Abstract: An explicit representation of phase-type distributions as an infinite mixture of Erlang distributions is introduced. The representation unveils a novel and useful connection between a class of Bayesian nonparametric mixture models and phase-type distributions. In particular, this sheds some light on two hot topics, estimation techniques for phase-type distributions, and the availability of closed-form expressions for some functionals related to Dirichlet process mixture models. The power of this connection is illustrated via a posterior inference algorithm to estimate phase-type distributions, avoiding some difficulties with the simulation of latent Markov jump processes, commonly encountered in phase-type Bayesian inference. On the other hand, closed-form expressions for functionals of Dirichlet process mixture models are illustrated with density and renewal function estimation, related to the optimal salmon weight distribution of an aquaculture study. (Paper)

Abstract: Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the semi-hierarchical Dirichlet process, a novel hierarchical prior that extends the hierarchical Dirichlet process of Teh et al. (2006) and that avoids the degeneracy issues of nested processes recently described by Camerlenghi et al. (2019a). We go beyond the simple yes/no answer to the homogeneity question and embed the proposed prior in a random partition model; this procedure allows us to give a more comprehensive response to the above question and in fact find groups of populations that are internally homogeneous when I greater or equal than 2 such populations are considered. We study theoretical properties of the semi-hierarchical Dirichlet process and of the Bayes factor for the homogeneity test when I = 2. Extensive simulation studies and applications to educational data are also discussed. (Technical report)

Abstract: We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with t marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew-Gaussian process, thus obtaining a process with skew-t marginal distributions. For the proposed (skew) t process we study the second-order and geometrical properties and in the t case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the t process. Moreover we compare the performance of the optimal linear predictor of the t process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australia. (Paper)

Abstract: In some large clinical studies, it may be impractical to perform the physical examination to every subject at his/her last monitoring time in order to diagnose the occurrence of the event of interest. This gives rise to survival data with missing censoring indicators where the probability of missing may depend on time of last monitoring and some covariates. We present a fully Bayesian semi‐parametric method for such survival data to estimate regression parameters of the proportional hazards model of Cox. Theoretical investigation and simulation studies show that our method performs better than competing methods. We apply the proposed method to analyze the survival data with missing censoring indicators from the Orofacial Pain: Prospective Evaluation and Risk Assessment study. (Paper)

Abstract: We consider a natural generalization of classical scheduling problems to a setting in which using a time unit for processing a job causes some time-dependent cost, the time-of-use tariff, which must be paid in addition to the standard scheduling cost. We focus on preemptive single-machine scheduling and two classical scheduling cost functions, the sum of (weighted) completion times and the maximum completion time, that is, the makespan. While these problems are easy to solve in the classical scheduling setting, they are considerably more complex when time-of-use tariffs must be considered. We contribute optimal polynomial-time algorithms and best possible approximation algorithms. For the problem of minimizing the total (weighted) completion time on a single machine, we present a polynomial-time algorithm that computes for any given sequence of jobs an optimal schedule, i.e., the optimal set of time slots to be used for preemptively scheduling jobs according to the given sequence. This result is based on dynamic programming using a subtle analysis of the structure of optimal solutions and a potential function argument. With this algorithm, we solve the unweighted problem optimally in polynomial time. For the more general problem, in which jobs may have individual weights, we develop a polynomial-time approximation scheme (PTAS) based on a dual scheduling approach introduced for scheduling on a machine of varying speed. As the weighted problem is strongly NP-hard, our PTAS is the best possible approximation we can hope for. For preemptive scheduling to minimize the makespan, we show that there is a comparably simple optimal algorithm with polynomial running time. This is true even in a certain generalized model with unrelated machines. (Paper)

Abstract: We study estimation and prediction of Gaussian processes with space-time covariance models belonging to the Dynamical General- ized Wendland family (DGW) (Porcu et al., 2020, Statistica Sinica), under fixed-domain asymptotics. Such a class is nonseparable, has dynamical compact supports, and parameterizes differentiability at the origin similarly to the space-time Mat ́ern class (Ip and Li, 2017, Statistica Sinica). The results of the paper are classified into two parts. In the first part, we establish strong consistency and asymptotic normality for the maximum likelihood estimator of the microergodic parameter as- sociated to the DGW covariance model, under fixed-domain asymp- totics. The last part focuses on optimal kriging prediction under the DGW model and asymptotically correct estimation of mean square error using a misspecified model. Theoretical results are in turn based on equivalence of Gaussian measures under some given fami- lies of space-time covariance functions, where both space or time are compact. Such technical results are provided in the Online Supple- ment to this paper. (Paper)

Abstract: In this paper, we study a semiparametric additive beta regression model using a parameterization based on the mean and a dispersion parameter. This model is useful for situations where the response variable is continuous and restricted to the unit interval, in addition to being related to other variables through a semiparametric regression structure. First, we formulate the model and then estimation of its parameters is discussed. A back-fitting algorithm is derived to attain the maximum penalized likelihood estimates by using natural cubic smoothing splines. We provide closed-form expressions for the score function, Fisher information matrix and its inverse. Local influence methods are derived as diagnostic tools. Finally, a practical illustration based on real data is presented and discussed. (Paper)

