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Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
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…
Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty…
Fisher's Method of Maximum Likelihood is shown to be a procedure for the construction of likelihood intervals or regions, instead of a procedure of point estimation. Based on Fisher's articles and books it is justified that by estimation…
The Fisher Information Matrix formalism is extended to cases where the data is divided into two parts (X,Y), where the expectation value of Y depends on X according to some theoretical model, and X and Y both have errors with arbitrary…
We present a method to estimate the quantum Fisher information (QFI) of many-body quantum states in the presence of decoherence, where its direct evaluation requires the full spectral resolution of the density matrix. We show that, for…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. The highlight of this representation is that all…
Motivation: Recent work has demonstrated the feasibility of using non-numerical, qualitative data to parameterize mathematical models. However, uncertainty quantification (UQ) of such parameterized models has remained challenging because of…
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation…
Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
Motivated by constraints on the dark energy equation of state from supernova-data, we propose a formalism for the Bayesian inference of functions: Starting at a functional variant of the Kullback-Leibler divergence we construct a functional…
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…
We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data.…
The three and five-dimensional convex sets of two-level complex and quaternionic quantum systems are studied in the Bayesian thermostatistical framework introduced by Lavenda. Associated with a given parameterization of each such set is a…
The force estimation problem in quantum metrology with an arbitrary non-Markovian Gaussian bath is considered. No assumptions are made on the bath spectrum and coupling strength with the probe. Considering the natural global unitary…
In quantum theory, the inescapable interaction between a system and its surroundings would lead to a loss of coherence and leakage of information into the environment. An effective approach to retain the quantum characteristics of the…