Related papers: Approximate Computational Approaches for Bayesian …

We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…

Quantum sensors typically translate external fields into a periodic response whose frequency is then determined by analyses performed in Fourier space. This allows for a linear inference of the parameters that characterize external signals.…

Achieving ultimate bounds in estimation processes is the main objective of quantum metrology. In this context, several problems require measurement of multiple parameters by employing only a limited amount of resources. To this end,…

The sensor placement problem is a common problem that arises when monitoring correlated phenomena, such as temperature, precipitation, and salinity. Existing approaches to this problem typically formulate it as the maximization of…

Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider…

Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical…

Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…

Bayesian optimal experimental design (BOED) seeks to maximize the expected information gain (EIG) of experiments. This requires a likelihood estimate, which in many settings is intractable. Simulation-based inference (SBI) provides powerful…

A lower bound on the minimum mean-squared error (MSE) in a Bayesian estimation problem is proposed in this paper. This bound utilizes a well-known connection to the deterministic estimation setting. Using the prior distribution, the bias…

Mutual information (MI) is a fundamental quantity in information theory and machine learning. However, direct estimation of MI is intractable, even if the true joint probability density for the variables of interest is known, as it involves…

Approximate Bayesian deep learning methods hold significant promise for addressing several issues that occur when deploying deep learning components in intelligent systems, including mitigating the occurrence of over-confident errors and…

We present a comprehensive and pedagogical formulation of Bayesian multiparameter quantum estimation. Within this framework, we analyse the role of measurement incompatibility and establish its quantitative effect on attainable precision.…

A predictive Bayesian model selection approach is presented to discriminate coupled models used to predict an unobserved quantity of interest (QoI). The need for accurate predictions arises in a variety of critical applications such as…

The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…

Bayesian optimal design of experiments (BODE) has been successful in acquiring information about a quantity of interest (QoI) which depends on a black-box function. BODE is characterized by sequentially querying the function at specific…

Identifying a gas source in turbulent environments presents a significant challenge for critical applications such as environmental monitoring and emergency response. This issue is addressed through an approach that combines distributed IoT…

Calibration is nowadays one of the most important processes involved in the extraction of valuable data from measurements. The current availability of an optimum data cube measured from a heterogeneous set of instruments and surveys relies…

In many scientific and engineering domains, physical experiments are often costly, non-replicable, or time-consuming. The Kennedy and O'Hagan (KOH) model framework has become a widely used approach for combining simulator runs with limited…

In this paper, a Bayesian fusion technique for remotely sensed multi-band images is presented. The observed images are related to the high spectral and high spatial resolution image to be recovered through physical degradations, e.g.,…

The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation…