Related papers: Bayesian one- and two-sided inference on the local…
We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…
The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of…
We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…
Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially…
Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic…
Being able to reliably assess not only the \emph{accuracy} but also the \emph{uncertainty} of models' predictions is an important endeavour in modern machine learning. Even if the model generating the data and labels is known, computing the…
We characterize the local smoothness and the asymptotic growth rate of the L\'evy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend known results in two ways. First, we obtain new bounds for…
Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this paper we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorithms, statistics, and machine learning. By leveraging a…
In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…
We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…
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…
For decades researchers have studied the On/Off counting problem, where a measured rate consists of two parts. One due to a signal process and another due to a background process, of which both magnitudes are unknown. While most frequentist…
Causal effect estimation from observational data is a challenging problem, especially with high dimensional data and in the presence of unobserved variables. The available data-driven methods for tackling the problem either provide an…
The reconstruction of the unknown acoustic source is studied using the noisy multiple frequency data on a remote closed surface. Assume that the unknown source is coded in a spatial dependent piecewise constant function, whose support set…