Abstract: BACKGROUND: Mass vaccination campaigns to prevent coronavirus disease 2019 (Covid-19) are occurring in many countries; estimates of vaccine effectiveness are urgently needed to support decision making. A countrywide mass vaccination campaign with the use of an inactivated severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine (CoronaVac) was conducted in Chile starting on February 2, 2021. METHODS: We used a prospective national cohort, including participants 16 years of age or older who were affiliated with the public national health care system, to assess the effectiveness of the inactivated SARS-CoV-2 vaccine with regard to preventing Covid-19 and related hospitalization, admission to the intensive care unit (ICU), and death. We estimated hazard ratios using the extension of the Cox proportional-hazards model, accounting for time-varying vaccination status. We estimated the change in the hazard ratio associated with partial immunization (≥14 days after receipt of the first dose and before receipt of the second dose) and full immunization (≥14 days after receipt of the second dose). Vaccine effectiveness was estimated with adjustment for individual demographic and clinical characteristics. RESULTS: The study was conducted from February 2 through May 1, 2021, and the cohort included approximately 10.2 million persons. Among persons who were fully immunized, the adjusted vaccine effectiveness was 65.9% (95% confidence interval [CI], 65.2 to 66.6) for the prevention of Covid-19 and 87.5% (95% CI, 86.7 to 88.2) for the prevention of hospitalization, 90.3% (95% CI, 89.1 to 91.4) for the prevention of ICU admission, and 86.3% (95% CI, 84.5 to 87.9) for the prevention of Covid-19–related death. CONCLUSIONS: Our results suggest that the inactivated SARS-CoV-2 vaccine effectively prevented Covid-19, including severe disease and death, a finding that is consistent with results of phase 2 trials of the vaccine. (Funded by Agencia Nacional de Investigación y Desarrollo and others.) (Paper)

Abstract: Early case detection and isolation of infected individuals are critical to controlling COVID-19. RT-PCR is considered the gold standard for the diagnosis of SARS-CoV-2 infection, but false-negatives occur. We built a user-friendly online tool to estimate the probability of having COVID-19 with negative RT-PCR results and thus avoid preventable transmission. (Paper)

Abstract: A spatio-temporal blockwise Euclidean likelihood method for the estimation of covariance models when dealing with large spatio-temporal Gaussian data is proposed. The method uses moment conditions coming from the score of the pairwise composite likelihood. The blockwise approach guarantees considerable computational improvements over the standard pairwise composite likelihood method. In order to further speed up computation, a general purpose graphics processing unit implementation using OpenCL is implemented. The asymptotic properties of the proposed estimator are derived and the finite sample properties of this methodology by means of a simulation study highlighting the computational gains of the OpenCL graphics processing unit implementation. Finally, there is an application of the estimation method to a wind component data set. (Paper)

Abstract: Motivated by classes of problems frequently found in the analysis of gene expression data, we propose a semiparametric Bayesian model to detect biclusters, that is, subsets of individuals sharing similar patterns over a set of conditions. Our approach is based on the well-known plaid model by Lazzeroni and Owen (2002). By assuming a truncated stick-breaking prior we also find the number of biclusters present in the data as part of the inference. Evidence from a simulation study shows that the model is capable of correctly detecting biclusters and performs well compared to some competing approaches. The flexibility of the proposed prior is demonstrated with applications to the analysis of gene expression data (continuous responses) and histone modifications data (count responses). (Paper)

Abstract: Combination chemotherapy treatment regimens created for patients diagnosed with childhood acute lymphoblastic leukemia have had great success in improving cure rates. Unfortunately, patients prescribed these types of treatment regimens have displayed susceptibility to the onset of osteonecrosis. Some have suggested that this is due to pharmacokinetic interaction between two agents in the treatment regimen (asparaginase and dexamethasone) and other physiological variables. Determining which physiological variables to consider when searching for interactions in scenarios like these, minus a priori guidance, has proved to be a challenging problem, particularly if interactions influence the response distribution in ways beyond shifts in expectation or dispersion only. In this paper we propose an exploratory technique that is able to discover associations between covariates and responses in a very general way. The procedure connects covariates to responses very flexibly through dependent random partition prior distributions, and then employs machine learning techniques to highlight potential associations found in each cluster. We provide a simulation study to show utility and apply the method to data produced from a study dedicated to learning which physiological predictors influence severity of osteonecrosis multiplicatively. (Paper)

Abstract: Data mining is employed to extract useful information and to detect patterns from often large data sets, closely related to knowledge discovery in databases and data science. In this investigation, we formulate models based on machine learning algorithms to extract relevant information predicting student retention at various levels, using higher education data and specifying the relevant variables involved in the modeling. Then, we utilize this information to help the process of knowledge discovery. We predict student retention at each of three levels during their first, second, and third years of study, obtaining models with an accuracy that exceeds 80% in all scenarios. These models allow us to adequately predict the level when dropout occurs. Among the machine learning algorithms used in this work are: decision trees, k-nearest neighbors, logistic regression, naive Bayes, random forest, and support vector machines, of which the random forest technique performs the best. We detect that secondary educational score and the community poverty index are important predictive variables, which have not been previously reported in educational studies of this type. The dropout assessment at various levels reported here is valid for higher education institutions around the world with similar conditions to the Chilean case, where dropout rates affect the efficiency of such institutions. Having the ability to predict dropout based on student’s data enables these institutions to take preventative measures, avoiding the dropouts. In the case study, balancing the majority and minority classes improves the performance of the algorithms. (Paper)

Abstract: Improving air quality is an important environmental challenge of our time. Chile currently has one of the most stable and emerging economies in Latin America, where human impact on natural resources and air quality does not go unperceived. Santiago, the capital of Chile, is one of the cities in which particulate matter (PM) levels exceed national and international limits. Its location and climate cause critical conditions for human health when interaction with anthropogenic emissions is present. In this paper, we propose a predictive model based on bivariate regression to estimate PM levels, related to PM2.5 and PM10, simultaneously. Birnbaum-Saunders distributions are used in the joint modeling of real-world PM2.5 and PM10 data by considering as covariates some relevant meteorological variables employed in similar studies. The Mahalanobis distance is utilized to assess bivariate outliers and to detect suitability of the distributional assumption. In addition, we use the local influence technique for analyzing the impact of a perturbation on the overall estimation of model parameters. In the predictions, we check the categorization for the observed and predicted cases of the model according to the primary air quality regulations for PM. (Paper)

