords: Dictionary learning; Posterior contraction; Sparse linear regression. Baysian inference in semiparametric hidden Markov models Elisabeth Gassiat, Université Paris-Sud (France), elisabeth.gassiat@math.u-psud.fr Joint with: Judith Rousseau And Elodie Vernet. (LSC:1007) ABSTRACT. We consider hidden Markov models with finite state space and nonparametric modelling of the emission distributions. Recent work has proved that such models are identifiable and may be efficiently estimated using various methods. Here we focus on the semiparametric estimation of the transition matrix of the hidden chain. We show how Bernstein von Mises theorems may be obtained for the posterior distribution. We also investigate model selection strategies in the non asymptotic frame. 33

34 On asymptotics for complex models Keywords: Bernstein-von mises theorem; Hidden markov model. Estimating a smooth function on a large graph by Bayesian Laplacian regularisation Harry Van Zanten, University of Amsterdam (Netherlands), hvzanten@uva.nl Joint with: Alice Kirichenko. (LSC:1008) ABSTRACT. We study a Bayesian approach to estimating a smooth function in the context of regression or classification problems on large graphs. We derive theoretical results that show how asymptotically optimal Bayesian regularization can be achieved under an asymptotic shape assumption on the underlying graph and a smoothness condition on the target function, both formulated in terms of the graph Laplacian. The priors we study are randomly scaled Gaussians with precision operators involving the Laplacian of the graph. Keywords:.

35 124 - Bayesian Analysis in Finance and Economics Bayesian Analysis Under Restricted Predictive Moments Siddhartha Chib, Washington University in St. Louis (United States), chib@wustl.edu Joint with: Xiaming Zeng. (LSC:1009) ABSTRACT. We consider the analysis of Bayesian regression models that generate predictive distributions with restricted moments. The motivating model is one that arises in finance where one is interested in estimating a predictive model of the market index under the requirement that the predictive mean is non-negative. The method proposed in this paper provides a simple and elegant solution to this problem. It proceeds by modifying the usual posterior distribution of the parameters (say under a conjugate prior) so that the Kullback-Leibler divergence between the corrected and uncorrected posteriors is minimized, subject to meeting the restriction on the predictive mean. The method is implemented sequentially with the aim of enforcing the constraint on the predictive distribution for each observation in the sample. Illustrations of the technique are provided. Keywords: Kullback-leibler divergence. Bayesian Modeling of High-Frequency Crude Oil Prices Jonathan Stroud, Georgetown University (United States), jrs390@georgetown.edu Joint with: Michael Johannes, Norman Seeger. (LSC:1010) ABSTRACT. We propose a new class of stochastic volatility models for around-the-clock 5-minute returns on crude oil prices. Our models incorporate the following key features: multiple persistent stochastic volatility factors, jumps in prices and volatilities, seasonal components capturing time of the day patterns, correlations between return and volatility shocks, and announcement effects. We develop an integrated MCMC approach to estimate interday and intraday parameters and states using high-frequency data without resorting to various aggregation measures like realized volatility. We provide a case study using data from 2008 to 2015, and use particle filters to construct likelihood functions for model comparison and out-of-sample forecasting. We show that our approach improves 35

