Related papers: Multi-level Bayes and MAP monotonicity testing

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

There are several challenges associated with inverse problems in which we seek to reconstruct a piecewise constant field, and which we model using multiple level sets. Adopting a Bayesian viewpoint, we impose prior distributions on both the…

Maximum a posteriori (MAP) estimation, like all Bayesian methods, depends on prior assumptions. These assumptions are often chosen to promote specific features in the recovered estimate. The form of the chosen prior determines the shape of…

We study linear models under heavy-tailed priors from a probabilistic viewpoint. Instead of computing a single sparse most probable (MAP) solution as in standard deterministic approaches, the focus in the Bayesian compressed sensing…

We propose a MAP Bayesian approach to perform and evaluate a co-clustering of mixed-type data tables. The proposed model infers an optimal segmentation of all variables then performs a co-clustering by minimizing a Bayesian model selection…

Multiplicative noise arises in inverse problems when, for example, uncertainty on measurements is proportional to the size of the measurement itself. The likelihood that arises is hence more complicated than that from additive noise. We…

When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…

When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…

Many Bayesian statistical inference problems come down to computing a maximum a-posteriori (MAP) assignment of latent variables. Yet, standard methods for estimating the MAP assignment do not have a finite time guarantee that the algorithm…

We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed…

This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process,…

We present a novel probabilistic approach for generating multi-fidelity data while accounting for errors inherent in both low- and high-fidelity data. In this approach a graph Laplacian constructed from the low-fidelity data is used to…

Consider the multiple testing problem of testing k null hypotheses, where the unknown family of distributions is assumed to satisfy a certain monotonicity assumption. Attention is restricted to procedures that control the familywise error…

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…

Heteroskedasticity poses several methodological challenges in designing valid and powerful procedures for simultaneous testing of composite null hypotheses. In particular, the conventional practice of standardizing or re-scaling…

In this paper, we introduce and study the multilevel-planarity testing problem, which is a generalization of upward planarity and level planarity. Let $G = (V, E)$ be a directed graph and let $\ell: V \to \mathcal P(\mathbb Z)$ be a…

We consider the structured-output prediction problem through probabilistic approaches and generalize the "perturb-and-MAP" framework to more challenging weighted Hamming losses, which are crucial in applications. While in principle our…

The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…

We describe here an iterative method for jointly estimating the noise power spectrum from a scanning experiment's time-ordered data, together with the maximum-likelihood map. We test the robustness of this method on simulated datasets with…

This paper considers maximum-a-posteriori (MAP) and linear discriminant based MAP detectors to detect changes in the mean and covariance of a stochastic input, driving specific network nodes, using noisy measurements from sensors…