Abstract: Finite or infinite mixture models are routinely used in Bayesian statistical practice for tasks such as clustering or density estimation. Such models are very attractive due to their flexibility and tractability. However, a common problem in fitting these or other discrete models to data is that they tend to produce a large number of overlapping clusters. Some attention has been given in the statistical literature to models that include a repulsive feature, i.e., that encourage separation of mixture components. We study here a method that has been shown to achieve this goal without sacrificing flexibility or model fit. The model is a special case of Gibbs measures, with a parameter that controls the level of repulsion that allows construction of d-dimensional probability densities whose coordinates tend to repel each other. This approach was successfully used for density regression in Quinlan et al. (J Stat Comput Simul 88(15):2931–2947, 2018). We detail some of the global properties of the repulsive family of distributions and offer some further insight by means of a small simulation study. (Paper)

Abstract: Breaking symmetries is a popular way of speeding up the branch-and-bound method for symmetric integer programs. We study polyhedra that break all symmetries, namely, fundamental domains. Our long-term goal is to understand the relationship between the complexity of such polyhedra and their symmetry breaking capability. Borrowing ideas from geometric group theory, we provide structural properties that relate the action of the group with the geometry of the facets of fundamental domains. Inspired by these insights, we provide a new generalized construction for fundamental domains, which we call generalized Dirichlet domain (GDD). Our construction is recursive and exploits the coset decomposition of the subgroups that fix given vectors in Rn. We use this construction to analyze a recently introduced set of symmetry breaking inequalities by Salvagnin [23] and Liberti and Ostrowski [15], called Schreier-Sims inequalities. In particular, this shows that every permutation group admits a fundamental domain with less than n facets. We also show that this bound is tight. Finally, we prove that the Schreier-Sims inequalities can contain an exponential number of isomorphic binary vectors for a given permutation group G, which provides evidence of the lack of symmetry breaking effectiveness of this fundamental domain. Conversely, a suitably constructed GDD for G has linearly many inequalities and contains unique representatives for isomorphic binary vectors. (Paper)

Abstract: Bayesian nonparametric models provide a general framework for flexible statistical modeling of modern complex data sets. We compare a rate-optimal and rate-suboptimal Bayesian nonparametric model for density estimation for data supported on a compact interval, by means of the analyses of simulated and real data. The results show that rate-optimal models are not uniformly better, across sample sizes, with respect to the way in which the posterior mass concentrates around a true model and that suboptimal models can outperform the optimal ones, even for relatively large sample sizes. (Paper)

Abstract: Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. [20] provides strong upper bounds on the uniform stability of the stochastic gradient descent (SGD) algorithm on sufficiently smooth convex losses. These results led to important progress in understanding of the generalization properties of SGD and several applications to differentially private convex optimization for smooth losses. Our work is the first to address uniform stability of SGD on nonsmooth convex losses. Specifically, we provide sharp upper and lower bounds for several forms of SGD and full-batch GD on arbitrary Lipschitz nonsmooth convex losses. Our lower bounds show that, in the nonsmooth case, (S)GD can be inherently less stable than in the smooth case. On the other hand, our upper bounds show that (S)GD is sufficiently stable for deriving new and useful bounds on generalization error. Most notably, we obtain the first dimension-independent generalization bounds for multi-pass SGD in the nonsmooth case. In addition, our bounds allow us to derive a new algorithm for differentially private nonsmooth stochastic convex optimization with optimal excess population risk. Our algorithm is simpler and more efficient than the best known algorithm for the nonsmooth case [16].(Paper)

Abstract: Respondent-Driven sampling (RDS) is a sampling method devised to overcome challenges with sampling hard-to-reach human populations. The sampling starts with a limited number of individuals who are asked to recruit a small number of their contacts. Every surveyed individual is subsequently given the same opportunity to recruit additional members of the target population until a pre-established sample size is achieved. The recruitment process consequently implies that the survey respondents are responsible for deciding who enters the study. Most RDS prevalence estimators assume that participants select among their contacts completely at random. The main objective of this work is to correct the inference for departure from this assumption, such as systematic recruitment based on the characteristics of the individuals or based on the nature of relationships. To accomplish this, we introduce three forms of non-random recruitment, provide estimators for these recruitment behaviors and extend three estimators and their associated variance procedures. The proposed methodology is assessed through a simulation study capturing various sampling and network features. Finally, the proposed methods are applied to a public health setting.(Paper)

Abstract: This paper proposes a new class of covariance functions for bivariate random fields on spheres, having the same properties as the bivariate Matérn model proposed in Euclidean spaces. The new class depends on the geodesic distance on a sphere; it allows for indexing differentiability (in the mean square sense) and fractal dimensions of the components of any bivariate Gaussian random field having such covariance structure. We find parameter conditions ensuring positive definiteness. We discuss other possible models and illustrate our findings through a simulation study, where we explore the performance of maximum likelihood estimation method for the parameters of the new covariance function. A data illustration then follows, through a bivariate data set of temperatures and precipitations, observed over a large portion of the Earth, provided by the National Oceanic and Atmospheric Administration Earth System Research Laboratory. (Paper)

Abstract: In this paper we aim to propose two models for regression and dependence analysis when dealing with positive spatial or spatio-temporal continuous data. Specifically we propose two (possibly non stationary) random processes with Gamma and Weibull marginals. Both processes stem from the same idea, namely from the transformation of a sum of independent copies of a squared Gaussian random process. We provide analytic expression for the bivariate distributions and we study the associated geometrical and extremal properties. Since maximum likelihood estimation method is not feasible, even for relatively small data-set, we suggest to adopt the pairwise likelihood. The effectiveness of our proposal is illustrated through a simulation study that we supplement with a new analysis of well-known dataset, the Irish wind speed data \citep{Haslett:Raftery:1989}. In our example we do not consider a preliminary transformation of the data differently from the previous studies. (Paper)

