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"Parameter estimation"
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Incompatibility in quantum parameter estimation
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some simple systems in order to track the effect of a local depolarizing noise on the incompatibility of the estimation task. A semidefinite program is described and used to numerically compute the figure of merit when the analytical tools are not sufficient, among these we include an upper bound computable from the symmetric logarithmic derivatives only. Finally we discuss how to obtain compatible models for a general unitary encoding on a finite-dimensional probe.
Journal Article
Open-Circuit Voltage Models for Battery Management Systems: A Review
A battery management system (BMS) plays a crucial role to ensure the safety, efficiency, and reliability of a rechargeable Li-ion battery pack. State of charge (SOC) estimation is an important operation within a BMS. Estimated SOC is required in several BMS operations, such as remaining power and mileage estimation, battery capacity estimation, charge termination, and cell balancing. The open-circuit voltage (OCV) look-up-based SOC estimation approach is widely used in battery management systems. For OCV lookup, the OCV–SOC characteristic is empirically measured and parameterized a priori. The literature shows numerous OCV–SOC models and approaches to characterize them and use them in SOC estimation. However, the selection of an OCV–SOC model must consider several factors: (i) Modeling errors due to approximations, age/temperature effects, and cell-to-cell variations; (ii) Likelihood and severity of errors when the OCV–SOC parameters are rounded; (iii) Computing system requirements to store and process OCV parameters; and (iv) The required computational complexity of real-time OCV lookup algorithms. This paper presents a review of existing OCV–SOC models and proposes a systematic approach to select a suitable OCV–SOC for implementation based on various constraints faced by a BMS designer in practical application.
Journal Article
Introduction to Bayesian Inference for Psychology
We introduce the fundamental tenets of Bayesian inference, which derive from two basic laws of probability theory. We cover the interpretation of probabilities, discrete and continuous versions of Bayes’ rule, parameter estimation, and model comparison. Using seven worked examples, we illustrate these principles and set up some of the technical background for the rest of this special issue of
Psychonomic Bulletin & Review
. Supplemental material is available via
https://osf.io/wskex/
.
Journal Article
ROBUST GAUSSIAN STOCHASTIC PROCESS EMULATION
We consider estimation of the parameters of a Gaussian Stochastic Process (GaSP), in the context of emulation (approximation) of computer models for which the outcomes are real-valued scalars. The main focus is on estimation of the GaSP parameters through various generalized maximum likelihood methods, mostly involving finding posterior modes; this is because full Bayesian analysis in computer model emulation is typically prohibitively expensive.
The posterior modes that are studied arise from objective priors, such as the reference prior. These priors have been studied in the literature for the situation of an isotropic covariance function or under the assumption of separability in the design of inputs for model runs used in the GaSP construction. In this paper, we consider more general designs (e.g., a Latin Hypercube Design) with a class of commonly used anisotropic correlation functions, which can be written as a product of isotropic correlation functions, each having an unknown range parameter and a fixed roughness parameter. We discuss properties of the objective priors and marginal likelihoods for the parameters of the GaSP and establish the posterior propriety of the GaSP parameters, but our main focus is to demonstrate that certain parameterizations result in more robust estimation of the GaSP parameters than others, and that some parameterizations that are in common use should clearly be avoided. These results are applicable to many frequently used covariance functions, for example, power exponential, Matérn, rational quadratic and spherical covariance. We also generalize the results to the GaSP model with a nugget parameter. Both theoretical and numerical evidence is presented concerning the performance of the studied procedures.
Journal Article
Forecast for cosmological parameter estimation with gravitational-wave standard sirens from the LISA-Taiji network
LISA and Taiji are expected to form a space-based gravitational-wave (GW) detection network in the future. In this work, we make a forecast for the cosmological parameter estimation with the standard siren observation from the LISA-Taiji network. We simulate the standard siren data based on a scenario with configuration angle of 40° between LISA and Taiji. Three models for the population of massive black hole binary (MBHB), i.e., pop III, Q3d, and Q3nod, are considered to predict the events of MBHB mergers. We find that, based on the LISA-Taiji network, the number of electromagnetic (EM) counterparts detected is almost doubled compared with the case of single Taiji mission. Therefore, the LISA-Taiji network’s standard siren observation could provide much tighter constraints on cosmological parameters. For example, solely using the standard sirens from the LISA-Taiji network, the constraint precision of
H
0
could reach 1.3%. Moreover, combined with the CMB data, the GW-EM observation based on the LISA-Taiji network could also tightly constrain the equation of state of dark energy, e.g., the constraint precision of
w
reaches about 4%, which is comparable with the result of CMB+BAO+SN. It is concluded that the GW standard sirens from the LISA-Taiji network will become a useful cosmological probe in understanding the nature of dark energy in the future.
Journal Article
Information Geometrical Characterization of Quantum Statistical Models in Quantum Estimation Theory
In this paper, we classify quantum statistical models based on their information geometric properties and the estimation error bound, known as the Holevo bound, into four different classes: classical, quasi-classical, D-invariant, and asymptotically classical models. We then characterize each model by several equivalent conditions and discuss their properties. This result enables us to explore the relationships among these four models as well as reveals the geometrical understanding of quantum statistical models. In particular, we show that each class of model can be identified by comparing quantum Fisher metrics and the properties of the tangent spaces of the quantum statistical model.
Journal Article
An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter
In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), and vaccinated (V). Initially, a mathematical analysis is carried out to illustrate the non-negativity, boundedness, epidemic equilibrium, existence, and uniqueness of the endemic equilibrium, and the basic reproduction number of the proposed model. Such numerical models can be, however, subject to various sources of uncertainties, due to an imperfect description of the biological processes governing the disease spread, which may strongly limit their forecasting skills. A data assimilation method, mainly, the ensemble Kalman filter (EnKF), is then used to constrain the model outputs and its parameters with available data. We conduct joint state-parameters estimation experiments assimilating daily data into the proposed model using the EnKF in order to enhance the model’s forecasting skills. Starting from the estimated set of model parameters, we then conduct short-term predictions in order to assess the predicability range of the model. We apply the proposed assimilation system on real data sets from Saudi Arabia. The numerical results demonstrate the capability of the proposed model in achieving accurate prediction of the epidemic development up to two-week time scales. Finally, we investigate the effect of vaccination on the spread of the pandemic.
Journal Article
A levy chaotic horizontal vertical crossover based artificial hummingbird algorithm for precise PEMFC parameter estimation
In this research, enhanced versions of the Artificial Hummingbird Algorithm are used to accurately identify unknown parameters in Proton Exchange Membrane Fuel Cell (PEMFC) models. In particular, we propose a multi strategy variant, the Lévy Chaotic Artificial Hummingbird Algorithm (LCAHA), which combines sinusoidal chaotic mapping, Lévy flights and a new cross update foraging strategy. The combination of this method with PEMFC parameters results in a significantly improved performance compared to traditional methods, such as Particle Swarm Optimization (PSO), Differential Evolution (DE), Grey Wolf Optimizer (GWO), and Sparrow Search Algorithm (SSA), which we use as baselines to validate PEMFC parameters. The quantitative results demonstrate that LCAHA attains a minimum Sum of Squared Errors (SSE) of 0.0254 and standard deviation of 4.59E−08 for the BCS 500W PEMFC model, which is much lower than the SSE values obtained for PSO (0.1924) and GWO (0.0364), thereby validating the superior accuracy and stability of LCAHA. Moreover, LCAHA converges faster than DE and SSA, reducing runtime by about 47%. The robustness and reliability of LCAHA-simulated and actual I–V curves across six PEMFC stacks are shown to be in close alignment.
Journal Article