36 Bayesian Analysis in Finance and Economics realized volatility forecasts over existing benchmarks like intraday GARCH models and interday realized volatility models. Keywords: Garch; Markov chain monte carlo; Particle filter; Realized volatility. Shape-constrained Semiparametric Additive Stochastic Volatility Models Xinyi Xu, The Ohio State University (United States), xinyi@stat.osu.edu Joint with: Jiangyong Yin, Peter Craigmile, And Steven Maceachern. (LSC:1011) ABSTRACT. The Gaussian stochastic process is the most commonly used approach for modeling time series data. The Gaussianity assumption, however, is known to be insufficient or inappropriate in many problems. On the other hand, nonparametric stochastic volatility models provide great flexibility for modeling the volatility equation, but they often fail to account for useful shape information. For example, a model may not use the knowledge that the autoregressive component of the volatility equation is monotonically increasing as the lagged volatility increases. In this work, we propose a class of additive stochastic volatility models, which capture the asymmetry and heavy tails of many real-world time series data and allow for different shape constraints to improve estimation efficiency. We develop a Bayesian fitting algorithm and demonstrate model performances on simulated and empirical datasets. Unlike general nonparametric models, our model sacrifices little when the true volatility equation is linear. In nonlinear situations we improve the model fit and the ability to estimate volatilities over general, unconstrained, nonparametric models. Keywords: Bayesian isotonic regression; Leverage effect; Nonlinear time series; Particle filter. Incorporating Expert Judgement into Bayesian Disaggregated Forecasts Junni Zhang, Guanghua School of Management, Peking University (China), zjn@gsm.pku.edu.cn Joint with: John Bryant. (LSC:1012) ABSTRACT. Forecasts of means, rates or probabilities for cells disaggregated by social, demographic and geographic variables are important for economic and financial planning. Bayesian hierarchical models are an effective method for constructing disaggregated forecasts. However, such models are essentially a sophisticated form of extrapolation of historical series. Pure extrapolation is not appropriate when there is a possibility of structural breaks, when there are potential limits on future values, or when there is extra information not contained in the historical series. In such cases it can be appropriate to incorporate expert judgement into the forecasts. The traditional approach

37 to incorporating expert judgement into Bayesian models is through informative priors. However, with the complicated models that are needed for disaggregated forecasts, the priors are typically multidimensional and on scales not familiar to subject matter experts. Eliciting such priors can be formidable. Our approach is instead to (1) ask experts to form judgements on aggregate quantities, and (2) treat these judgements as data to be included in the likelihood. We illustrate our approach with long-term disaggregated forecasts of life expectancy in the UK. Keywords: Disaggregation; Expert judgement. 37

38 Bayesian Analysis in Finance and Economics

39 125 - Spatio-temporal models for non-gaussian processes Geostatistical Modelling Using Non-Gaussian Matérn Fields David Bolin, Chalmers University of Technology (Sweden), davidbolin@gmail.com Joint with: Jonas Wallin. (LSC:1013) ABSTRACT. We present a class of non-gaussian spatial models useful for analysing geostatistical data. The models are constructed as solutions to stochastic partial differential equations driven by generalized hyperbolic noise and are incorporated in a standard geostatistical setting with irregularly spaced observations, measurement errors and covariates. We present a likelihood-based parameter estimation method and discuss spatio-temporal model extensions. Finally, an application to precipitation data is presented and the models are compared with Gaussian and trans-gaussian models. Keywords: Geostatistics; Matern covariances; Non-gaussian; Random fields. Spatio-temporal models for heavy tailed skewed processes Thais Fonseca, Universidade Federal do Rio de Janeiro (Brazil), thais@im.ufrj.br Joint with: Alexandra M. Schimidt And Renata S. Bueno. (LSC:1014) ABSTRACT. In the analysis of most spatio-temporal processes in environmental studies, observations present skewed distributions frequently with heavy tails. Usually, data transformations are used to approximate normality, and stationary Gaussian processes are assumed to model the transformed data. We propose a spatio-temporal model for skewed processes that accommodates heavier tails than the ones based on skew normal distributions. For each time t, the process is decomposed as the sum of two independent components, one is a log Gaussian and the other is a Gaussian process. We discuss important properties of the resultant process, such as the covariance structure, the kurtosis and skewness. We fit our proposed model to daily maximum temperature during the spring and summer of 2006 in the South of Brazil. We compare the results obtained from our proposed model to other ones proposed in the literature. This is joint work with Alexandra M. Schmidt and Renata 39

40 Spatio-temporal models for non-gaussian processes S. Bueno. Keywords: Skewness. Spatial temporal Pareto modelling of extreme value data Gabriel Huerta, University of New Mexico (United States), ghuerta@stat.unm.edu Joint with: Luis Enrique Nieto Barajas Department Of Statistics, Instituto Tecnologico Autonomo De Mexico (itam). (LSC:1015) ABSTRACT. In this work we introduce a novel spatio-temporal process with Pareto marginal distributions. A key aspect of this process is that dependence in space and time is constructed through the use of latent variables in a hierarchical fashion. For some specifications the process becomes strictly stationary in space and time. We review the construction of the process and study some of its properties via simulations. The performance of the process is illustrated and compared to other approaches for extreme value data with monthly maxima ozone concentrations that correspond to the metropolitan area of Mexico City. Keywords: Air-pollution modeling; Autoregressive model; Latent variables; Pareto process.