Abstract: We consider mixture models where location parameters are a priori encouraged to be well separated. We explore a class of determinantal point process (DPP) mixture models, which provide the desired notion of separation or repulsion. Instead of using the rather restrictive case where analytical results are partially available, we adopt a spectral representation from which approximations to the DPP density functions can be readily computed. For the sake of concreteness the presentation focuses on a power exponential spectral density, but the proposed approach is in fact quite general. We later extend our model to incorporate covariate information in the likelihood and also in the assignment to mixture components, yielding a trade-off between repulsiveness of locations in the mixtures and attraction among subjects with similar covariates. We develop full Bayesian inference, and explore model properties and posterior behavior using several simulation scenarios and data illustrations. Supplementary materials for this article are available online (Bianchini et al., 2020). (Paper)

Abstract: Gaussian random fields defined over compact two-point homogeneous spaces are considered and Sobolev regularity and Hölder continuity are explored through spectral representations. It is shown how spectral properties of the covariance function associated to a given Gaussian random field are crucial to determine such regularities and geometric properties. Furthermore, fast approximations of random fields on compact two-point homogeneous spaces are derived by truncation of the series expansion, and a suitable bound for the error involved in such an approximation is provided. (Paper)

Abstract: The study of racial/ethnic inequalities in health is important to reduce the uneven burden of disease. In the case of colorectal cancer (CRC), disparities in survival among non-Hispanic Whites and Blacks are well documented, and mechanisms leading to these disparities need to be studied formally. It has also been established that body mass index (BMI) is a risk factor for developing CRC, and recent literature shows BMI at diagnosis of CRC is associated with survival. Since BMI varies by racial/ethnic group, a question that arises is whether disparities in BMI is partially responsible for observed racial/ethnic disparities in CRC survival. This paper presents new methodology to quantify the impact of the hypothetical intervention that matches the BMI distribution in the Black population to a potentially complex distributional form observed in the White population on racial/ethnic disparities in survival. We perform a simulation that shows our proposed Bayesian density regression approach performs as well as or better than current methodology allowing for a shift in the mean of the distribution only, and that standard practice of categorizing BMI leads to large biases. When applied to motivating data from the Cancer Care Outcomes Research and Surveillance (CanCORS) Consortium, our approach suggests the proposed intervention is potentially beneficial for elderly and low income Black patients, yet harmful for young and high income Black populations. (Paper)

Abstract: We consider a new operator acting on rescaled weighted differences between two members of the class $\Phi_d$ of positive definite radial functions. In particular, we study the positive definiteness of the operator for the Matérn, Generalized Cauchy and Wendland families. (Paper)

Abstract: Stochastic convex optimization, where the objective is the expectation of a random convex function, is an important and widely used method with numerous applications in machine learning, statistics, operations research and other areas. We study the complexity of stochastic convex optimization given only statistical query (SQ) access to the objective function. We show that well-known and popular first-order iterative methods can be implemented using only statistical queries. For many cases of interest we derive nearly matching upper and lower bounds on the estimation (sample) complexity including linear optimization in the most general setting. We then present several consequences for machine learning, differential privacy and proving concrete lower bounds on the power of convex optimization based methods. The key ingredient of our work is SQ algorithms and lower bounds for estimating the mean vector of a distribution over vectors supported on a convex body in ℝd. This natural problem has not been previously studied and we show that our solutions can be used to get substantially improved SQ versions of Perceptron and other online algorithms for learning halfspaces. (Technical report)

Abstract: We develop a simple, yet powerful, technique based on linear regression models of parametrized closed curves which induces a probability distribution on the planar shape space. Such parametrization is driven by control points which can be estimated from the data. Our proposal is capable to infer about the mean shape, to predict the shape of an object at an unobserved location, and, while doing so, to consider the effect of predictors on the shape. In particular, the model is able to detect possible differences across the levels of the predictor, thus also applicable for two-sample tests. A simple MCMC algorithm for Bayesian inference is also presented and tested with simulated and real datasets. Supplementary material is available online. (Paper)

Abstract: We propose a Bayesian hypothesis testing procedure for comparing the distributions of paired samples. The procedure is based on a flexible model for the joint distribution of both samples. The flexibility is given by a mixture of Dirichlet processes. Our proposal uses a spike‐slab prior specification for the base measure of the Dirichlet process and a particular parametrization for the kernel of the mixture in order to facilitate comparisons and posterior inference. The joint model allows us to derive the marginal distributions and test whether they differ or not. The procedure exploits the correlation between samples, relaxes the parametric assumptions, and detects possible differences throughout the entire distributions. A Monte Carlo simulation study comparing the performance of this strategy to other traditional alternatives is provided. Finally, we apply the proposed approach to spirometry data collected in the United States to investigate changes in pulmonary function in children and adolescents in response to air polluting factors. (Paper)

Abstract: This study provides new classes of nonseparable space-time covariance functions with spatial (or temporal) margins that belong to the generalized Wendland class of compactly supported covariance functions. An interesting feature of our covariances, from a computational viewpoint, is that the compact support is a decreasing function of the temporal (spatial) lag. We provide conditions for the validity of the proposed class, and analyze the problem of differentiability at the origin for the temporal (spatial) margin. A simulation study explores the finite-sample properties and the computational burden associated with the maximum likelihood estimation of the covariance parameters. Finally, we apply the proposed covariance models to Irish wind speed data, and compare the results with those of Gneiting–Matern models in terms of fitting, prediction efficiency, and computational burden. The necessary and sufficient conditions, together with other results on dynamically varying compact supports, are provided in the online Supplementary Material. (Paper)

