Related papers: A flexible class of priors for orthonormal matrice…
Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…
Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…
In this paper, we propose a novel model to analyze serially correlated two-dimensional functional data observed sparsely and irregularly on a domain which may not be a rectangle. Our approach employs a mixed effects model that specifies the…
Power priors are used for incorporating historical data in Bayesian analyses by taking the likelihood of the historical data raised to the power $\alpha$ as the prior distribution for the model parameters. The power parameter $\alpha$ is…
We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…
Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical…
Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…
Interest in unsupervised methods for joint analysis of heterogeneous data sources has risen in recent years. Low-rank latent factor models have proven to be an effective tool for data integration and have been extended to a large number of…
We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated,…
We propose a new framework for modeling high-dimensional matrix-variate time series by a two-way transformation, where the transformed data consist of a matrix-variate factor process, which is dynamically dependent, and three other blocks…
Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…
Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…
The construction of valid and flexible cross-covariance functions is a fundamental task for modeling multivariate space-time data arising from climatological and oceanographical phenomena. Indeed, a suitable specification of the covariance…
Variational Bayesian Inference is a popular methodology for approximating posterior distributions over Bayesian neural network weights. Recent work developing this class of methods has explored ever richer parameterizations of the…
We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…
In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…
In Bayesian regression models with categorical predictors, constraints are needed to ensure identifiability when using all $K$ levels of a factor. The sum-to-zero constraint is particularly useful as it allows coefficients to represent…
Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the…
Low-rank matrix estimation from incomplete measurements recently received increased attention due to the emergence of several challenging applications, such as recommender systems; see in particular the famous Netflix challenge. While the…
In this paper we explore orthogonal systems in $\mathrm{L}_2(\mathbb{R})$ which give rise to a skew-Hermitian, tridiagonal differentiation matrix. Surprisingly, allowing the differentiation matrix to be complex leads to a particular family…