Precision Of Parameter Estimates Research Articles

Quantum Critical Metrology.

Quantum metrology fundamentally relies upon the efficient management of quantum uncertainties. We show that under equilibrium conditions the management of quantum noise becomes extremely flexible around the quantum critical point of a quantum many-body system: this is due to the critical divergence of quantum fluctuations of the order parameter, which, via Heisenberg's inequalities, may lead to the critical suppression of the fluctuations in conjugate observables. Taking the quantum Ising model as the paradigmatic incarnation of quantum phase transitions, we show that it exhibits quantum critical squeezing of one spin component, providing a scaling for the precision of interferometric parameter estimation which, in dimensions d>2, lies in between the standard quantum limit and the Heisenberg limit. Quantum critical squeezing saturates the maximum metrological gain allowed by the quantum Fisher information in d=∞ (or with infinite-range interactions) at all temperatures, and it approaches closely the bound in a broad range of temperatures in d=2 and 3. This demonstrates the immediate metrological potential of equilibrium many-body states close to quantum criticality, which are accessible, e.g., to atomic quantum simulators via elementary adiabatic protocols.

Bayesian DINA Modeling Incorporating Within-Item Characteristic Dependency.

The within-item characteristic dependency (WICD) means that dependencies exist among different types of item characteristics/parameters within an item. The potential WICD has been ignored by current modeling approaches and estimation algorithms for the deterministic inputs noisy "and" gate (DINA) model. To explicitly model WICD, this study proposed a modified Bayesian DINA modeling approach where a bivariate normal distribution was employed as a joint prior distribution for correlated item parameters. Simulation results indicated that the model parameters were well recovered and that explicitly modeling WICD improved model parameter estimation accuracy, precision, and efficiency. In addition, when potential item blocks existed, the proposed modeling approach still demonstrated good performance and high robustness. Furthermore, the fraction subtraction data were analyzed to illustrate the application and advantage of the proposed modeling approach.

Ecological Role of an Apex Predator Revealed by a Reintroduction Experiment and Bayesian Statistics

Recent studies suggest that apex predators play a pivotal role in maintaining healthy, balanced ecosystems. However, a criticism of studies investigating the ecological role of apex predators is that understanding does not come from manipulative experiments. Here, we use a before-after-control-impact-paired design to test predictions generated from trophic cascade theory (TCT) and mesopredator release hypothesis (MRH) by experimentally introducing dingoes into a 37-km2 paddock and measuring the resultant effects on mammal assemblages. To increase precision of parameter estimates generated by our experiment, we used a Bayesian framework which included prior information recorded from a mensurative study located in a comparable ecosystem that contrasted indices of mammal abundance where dingoes were common and rare. Results of the mensurative study were consistent with TCT and MRH. When using an uninformative prior, results of the experiment showed that dingo addition only had a negative effect on kangaroo activity. Use of an informative prior reduced uncertainty of the posterior mean parameter estimates from the experiment and suggested that red foxes were affected negatively and small mammals and rabbits were affected positively by dingo introduction. However, the prior had a strong influence on the posterior mean effect sizes for small mammals, rabbits and foxes. Opposite polarity of uninformed and prior parameter estimates for rabbits suggests that the prior was incompatible with the uninformed estimates from the manipulative experiment. Our study shows how use of logical informative priors can help to overcome statistical issues associated with low-replication in large-scale experiments, but the strong influence of the prior means that our findings were driven largely by the mensurative study.

The Certainty of Uncertainty: Potential Sources of Bias and Imprecision in Disease Ecology Studies.

Wildlife diseases have important implications for wildlife and human health, the preservation of biodiversity and the resilience of ecosystems. However, understanding disease dynamics and the impacts of pathogens in wild populations is challenging because these complex systems can rarely, if ever, be observed without error. Uncertainty in disease ecology studies is commonly defined in terms of either heterogeneity in detectability (due to variation in the probability of encountering, capturing, or detecting individuals in their natural habitat) or uncertainty in disease state assignment (due to misclassification errors or incomplete information). In reality, however, uncertainty in disease ecology studies extends beyond these components of observation error and can arise from multiple varied processes, each of which can lead to bias and a lack of precision in parameter estimates. Here, we present an inventory of the sources of potential uncertainty in studies that attempt to quantify disease-relevant parameters from wild populations (e.g., prevalence, incidence, transmission rates, force of infection, risk of infection, persistence times, and disease-induced impacts). We show that uncertainty can arise via processes pertaining to aspects of the disease system, the study design, the methods used to study the system, and the state of knowledge of the system, and that uncertainties generated via one process can propagate through to others because of interactions between the numerous biological, methodological and environmental factors at play. We show that many of these sources of uncertainty may not be immediately apparent to researchers (for example, unidentified crypticity among vectors, hosts or pathogens, a mismatch between the temporal scale of sampling and disease dynamics, demographic or social misclassification), and thus have received comparatively little consideration in the literature to date. Finally, we discuss the type of bias or imprecision introduced by these varied sources of uncertainty and briefly present appropriate sampling and analytical methods to account for, or minimise, their influence on estimates of disease-relevant parameters. This review should assist researchers and practitioners to navigate the pitfalls of uncertainty in wildlife disease ecology studies.