Abstract: We provide a non-parametric spectral approach to the modeling of correlation functions on spheres. The sequence of Schoenberg coefficients and their associated covariance functions are treated as random rather than assuming a parametric form. We propose a stick-breacking representation for the spectrum, and show that such a choice spans the support of the class of geodesically-isotropic covariance functions under uniform convergence. Further, we examine the first order properties of such representation, from which geometric properties can be inferred, in terms of Hölder continuity, of the associated Gaussian random field. The properties of the posterior, in terms of existence, uniqueness, and Lipschitz continuity, are then inspected. Our findings are validated with MCMC simulations and illustrated using a global data set on surface temperatures. (Paper)

Abstract: The paper considers reduction problems and deformation approaches for nonstationary covariance functions on the (d−1)-dimensional spheres, 𝕊d−1, embedded in the d-dimensional Euclidean space. Given a covariance function C on 𝕊d−1, we chase a pair (R,Ψ) for a function R:[−1,+1]→ R and a smooth bijection Ψ, such that C can be reduced to a geodesically isotropic one: C(x,y)=R(⟨Ψ(x),Ψ(y)⟩), with ⟨⋅,⋅⟩ denoting the dot product. The problem finds motivation in recent statistical literature devoted to the analysis of global phenomena, defined typically over the sphere of R^3. The application domains considered in the manuscript makes the problem mathematically challenging. We show the uniqueness of the representation in the reduction problem. Then, under some regularity assumptions, we provide an inversion formula to recover the bijection Ψ, when it exists, for a given C. We also give sufficient conditions for reducibility. (Paper)

Abstract: The paper considers reduction problems and deformation approaches for nonstationary covariance functions on the (d−1)-dimensional spheres, 𝕊d−1, embedded in the d-dimensional Euclidean space. Given a covariance function C on 𝕊d−1, we chase a pair (R,Ψ), for a function R:[−1,+1]→ℝ and a smooth bijection Ψ, such that C can be reduced to a geodesically isotropic one: C(x,y)=R(⟨Ψ(x),Ψ(y)⟩), with ⟨⋅,⋅⟩ denoting the dot product. The problem finds motivation in recent statistical literature devoted to the analysis of global phenomena, defined typically over the sphere of ℝ3. The application domains considered in the manuscript makes the problem mathematically challenging. We show the uniqueness of the representation in the reduction problem. Then, under some regularity assumptions, we provide an inversion formula to recover the bijection Ψ, when it exists, for a given C. We also give sufficient conditions for reducibility. (Paper)

Abstract: Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate to assume a location/scale representation, where the error distribution has unchanging shape over the predictor space. In fact, it often happens in applied research that the distribution of responses under study changes with predictors in ways that cannot be reasonably represented by a finite dimensional functional form. This can seriously affect the answers to the scientific questions of interest, and therefore more general approaches are indeed needed. This gives rise to the study of fully nonparametric regression models. We review some of the main Bayesian approaches that have been employed to define probability models where the complete response distribution may vary flexibly with predictors. We focus on developments based on modifications of the Dirichlet process, historically termed dependent Dirichlet processes, and some of the extensions that have been proposed to tackle this general problem using nonparametric approaches..(Paper)

Abstract: Equating is a family of statistical models and methods used to adjust scores on different test forms so that they can be comparable and used interchangeably. Equated scores are obtained estimating the equating transformation function, which maps the scores on the scale of one test form into their equivalents on the scale of other one. All the statistical models that have been proposed for estimating this function are based on continuous approximations of the score distributions, leading to equated scores lying on a continuous scale even though score scales are usually subsets of the integer numbers (e.g., the total number of correct answers). In this article, we develop a new equating method from which equated scores defined on the original discrete scale are obtained. Considering scores as ordinal random variables, we propose a continuous latent variable formulation to perform an equipercentile-like equating based on a Bayesian nonparametric model for score distributions. The proposed model is applied to simulated and real data collected under an equivalent group design. Some methods to assess the performance of our model are also discussed. Compared with discrete versions of equated scored obtained from traditional equating methods, the results show that the proposed method has better performance.. (Paper)

Abstract: Censored data arise frequently in diverse applications in which observations to be measured may be subject to some upper and lower detection limits due to the restriction of experimental apparatus such that they are not exactly quantifiable. Mixtures of factor analyzers with censored data (MFAC) have been recently proposed for model-based density estimation and clustering of high-dimensional data in the presence of censored observations. In this paper, we consider an extended version of MFAC by considering regression equations to describe the relationship between covariates and multiply censored dependent variables. Two analytically feasible EM-type algorithms are developed for computing maximum likelihood estimates of model parameters with closed-form expressions. Moreover, we provide an information-based method to compute asymptotic standard errors of mixing proportions and regression coefficients. The utility and performance of our proposed methodology are illustrated through a simulation study and two real data examples. (Paper)

Abstract: The issue of model-based clustering of longitudinal data has attracted increasing attention in past two decades. Finite mixtures of Student’s- linear mixed-effects (FM-tLME) models have been considered for implementing this task especially when data contain extreme observations. This paper presents an extended finite mixtures of Student’s- linear mixed-effects (EFM-tLME) model, where the categorical component labels are assumed to be influenced by the observed covariates. As compared with the naive methods assuming the mixing proportions to be fixed but unknown, the proposed EFM-tLME model exploits a logistic function to link the relationship between the prior classification probabilities and the covariates of interest. To carry out maximum likelihood estimation, an alternating expectation conditional maximization (AECM) algorithm is developed under several model reduction schemes. The technique for extracting the information-based standard errors of parameter estimates is also investigated. The proposed method is illustrated using simulation experiments and real data from an AIDS clinical study. (Paper)