41 131 - Bayesian analysis of Network Models Multiresolution models for networks Bailey Fosdick, Colorado State University (United States), bailey@stat.colostate.edu Joint with: Tyler Mccormick, Theodore Westling. (LSC:1016) ABSTRACT. Many social networks exhibit both global sparsity and local density. That is, overall the propensity for interaction between any two randomly selected actors is infinitesimal, but for any given individual there is massive variability in the propensity to interact with others in the network. In this talk, we propose a class of statistical models that account for such variability by mixing models that represent structure in different levels of the graph. As a byproduct of this approach, we are able to characterize and compare structure within and across dense subgraphs. We demonstrate the utility of our method using simulation and data on social network interactions from Karnataka, India. Keywords: Latent space; Multiscale. Bayesian Multiplicity Control for Multiple Graphs Peter Mueller, University of Texas at Austin (United States), pmueller@math.utexas.edu Joint with: Riten Mitra, And Yuan Ji. (LSC:1017) ABSTRACT. We discuss inference for graphical models as a multiple comparison problem. We argue that posterior inference under a suitable hierarchical model can adjust for the multiplicity problem that arises by deciding inclusion for each of many possible edges. We show that inference under that hierarchical model differs substantially from inference under a comparable non-hierarchical model. We discuss several stylized inference problems, including estimation of one graph, comparison of a pair of graphs, estimation of a pair of graphs and, finally, estimation for multiple graphs. Throughout the discussion we the graph to identify conditional independence structure. Conditional on the graph a sampling model is proposed for the observed data. Most of the discussion is general and remains valid for any sampling model. The discussion is motivated by two case studies. The first application 41

42 Bayesian analysis of Network Models is to model single cell mass spectrometry data for inference about the joint distribution of a set of markers that are recorded for each cell. Another application is to model RPPA protein expression data. Keywords: Gaussian graphical model; Mrf. Inferring Brain Signal Synchronicity from a Sample of EEG Readings Donatello Telesca, University of California Los Angeles (United States), donatello.telesca@gmail.com Joint with: Qian Li, Damla Senturk, Catherine Sugar. (LSC:1018) ABSTRACT. Inferring patterns of synchronous brain activity from a heterogeneous sample of electroencephalograms (EEG) is scientifically and methodologically challenging. While it is statistically appealing to rely on readings from more than one individual in order to highlight patterns of recurrent brain activation, pooling information across subjects presents with non trivial methodological problems. We discuss some of the scientific issues associated with the understanding of coordinated neuronal activity and propose a methodological framework for statistical inference from a sample of EEG readings. Our work builds on classical cotributions in time-series, cluster and functional data analysis, in an effort to reframe a challenging inferential problem in the context of familiar analytical techniques. Some attention will be paid to computational issues, with a proposal based on the hybrid combination of machine learnig and Bayesian techniques. Keywords: Consensus clustering; Longitudinal functional data; Spectral clustering.

43 132 - Joint Species Distribution Modeling Generalized joint attribute modeling for biodiversity analysis James Clark, Duke University (United States), jimclark@duke.edu (LSC:1019) ABSTRACT. Probabilistic forecasts of species distribution and abundance require models that accommodate a joint distribution of multiple species recorded as many combinations of continuous and discrete observations, mostly zeros. Some species groups are counted. Those not easily measured are recorded in ordinal classes, such as rare, moderate, and abundant. Presence-absence of a predator, pathogen, or mutualist might be recorded. Attributes such as body condition, infection status, and herbivore damage are often included in field data. Microbial data are typically compositional. How would a model combine insect counts from pitfall traps with herbaceous cover? Or fishing returns with presence-absence by-catch of threatened species? Or soil microbiome data with nitrogen mineralization rates? All of these variables are responses, not predictors. All are recorded on different scales. We develop a generalized joint attribute model (GJAM) that accommodates combinations of presence-absence, ordinal, continuous, discrete, composition, zero-inflated, and censored. It does so as a joint distributions over all species providing inference on sensitivity to input variables, correlations between species on the data scale, prediction, sensitivity analysis, definition of community structure, and missing data imputation. Application to forest inventory data demonstrates species relationships responding as a community to environmental variables. It shows that the environment can be predicted from the joint distribution of species. Application to microbiome data demonstrates how inverse prediction in the GJAM framework accelerates variable selection, by isolating effects of each input variable s influence across all species. Keywords: Biodiversity; Composition data; Joint species distribution modeling. Interpreting species covariance patterns in space and time Andrew Latimer, University of California Davis (United States), amlatimer@ucdavis.edu 43

