Related papers: A Bayesian Approach to Inverse Quantum Statistics
We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose…
The Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in analysis of cosmological models has been limited by difficulties in calculating it, with current…
In nuclear reactor system design and safety analysis, the Best Estimate plus Uncertainty (BEPU) methodology requires that computer model output uncertainties must be quantified in order to prove that the investigated design stays within…
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…
We present a Bayesian nonparametric system reliability model which scales well and provides a great deal of flexibility in modeling. The Bayesian approach naturally handles the disparate amounts of component and subsystem data that may…
We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…
Ultra-cold atomic gases are unique in terms of the degree of controllability, both for internal and external degrees of freedom. This makes it possible to use them for the study of complex quantum many-body phenomena. However in many…
We establish a unified statistical framework that underscores the crucial role statistical inference plays in Quantum Amplitude Estimation (QAE), a task essential to fields ranging from chemistry to finance and machine learning. We use this…
Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation…
The ability to efficiently infer system parameters is essential in any signal-processing task that requires fast operation. Dealing with quantum systems, a serious challenge arises due to substantial growth of the underlying Hilbert space…
In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…
In both classical and quantum physics, irreversible processes are described by maps that contract the space of states. The change in volume has often been taken as a natural quantifier of the amount of irreversibility. In Bayesian…
Mixed modeling of extreme values and random effects is relatively unexplored topic. Computational difficulties in using the maximum likelihood method for mixed models and the fact that maximum likelihood method uses available data and does…
Inverse Uncertainty Quantification (IUQ) method has been widely used to quantify the uncertainty of Physical Model Parameters (PMPs) in nuclear Thermal Hydraulics (TH) systems. This paper introduces a novel hierarchical Bayesian model which…
An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through…
In this letter we revisit the problem of optimal design of quantum tomographic experiments. In contrast to previous approaches where an optimal set of measurements is decided in advance of the experiment, we allow for measurements to be…
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…
We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy…
Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…