Abstract: Solving discrete linear inverse problems is one of the cornerstones of modern science and engineering. In abstract terms, these problems seek to recover an unknown vector from an incomplete set of linear measurements. When the object is a sparse convex combination of a known collection of atoms, the gauge associated to the convex hull of this collection, i.e., the atomic gauge, can be minimized subject to data consistency constraints to attempt to recover the original vector. In some practical applications, such as magnetic resonance imaging, the vector is complex-valued and it is the magnitude vector, i.e., the vector containing the magnitude of the components, that is a sparse convex combination of known real-valued atoms. To apply the atomic gauge to this setting, we propose extending the collection of real-valued atoms by considering their modulations by a collection of suitable phases. Furthermore, under minor assumptions, we provide computationally tractable expressions to evaluate both the gauge associated to the modulated set of atoms and its proximal map. Our results show the complexity of using the gauge associated to a collection of modulated atoms is comparable to that of using a collection of real-valued atoms. (Paper)

Abstract: Failure times of a machinery cannot always be assumed independent and identically distributed, eg, if after reparations the machinery is not restored to a same-as-new condition. Framed within the renewal processes approach, a generalization that considers exchangeable inter-arrival times is presented. The resulting model provides a more realistic approach to capture the dependence among events occurring at random times, while retaining much of the tractability of the classical renewal process. Extensions of some classical results and special cases of renewal functions are analysed, in particular, the one corresponding to an exchangeable sequence driven by a Dirichlet process. The proposal is tested through an estimation procedure using simulated data sets and with an application to the reliability of hydraulic subsystems in load-haul-dump machines. (Paper)

Abstract: We study composite likelihood estimation of the covariance parameters with data from a one-dimensional Gaussian process with exponential covariance function under fixed domain asymptotics. We show that the weighted pairwise maximum likelihood estimator of the microergodic parameter can be consistent or inconsistent , depending on the range of admissible parameter values in the likelihood optimization. On the contrary, the weighted pairwise conditional maximum likelihood estimator is always consistent. Both estimators are also asymptotically Gaussian when they are consistent, with asymptotic variance larger or strictly larger than that of the maximum likelihood estimator. A simulation study is presented in order to compare the finite sample behavior of the pairwise likelihood estimators with their asymptotic distributions. (Paper)

Abstract: We study estimation and prediction of Gaussian processes with covariance model belonging to the generalized Cauchy (GC) family, under fixed domain asymptotics. Gaussian processes with this kind of covariance function provide separate characterization of fractal dimension and long range dependence, an appealing feature in many physical, biological or geological systems. The results of the paper are classified into three parts. In the first part, we characterize the equivalence of two Gaussian measures with GC covariance function. Then we provide sufficient conditions for the equivalence of two Gaussian measures with Matèrn (MT) and GC covariance functions and two Gaussian measures with Generalized Wendland (GW) and GC covariance functions. In the second part, we establish strong consistency and asymptotic distribution of the maximum likelihood estimator of the microergodic parameter associated to GC covariance model, under fixed domain asymptotics. The last part focuses on optimal prediction with GC model and specifically, we give conditions for asymptotic efficiency prediction and asymptotically correct estimation of mean square error using a misspecified GC, MT or GW model, under fixed domain asymptotics. Our findings are illustrated through a simulation study: the first compares the finite sample behavior of the maximum likelihood estimation of the microergodic parameter of the GC model with the given asymptotic distribution. We then compare the finite-sample behavior of the prediction and its associated mean square error when the true model is GC and the prediction is performed using the true model and a misspecified GW model. (Paper)

Abstract:We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As the Matérn case, this class allows a continuous parameterization of smoothness of the underlying Gaussian random field, being additionally compactly supported. The paper is divided into two parts: First, we characterize the equivalence of two Gaussian measures with GW covariance function, and we provide sufficient conditions for the equivalence of two Gaussian measures with Matérn and GW covariance functions. We elucidate the consequences of these facts in terms of (misspecified) best linear unbiased predictors. In the second part, we establish strong consistency and asymptotic distribution of the maximum likelihood estimator of the microergodic parameter associated to GW covariance model, under fixed domain asymptotics. Our findings are illustrated through a simulation study: The first compares the finite sample behavior of the maximum likelihood estimation of the microergodic parameter with the given asymptotic distribution. We then compare the finite-sample behavior of the prediction and its associated mean square error when using two equivalent Gaussian measures with Matérn and GW covariance model, using covariance tapering as benchmark. (Paper)

Abstract: We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and randomized algorithms applied to essentially any of the interesting geometries and nonsmooth, weakly-smooth, or smooth objective functions. In particular, we show that it is not possible to obtain a polylogarithmic (in the sequential complexity of the problem) number of parallel rounds with a polynomial (in the dimension) number of queries per round. In the majority of these settings and when the dimension of the space is polynomial in the inverse target accuracy, our lower bounds match the oracle complexity of sequential convex optimization, up to at most a logarithmic factor in the dimension, which makes them (nearly) tight. Prior to our work, lower bounds for parallel convex optimization algorithms were only known in a small fraction of the settings considered in this paper, mainly applying to Euclidean (l2) and l∞ spaces. Our work provides a more general and streamlined approach for proving lower bounds in the setting of parallel convex optimization. (Paper)

Abstract: We propose a Bayesian nonparametric strategy to test for differences between a control group and several treatment regimes. Most of the existing tests for this type of comparison are based on the differences between location parameters. In contrast, our approach identifies differences across the entire distribution, avoids strong modeling assumptions over the distributions for each treatment, and accounts for multiple testing through the prior distribution on the space of hypotheses. The proposal is compared to other commonly used hypothesis testing procedures under simulated scenarios. Two real applications are also analyzed with the proposed methodology. (Paper)

Abstract: This work presents a Bayesian predictive approach to statistical shape analysis. A modeling strategy that starts with a Gaussian distribution on the configuration space, and then removes the effects of location, rotation and scale, is studied. This boils down to an application of the projected normal distribution to model the configurations in the shape space, which together with certain identifiability constraints, facilitates parameter interpretation. Having better control over the parameters allows us to generalize the model to a regression setting where the effect of predictors on shapes can be considered. The methodology is illustrated and tested using both simulated scenarios and a real data set concerning eight anatomical landmarks on a sagittal plane of the corpus callosum in patients with autism and in a group of controls. (Paper)