44 Joint Species Distribution Modeling (LSC:1020) ABSTRACT. Geographical patterns of species abundances and their responses to environmental change depend on non-biological factors including climate, but also on the abundances of other species. Further, a partial list of species at a location contains much information about what other species are present. Joint species distribution models infer environmental responses of multiple species while accounting for species-level covariances. Recent work has developed flexible models that can accommodate many species and multiple data types. What underlies most models is a multivariate normal distribution on a vector of species abundances (or on a latent intensity variable) for each location and time. This structure allows such models to quantify unexplained associations among species and to use these associations to improve predictions at unsampled or partially sampled sites. We apply joint species distribution models to data on plant abundance and mortality at a range of scales: 1) a single reserve sampled though time; 2) California s Sierra Nevada mountains; and 3) the western US. We use the inferred covariance matrix parameters to evaluate what we can learn ecologically and biogeographically from the joint model. We extend existing models to incorporate biological information into the modeled interspecific associations via phylogenetic and functionally structured covariance matrices. We assess whether including such biological, species-level information improves multispecies inference. Preliminary results indicate that at a regional scale, covariance parameters tend to capture spatial distribution differences among similar species, while at smaller scales, covariance structure can represent functional similarity among co-occurring species.. Keywords: Ecology; Phylogenetic covariance. Analyzing community data with joint species distribution models: traits, co-occurrence, space and time Otso Ovaskainen, University of Helsinki (Finland), otso.ovaskainen@helsinki.fi (LSC:1021) ABSTRACT. A key aim in community ecology is to understand the factors that determine the identities and abundances of species found at any given locality. Central concepts in this research field include the regional and local species pools, environmental filtering and biotic assembly rules. Typical datasets involve a matrix of presence-absences (or abundances) for a group of species at different sites, some environmental and geographical characteristics of those sites, and possibly information on the ecological traits and phylogenetic relationships of the species. The analysis of such data have been traditionally based on ordination approaches, but there is increasing interest to move to model based approaches, in particular joint species distribution models. I present a joint species distribution model that captures the influences of environmental filtering at the community-level by measuring the amount of variation and covariation in the responses of individual species to

45 environmental characteristics. Biotic assembly rules are reflected in the model with the help of an association matrix, which models positive or negative co-occurrence patterns not explained by the responses of the species to their environment. I use a latent factor approach (which can be spatially or temporally structured) to enable model parameterization with data on species-rich communities and thus with high-dimensional association matrices. I illustrate the performance of the approach both with simulated and real data. Keywords: Joint species distribution model; Latent factor. 45

46 Joint Species Distribution Modeling

47 133 - Random measures in Bayesian Nonparametrics Bayesian nonparametric continuous time processes Ramses Mena, Universidad Nacional Autónoma de México (Mexico), ramses@sigma.iimas.unam.mx Joint with: Stephen Walker. (LSC:1023) ABSTRACT. The Bayesian nonparametric approach to the problem of statistical induction considers both, the random and the epistemic uncertainty associated to a random phenomenon. Such approach is formalised through the concept of exchangeable random variables and the proposal of suitable models for the random probability measures that characterise them. However, in several situations moving away from the exchangeability assumption, considering other kind of dependence structures, is required. Motivated by the modelling of random phenomena evolving in continuous time, we study a construction of dynamic random probability measures. The construction is based on a nonparametric mixture of Fellerian generators corresponding to a flexible class of stationary Markov processes. Some special cases, e.g. random probability measure-valued Markov chains and random probability measure-diffusion processes are studied and various properties, such as stationarity, reversibility and ergodicity, are treated. An estimation algorithm is also proposed and tested with simulated and real datasets. Keywords: Dependent process; Diffusion model. Nested processes based on completely random measures Federico Camerlenghi, Bocconi University (Italy), federico.camerlenghi@carloalberto.org Joint with: David B. Dunson, Antonio Lijoi, Igor Pruenster, And Abel Rodriguez. (LSC:1024) ABSTRACT. A large amount of Bayesian nonparametric literature has been carried out under the hypothesis that observations are exchangeable. However in most applications data are heterogeneous, since they have been originated by different, though related, experiments: in such situations partial exchangeability is a more appropriate assumption. In particular the construction of dependent random probability measures to deal with partially exchangeable observations has recently attracted 47