Precision of polarimetric orthogonal state contrast estimation in coherent images corrupted by speckle, Poisson, and additive noise.

We consider laser-illuminated active polarimetric imaging systems that measure the orthogonal state contrast (OSC), a frequently used surrogate to the degree of polarization, that can be used, for example, to discriminate manmade objects from natural backgrounds in remote sensing. We investigate the estimation precision of the OSC parameter in the presence of speckle, Poisson, and additive noise by using the Cramer-Rao lower bound (CRLB). Using Monte Carlo simulations and optical experiments, we show that the expression of the CRLB models the actual OSC estimation performance with excellent accuracy. This result is important for the design and sizing of active polarimetric imagers since the closed-form expression of the CRLB makes it handy for back-of-the-envelope calculations.

Accuracy and precision of quantitative DCE-MRI parameters: How should one estimate contrast concentration?

IntroductionPharmacokinetic parameters derived from dynamic contrast-enhanced MRI (DCE-MRI) data are sensitive to acquisition and post-processing techniques, which makes it difficult to compare results obtained using different methods. In particular, one of the most important factors affecting estimation of model parameters is how to convert MRI signal intensities to contrast agent concentration. The purpose of our study was to quantitatively compare a linear signal-to-concentration conversion (LC) as an approximation and a non-linear conversion (NLC) based on the MRI signal equation, in terms of the accuracy and precision of the pharmacokinetic parameters in T1-weighted DCE-MRI. Materials and methodsNumerical simulation studies were conducted to compare LC and NLC in terms of the accuracy and precision in contrast kinetic parameter estimation, and to evaluate their dependency on flip angle (FA), pre-contrast T1 (T10) and arterial input function (AIF). In addition, the effect of the conversion method on the diagnostic accuracy was evaluated with 36 breast lesions (19 benign and 17 malignant). ResultsThe transfer rate (Ktrans) estimated using LC and measured AIF (mAIF) were up to 38% higher than the true Ktrans values, while the LC Ktrans estimates with the presumed AIF (pAIF) were up to 7% lower than the true Ktrans values, when FA = 45°. When using a small FA, such as 12°, the LC Ktrans with pAIF had least sensitivity to the error in T10 compared to the Ktrans estimated using LC with mAIF, and NLC with pAIF or mAIF. The breast DCE-MRI study showed that both LC and NLC Ktrans were significantly different (p < 0.05) between the malignant and benign lesions. The effect size between benign and malignant values as measured by Cohen's d was 1.06 for LC Ktrans and 1.02 for NLC Ktrans. ConclusionThe present study results show that, when precontrast T1 measurement is not available and a low FA is used for DCE-MRI, the uncertainty in the contrast kinetic parameter estimation can be reduced by using the LC method with pAIF, without compromising the diagnostic accuracy.

On the Application of Joint-Domain Dictionary Mapping for Multiple Power Disturbance Assessment

This paper proposes a joint-domain dictionary mapping method to obtain high assessment accuracy of multiple power disturbances. Firstly, in order to achieve resolutions in both the time and frequency domains, a joint-domain dictionary is proposed which consists of a discrete Hartley base and an identity matrix. Due to the low correlation between the discrete Hartley base and the identity matrix, the joint-domain dictionary mapping can separately capture the approximations of the sinusoidal components and transients. Since the mapping coefficients contain the physical quantities, the eigenvalues of each component can be effectively estimated. A quantified eigenvalue classifier was designed for identifying power disturbances using the estimated eigenvalues. The proposed method was compared with several advanced methods through simulated power disturbances under different noise conditions, and actual data from the Institute of Electrical and Electronics Engineers Power and Energy Society database. The results reveal that the joint-domain dictionary mapping technique shows good performance on parameter estimation and recognition precision, even dealing with complicated multiple power disturbances.

Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment

Quantum Fisher information (QFI) is an important feature for the precision of quantum parameter estimation based on the quantum Cramér–Rao inequality. When the quantum state satisfies the von Neumann–Landau equation, the local quantum uncertainty (LQU), as a kind of quantum correlation, present in a bipartite mixed state guarantees a lower bound on QFI in the optimal phase estimation protocol (Girolami et al., 2013). However, in the open quantum systems, there is not an explicit relation between LQU and QFI generally. In this paper, we study the relation between LQU and QFI in open systems which is composed of two interacting two-level systems coupled to independent non-Markovian environments with the entangled initial state embedded by a phase parameter θ. The analytical calculations show that the QFI does not depend on the phase parameter θ, and its decay can be restrained through enhancing the coupling strength or non-Markovianity. Meanwhile, the LQU is related to the phase parameter θ and shows plentiful phenomena. In particular, we find that the LQU can well bound the QFI when the coupling between the two systems is switched off or the initial state is Bell state.

Multi-objective optimization in quantum parameter estimation

We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is improved, it usually introduces a significant deformation to the system state. Moreover, we propose a multi-objective model to optimize the two conflicting objectives: (1) maximizing the Fisher information, improving the parameter estimation precision, and (2) minimizing the deformation of the system state, which maintains its fidelity. Finally, simulations of a simplified {\epsilon}-constrained model demonstrate the feasibility of the Hamiltonian control in improving the precision of the quantum parameter estimation.

Quantum-enhanced sensing from hyperentanglement

Hyperentanglement --- simultaneous entanglement between multiple degrees of freedom of two or more systems --- has been used to enhance quantum information tasks such as quantum communication and photonic quantum computing. Here we show that hyperentanglement can lead to increased quantum advantage in metrology, with contributions from the entanglement in each degree of freedom, allowing for Heisenberg scaling in the precision of parameter estimation. Our experiment employs photon pairs entangled in polarization and spatial degrees of freedom to estimate a small tilt angle of a mirror. Precision limits beyond shot noise are saturated through a simple binary measurement of the polarization state. The broad validity of the dynamics considered here implies that similar strategies based on hyperentanglement can offer improvement in a wide variety of metrological tasks.

Influence of noice on tripartite quantum probe state

Quantum metrology is a subject of studying quantum measurement and quantum statistical deduction, and the precision of parameter estimation can be enhanced by quantum properties. In general, the process of parameter estimation includes four steps:preparation of probe state, parameterization process, measurement, and data processing. Of these four steps, the preparation of probe state is the most crucial. However, in practical applications, in the process of preparing quantum probe state, the probe system will couple to its environment, which will inevitably cause the quantum properties of the probe system to deteriorate, and thus reducing the precision of quantum parameter estimation. The dynamics of quantum Fisher information (QFI) for W state and Greenberger-Horne-Zeilinger (GHZ) state have been studied in decoherence channels. Because W state and GHZ state have different entanglement properties, the studies of the dynamics of QFI for the superposition of W state and GHZ state are of practical significance in quantum metrology field. In this paper, the dynamics of QFIs for the superposition of W state and GHZ state in three typical decoherence channels (depolarization channel, amplitude damping channel and phase damping channel) are studied. In the four steps of quantum parameter estimation, our major attention is paid to the first step (i.e., the preparation of probe state). For comparison, the QFIs of different probe states are studied, with the other three steps fixed, i.e., all the probe states will undergo the same parameterization, measurement and estimation process. The parameterization process involved here is a quantum spin operation (specified by the spin rotation direction), which is chosen to maximize the QFI of the probe state. The initial probe states under consideration are the superpositions of W state and GHZ state of three-particle and five-particle systems, and the QFI dynamics of those probe states are studied in the three different typical decoherence channels. By using the operator-sum (Kraus) representation of those three typical decoherence channels, the QFI dynamics of the probe state can be analytically derived in three different decoherence channels. The results show that in the depolarization channel, the maximum QFI of the probe state decreases with the decoherence evolving to zero in the end; in the amplitude damping channel, the QFI of the probe state decreases to the minimum with the decoherence evolution and then increases to the shot noise limit; in the phase damping channel, the QFI of the probe state decreases with the evolution of decoherence, but the final stable value is not zero. Further analyses show that W state component of the superposition plays a role in resisting phase damping and the GHZ state component plays a role in resisting amplitude damping. These results can help us to choose the optimal probe state for maximizing the estimation precision in practice.