Abstract: In biomedical studies and clinical trials, repeated measures are often subject to some upper and/or lower limits of detection. Hence, the responses are either left or right censored. A complication arises when more than one series of responses is repeatedly collected on each subject at irregular intervals over a period of time and the data exhibit tails heavier than the normal distribution. The multivariate censored linear mixed effect (MLMEC) model is a frequently used tool for a joint analysis of more than one series of longitudinal data. In this context, we develop a robust generalization of the MLMEC based on the scale mixtures of normal distributions. To take into account the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is considered. For this complex longitudinal structure, we propose an exact estimation procedure to obtain the maximum‐likelihood estimates of the fixed effects and variance components using a stochastic approximation of the EM algorithm. This approach allows us to estimate the parameters of interest easily and quickly as well as to obtain the standard errors of the fixed effects, the predictions of unobservable values of the responses, and the log‐likelihood function as a byproduct. The proposed method is applied to analyze a set of AIDS data and is examined via a simulation study. (Paper)

Abstract: Motivated by data gathered in an oral health study, we propose a Bayesian nonparametric approach for population-averaged modeling of correlated time-to-event data, when the responses can only be determined to lie in an interval obtained from a sequence of examination times and the determination of the occurrence of the event is subject to misclassification. The joint model for the true, unobserved time-to-event data is defined semiparametrically; proportional hazards, proportional odds, and accelerated failure time (proportional quantiles) are all fit and compared. The baseline distribution is modeled as a flexible tailfree prior. The joint model is completed by considering a parametric copula function. A general misclassification model is discussed in detail, considering the possibility that different examiners were involved in the assessment of the occurrence of the events for a given subject across time. We provide empirical evidence that the model can be used to estimate the underlying time-to-event distri- bution and the misclassification parameters without any external information about the latter parameters. We also illustrate the effect on the statistical inferences of neglecting the presence of misclassification. (Paper) (Supplementary material)

Abstract: We analyze time‐course protein activation data to track the changes in protein expression over time after exposure to drugs such as protein inhibitors. Protein expression is expected to change over time in response to the intervention in different ways due to biological pathways. We therefore allow for clusters of proteins with different treatment effects, and allow these clusters to change over time. As the effect of the drug wears off, protein expression may revert back to the level before treatment. In addition, different drugs, doses, and cell lines may have different effects in altering the protein expression. To model and understand this process we develop random partitions that define a refinement and coagulation of protein clusters over time. We demonstrate the approach using a time‐course reverse phase protein array (RPPA) dataset consisting of protein expression measurements under different drugs, dose levels, and cell lines. The proposed model can be applied in general to time‐course data where clustering of the experimental units is expected to change over time in a sequence of refinement and coagulation. (Paper)

Abstract: The number of scientific fields that regularly collect data that are spatio-temporal continues to grow. An intuitive feature of this type of data is that measurements taken on experimental units near each other in time and space tend to be similar. As such, many methods developed to accommodate spatio-temporal dependent structures attempt to borrow strength among units close in space and time, which constitutes an implicit space-time grouping. We develop a class of dependent random partition models that explicitly models this spatio-temporal clustering by way of a dependent random partition model. We first detail how temporal dependence is incorporated so that partitions evolve gently over time. Then conditional and marginal properties of the joint model are derived. We then demonstrate how space can be integrated. Computation strategies are detailed and we illustrate the methodology through simulations and an application. (Technical report)

Abstract: In many applied fields incomplete covariate vectors are commonly encountered. It is well known that this can be problematic when making inference on model parameters, but its impact on prediction performance is less understood. We develop a method based on covariate dependent partition models that seamlessly handles missing covariates while avoiding completely any type of imputation. The method we develop is not only able to make in-sample predictions, but out-of-sample as well even if the missing pattern in the new subjects' incomplete covariate vector was not seen in the training data. Further, both categorical and continuous covariates are permitted. Our proposal fares well when compared to other alternatives based on imputations. We illustrate the method using simulation studies and an ozone dataset. (Technical report)

Abstract: We congratulate Federico Camerlenghi, David Dunson, Antonio Lijoi, Igor Pruenster and Abel Rodrıguez, from now on referred to as CDLPR, for an an interesting paper. CDLPR are indeed to be commended by a very fine work. By focusing on partitions they uncovered a critical degeneracy issue underlying the nested Dirichlet process (NDP) and other discrete nested processes. The key tool to understand the problem is the partially exchangeable partition probability function (pEPPF), that describes the probability model on partitions induced by models such as the NDP. CDLPR explicitly find the pEPPF in the case of d = 2 samples, showing that it is expressed as a mixture of patterns that may be described as partially exchangeable (both samples are marginally exchangeable, arising from different discrete random probability measures) and fully exchangeable (both samples arise from a common discrete random measure). Specifi- cally, the pEPPF is a convex combination of these two forms. However, if it so happens that one atom is shared by these two random measures, then the structure degenerates to the fully exchangeable case. This is certainly a limitation of nested processes. As discussed in the manuscript, the problem is not restricted to the NDP, but will mani- fest itself in the case of any nested discrete random measure. CDLPR illustrate further this point with real data examples and synthetic data simulations. Solving the degen- eracy problem motivated the (very clever) introduction of their latent nested process (LNP) approach. By allowing idiosyncratic and shared components, CDLPR overcome the degeneracy while retaining modeling flexibility. Essentially, the shared component can explicitly provide atoms in the mixture that are common to both samples, while the idiosyncratic components can adjust to local behavior without being forced to combine all of the mass in a single random measure. Their specific construction involves three random measures with which they create the LNP by normalizing the sum of idiosyn- cratic (μl) and shared measures (μS) thus yielding p ̃l, as given in (14), where l = 1,2. The structure is emphasized by noting that each p ̃l can be expressed as a convex com- bination of normalized versions of μl and μS. Indispensable to the proposal is the fact that flexibility does not come at the expense of practical tractability, which is of course vital for the practical success of models based on LNPs. We discuss next some possible extensions to the model constructed by CDLPR. (Paper)