48 Random measures in Bayesian Nonparametrics great attention. Here we define general classes of nested processes, based on transformations of completely random measures, and we thoughtfully investigate the associated partition structures. The proposed models are able to capture various forms of dependence ranging from exchangeability to independence across samples. Finally we identify an MCMC sampler that allows to derive Bayesian estimates and address testing for distributional homogeneity across data. Keywords: Bayesian nonparametrics; Completely random measures; Nested processes; Partial exchangeability. Gamma Belief Networks Mingyuan Zhou, University of Texas at Austin (United States), mingyuan.zhou@mccombs.utexas.edu Joint with: Yulai Cong, Bo Chen. (LSC:1025) ABSTRACT. To infer multilayer deep representations of high-dimensional discrete or nonnegative real vectors, we propose the gamma belief network (GBN) that factorizes each of its hidden layers into the product of a sparse connection weight matrix and the nonnegative real hidden units of the next layer. The GBN s hidden layers are jointly trained with an upward-downward Gibbs sampler, each iteration of which upward propagates latent counts and samples Dirichlet distributed connection weight vectors starting from the first layer (bottom data layer), and then downward samples gamma distributed hidden units starting from the top hidden layer, with each layer solved with the same subroutine. The gamma-negative binomial process combined with a layer-wise training strategy allows the GBN to infer the width of each layer given a fixed budget on the width of the first layer. Example results on both text and image analysis illustrate interesting relationships between the width of the first layer and the inferred network structure, and demonstrate that the GBN, whose hidden units are imposed with correlated gamma priors, can add more layers to improve its performance, given the same limit on the width of the first layer. For exploratory data analysis, we extract trees from the deep network to visualize how the factors discovered at the bottom layer and the increasingly more general factors discovered at higher hidden layers are related to each other, and we generate synthetic data by propagating random variables through the deep network from the top hidden layer back to the bottom data layer. Keywords: Bayesian nonparametrics; Deep learning; Multilayer representation; Poisson factor analysis.

49 134 - Advances in Bayesian Modeling With Business Applications Bayesian Estimation of Generalized Long Memory Stochastic Volatility Models Manabu Asai, Soka University (Japan), m-asai@soka.ac.jp (LSC:1026) ABSTRACT. We consider a process of stochastic volatility (SV) which follows a generalized long memory model, called the Gegenbauer process. We develop estimation technique using Bayesian Markov chain Monte Carlo method. The empirical analysis for daily exchange rate returns indicate that the new models fits better than the conventional long memory SV model. Keywords: Gegenbauer process; Long memory. Bayesian Forecasting of Value-at-Risk Based on Variant Smooth Transition Heteroskedastic Models Cathy W.s Chen, Feng Chia University (Taiwan), chenws@mail.fcu.edu.tw Joint with: Monica M.c. Weng And Toshiaki Watanabe. (LSC:1027) ABSTRACT. To allow for a higher degree of flexibility in model parameters, we propose a general and time-varying nonlinear smooth transition (ST) heteroskedastic model with a second-order logistic function of varying speed in the mean and variance. This paper evaluates the performance of Valueat-Risk (VaR) measures in a class of risk models, specially focusing on three distinct ST functions with GARCH structures: first-and second-order logistic functions, and the exponential function. The likelihood function is non-differentiable in terms of the threshold values and delay parameter. We employ Bayesian Markov chain Monte Carlo sampling methods to update the estimates and quantile forecasts. The proposed methods are illustrated using simulated data and an empirical study. We estimate VaR forecasts for the proposed models alongside some competing asymmetric models with 49