Translation compensation and micro-motion parameter estimation of laser micro-Doppler effect

Precise target identification is significant for commanding and identifying enemies. The micro-Doppler effect (MDE) can reflect the subtle movement characteristics of the targets, which provides a new way of detecting and recognizing the target. However, the current research mainly focuses on the micro-motion feature extraction and classification of the targets, which is not capable of identifying the targets of the same type. In fact, by accurately estimating the micro-motion parameters and combining sufficient prior knowledge, the target can be accurately identified. Compared with the microwave radar, the laser detected MDE has high sensitivity and precision in micro-motion parameter estimation. This is more conducive to realizing the accurate classification and fine identification of the targets. In real detection, the MDE always exists in the moving targets. This will generate a mixed echo signal modeled by the polynomial phase signal and sinusoidal frequency modulation (SFM) signal. So far, there have been no effective methods of estimating the micro-motion parameters in such mixed signals. In this regard, a set of translational motion compensation and micro-motion parameter estimation methods is proposed in this paper. A bandwidth searching method based on the fractional Fourier transform (FrFT) is presented to precisely estimate the translation parameters, which will be used to realize the compensation for the translational motion. The advanced particle filtering (PF) method using the static parameter model is designed for the micro-motion parameters in the remaining SFM term. Given the lack of particle diversity in static parameter PF, the Markov chain Monte Carlo sampling is employed, which also helps to improve the algorithm efficiency. Meanwhile, a new likelihood function in calculating the particle weights is designed by using the cumulative residual. With this improvement, the correct convergence under multi-dimensional parameter condition is guaranteed. The proposed method can avoid the influence from error transfer and achieve efficient and accurate estimation. Compared with the typical method that combines the time-frequency analysis and the polynomial fitting through the simulation, the proposed FrFT method is verified to have little computation complexity and high estimation accuracy, where the relative estimation errors of the translational parameters are kept at 0.64% and 0.45%, respectively. The waveform similarity of the SFM signal phase between the compensated signal and the real one indicates that the accuracy fully meets the requirement for accurate estimation of the micro-motion parameters. Further, the simulation result also shows the high efficiency of the improved PF algorithm. The convergence time consumed by the proposed algorithm is 0.353 s, while the traditional method needs 0.844 s. In the end, the comparison with the experimental data from the traditional inverse Radon transform shows the effectiveness and necessity of the proposed method. The research results are conducive to the accurate and rapid estimation of micro-motion parameters, which lays a foundation for the fine target recognition based on the MDE.

ISAR imaging of complex motion targets based on Radon transform cubic chirplet decomposition

ABSTRACTFor targets with complex motion, the echo of inverse synthetic aperture radar (ISAR) is a time-varying frequency signal in azimuth. Hence, the traditional range-Doppler (R-D) algorithm based on a constant frequency is invalid. In this letter, a novel ISAR imaging method for targets with complex motion is presented. The echo in azimuth is characterized as an amplitude-modulated (AM)-cubic phase signal, which is closer to the real ISAR scene, and Radon transform cubic chirplet decomposition (RTCCD) algorithm is proposed to process the signal. By introducing Radon transform and improved cubic chirplet function (CPF), the proposed algorithm estimates the chirp rate and the cubic chirp rate simultaneously to avoid error accumulation. Therefore, the parameter estimation precision is improved, and a high quality ISAR image can be obtained. Simulations and real data experiment validate the effectiveness of the proposed method.

Near-Heisenberg-limited parameter estimation precision by a dipolar-Bose-gas reservoir engineering

We propose a scheme to obtain the Heisenberg-limited parameter estimation precision by immersing atoms in a thermally equilibrated quasi-one-dimensional dipolar Bose-Einstein condensate reservoir. We show that the collisions between the dipolar atoms and the immersed atoms can result in a controllable nonlinear interaction through tuning the relative strength and the sign of the dipolar and contact interaction. We find that the repulsive dipolar interaction reservoir is preferential for the spin squeezing and the appearance of an entangled non-Gaussian state. As a useful resource for quantum metrology, we also show that the non-Gaussian state results in the phase estimation precision in the Heisenberg scaling, outperforming that of the spin-squeezed state.

