Related papers: The majorizing measure approach to the sample boun…
We propose a procedure to design a state-quantizer with finitely many bins for a marginally stable stochastic linear system evolving in $\R^d$, and a bounded policy based on the resulting quantized state measurements to ensure bounded…
In this paper non-asymptotic exact exponential estimates are derived for the tail of maximum distribution of random field in the terms of majoring measures or, equally, generic chaining.
Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only…
Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…
We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use…
We generalize the measurement using an expanded concept of cover, in order to provide a new approach to size of set other than cardinality. The generalized measurement has application backgrounds such as a generalized problem in dimension…
We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting…
Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new…
Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the…
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…
Let $T$ be a tree with induced partial order $\preceq$. We investigate centered Gaussian processes $X=(X_t)_{t\in T}$ represented as $$ X_t=\sigma(t)\sum_{v \preceq t}\alpha(v)\xi_v $$ for given weight functions $\alpha$ and $\sigma$ on $T$…
The choice of sample size in the context of co-primary endpoints for a randomised trial is discussed. Current guidance can leave endpoints with unequal marginal power. A method is provided to achieve equal marginal power by using the…
We consider the averaging principle for deterministic or stochastic systems with a fast stochastic component (family of continuous-time Markov chains depending on the state of the system as a parameter). We show that, due to bifurcations in…
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…
We develop a method to carry out MAP estimation for a class of Bayesian regression models in which coefficients are assigned with Gaussian-based spike and slab priors. The objective function in the corresponding optimization problem has a…
This paper addresses the case where data come as point sets, or more generally as discrete measures. Our motivation is twofold: first we intend to approximate with a compactly supported measure the mean of the measure generating process,…
We develop conservative tests for the mean of a bounded population under stratified sampling and apply them to risk-limiting post-election audits. The tests are ``anytime valid'' under sequential sampling, allowing optional stopping in each…
We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The alternative is independent identically distributed zero-mean Gaussian random variables with…
We give an improved estimate for the regularity of the conditional distribution of the empiric mean of a finite sample of IID random variables, conditional on the sample "fluctuations", extending the well-known property of Gaussian IID…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…