Abstract: Mixtures of factor analyzers (MFA) provide a promising tool for modeling and clustering high-dimensional data that contain an overwhelmingly large number of attributes measured on individuals arisen from a heterogeneous population. Due to the restriction of experimental apparatus, measurements can be limited to some lower and/or upper detection bounds and thus the data are possibly censored. In this paper, we extend the MFA to accommodate censored data, and the new model is called the MFA with censoring (MFAC). A computationally feasible alternating expectation conditional maximization (AECM) algorithm is developed to carry out maximum likelihood estimation of the MFAC model. Practical issues related to model-based clustering and recovery of censored data are also discussed. Simulation studies are conducted to examine the effect of censoring in classification, estimation and cluster validation. We also present an application of the proposed approach to two real data examples in which a certain number of left-censored observations are present. (Paper)

Abstract: Comparability of measurements is an important practice in different fields. In educational measurement, equating methods are used to achieve the goal of having comparable scores from different test forms. Equated scores are obtained using the equating transformation which maps the scores on the scale of one test form into their equivalents on the scale of another for the case of sum scores. Such transformation has been typically computed using continuous approximations of the score distributions, leading to equated scores that are not necessarily defined on the original discrete scale. Considering scores as ordinal random variables, we propose a latent variable formulation based on a flexible Bayesian nonparametric model to perform an equipercentile-like equating that is capable to produce equated scores on the original discrete scale. The performance of our model is assessed using simulated data under the equivalent groups equating design. The results show that the proposed method has better performance with respect to a discrete version of estimated equated scores from traditional equating methods. (Paper)

Abstract: Non-alcoholic fatty liver disease (NAFLD) is the most common liver disease in the world and it is becoming one of the most frequent cause of liver transplantation. Unfortunately, the only available method that can reliably determine the stage of this disease is liver biopsy, however, it is invasive and risky for patients. The purpose of this study is to investigate changes in the intracellular composition of the liver fatty acids during the progression of the NAFLD in a mouse model fed with Western diet, with the aim of identify non-invasive biomarkers of NAFLD progression based in 1H-MRS. Our results showed that the intracellular liver fatty acid composition changes as NAFLD progresses from simple steatosis to steatohepatitis (NASH). Using principal component analysis with a clustering method, it was possible to identify the three most relevant clinical groups: normal, steatosis and NASH by using 1H-MRS. These results showed a good agreement with the results obtained by GC-MS and histology. Our results suggest that it would be possible to detect the progression of simple steatosis to NASH using 1H-MRS, that has the potential to be used routinely in clinical application for screening high-risk patients. (Paper)

Abstract: The equivalence of Gaussian measures is a fundamental tool to establish the asymptotic properties of both prediction and estimation of Gaussian fields under fixed domain asymptotics. The paper solves Problem 18 in the list of open problems proposed by Gneiting (2013). Specifically, necessary and sufficient conditions are given for the equivalence of Gaussian measures associated to random fields defined on the d-dimensional sphere S^d, and with covariance functions depending on the great circle distance. We also focus on a comparison of our result with existing results on the equivalence of Gaussian measures for isotropic Gaussian fields on R^{d+1} restricted to the sphere S^d. For such a case, the covariance function depends on the chordal distance being an approximation of the true distance between two points located on the sphere. Finally, we provide equivalence conditions for some parametric families of covariance functions depending on the great circle distance. An important implication of our results is that all the parameters indexing some families of covariance functions on spheres can be consistently estimated. A simulation study illustrates our findings in terms of implications on the consistency of the maximum likelihood estimator under fixed domain asymptotics. (Paper)

Abstract: Measurement error models constitute a wide class of models, that include linear and nonlinear regression models. They are very useful to model many real life phenomena, particularly in the medical and biological areas. The great advantage of these models is that, in some sense, they can be represented as mixed effects models, allowing to us the implementation of well-known techniques, like the EM-algorithm for the parameter estimation. In this paper, we consider a class of multivariate measurement error models where the observed response and/or covariate are not fully observed, i.e., the observations are subject to certain threshold values below or above which the measurements are not quantifiable. Consequently, these observations are considered censored. We assume a Student-t distribution for the unobserved true values of the mismeasured covariate and the error term of the model, providing a robust alternative for parameter estimation. Our approach relies on a likelihood-based inference using an EM-type algorithm. The proposed method is illustrated through some simulation studies and the analysis of an AIDS clinical trial dataset. (Paper)

Abstract: A standard approach for dealing with unobserved heterogeneity and clustered time‐to‐event data within the proportional hazards (PH) context has been the introduction of a cluster‐specific random effect (frailty), common to subjects within the same cluster. However, the conditional PH assumption could be too strong for some applications. For example, the marginal association of survival functions within a cluster does not depend on the subject‐specific covariates. We propose an alternative partially PH modeling approach based on the introduction of cluster‐dependent random hazard functions and on the use of mixture models induced by completely random measures. The proposed approach accommodates for different degrees of association within a cluster, which varies as a function of cluster‐level and individual covariates. Moreover, a particular specification of the proposed model has the appealing property of preserving marginally the PH structure. We illustrate the performances of the proposed modeling approach on simulated and real data sets. (Paper)

Abstract: We propose new covariance functions for bivariate Gaussian random fields that are very general and include as special cases other popular models proposed in earlier literature, namely, the bivariate Matérn and bivariate Cauchy models. The proposed model allows the covariance margins to belong to different parametric families with. To our knowledge, this is the first model of this type to be proposed in the literature. For instance, one of the margins can be of the Matérn type, whereas the latter can index long‐range dependence. Estimation of the model is illustrated through simulation. (Paper)