Practical performance of real-time shot-noise measurement in continuous-variable quantum key distribution

In a practical continuous-variable quantum key distribution (CVQKD) system, real-time shot-noise measurement (RTSNM) is an essential procedure for preventing the eavesdropper exploiting the practical security loopholes. However, the performance of this procedure itself is not analyzed under the real-world condition. Therefore, we indicate the RTSNM practical performance and investigate its effects on the CVQKD system. In particular, due to the finite-size effect, the shot-noise measurement at the receiver’s side may decrease the precision of parameter estimation and consequently result in a tight security bound. To mitigate that, we optimize the block size for RTSNM under the ensemble size limitation to maximize the secure key rate. Moreover, the effect of finite dynamics of amplitude modulator in this scheme is studied and its mitigation method is also proposed. Our work indicates the practical performance of RTSNM and provides the real secret key rate under it.

Integrated population models facilitate ecological understanding and improved management decisions

ABSTRACTIntegrated population models (IPMs) represent a formal statistical methodology for combining multiple data sets such as population counts, band recoveries, and fecundity estimates into a single unified analysis with dual objectives: better estimating population size, trajectory, and vital rates; and formally describing the ecological processes that generated these patterns. Although IPMs have been used in population ecology and fisheries management, their use in wildlife management has been limited. Data sets available for North American waterfowl are unprecedented in terms of time span (&gt;60 years) and geographic coverage, and are especially well‐suited for development of IPMs that could improve the understanding of population ecology and help guide future harvest and habitat management decisions. In this overview, we illustrate 3 potential benefits of IPMs: integration of multiple data sources (i.e., population counts, mark‐recapture data, and fecundity estimates), increased precision of parameter estimates, and ability to estimate missing demographic parameters by reanalyzing results from a historical study of canvasbacks (Aythya valisineria). Drawing from our own published and unpublished work, we demonstrate how IPMs could be used to identify the critical vital rates that have had the greatest influence on population change in lesser scaup (Aythya affinis), evaluate potential mechanisms of harvest compensation for American black ducks (Anas rubripes), or prioritize the most appropriate places to conduct habitat management to benefit northern pintails (Anas acuta). Integrated population models provide a powerful platform for evaluating alternative hypotheses about population regulation and they have potential to advance the understanding of wildlife ecology and help managers make ecologically based decisions. © 2017 The Wildlife Society.

Bayesian inference of epidemiological parameters from transmission experiments

Epidemiological parameters for livestock diseases are often inferred from transmission experiments. However, there are several limitations inherent to the design of such experiments that limits the precision of parameter estimates. In particular, infection times and latent periods cannot be directly observed and infectious periods may also be censored. We present a Bayesian framework accounting for these features directly and employ Markov chain Monte Carlo techniques to provide robust inferences and quantify the uncertainty in our estimates. We describe the transmission dynamics using a susceptible-exposed-infectious-removed compartmental model, with gamma-distributed transition times. We then fit the model to published data from transmission experiments for foot-and-mouth disease virus (FMDV) and African swine fever virus (ASFV). Where the previous analyses of these data made various assumptions on the unobserved processes in order to draw inferences, our Bayesian approach includes the unobserved infection times and latent periods and quantifies them along with all other model parameters. Drawing inferences about infection times helps identify who infected whom and can also provide insights into transmission mechanisms. Furthermore, we are able to use our models to measure the difference between the latent periods of inoculated and contact-challenged animals and to quantify the effect vaccination has on transmission.

Hierarchical Bayesian models for small area estimation of forest variables using LiDAR

Light detection and ranging (LiDAR) data have become almost ubiquitous as a remote sensing tool in forestry estimation and mapping applications. Such initiatives commonly rely on spatially aligned forest inventory plot measurements and LiDAR covariates to inform model-based estimators for small area estimation. There are many examples where such linking models provide the desired accuracy and precision of forest parameter estimates for small areas where paucity of inventory plot observations preclude design-based inference. This paper builds on previous small area estimation (SAE) work by linking LiDAR covariates with variable radius forest inventory plot measurements within a hierarchical Bayesian framework. Using this framework, we compare SAE of forest aboveground biomass using: i) Fay-Herriot (FH); ii) FH with conditional autoregressive random effects (FHCAR); and iii) FHCAR with smoothed sampling variance (FHCAR-SMOOTH) models. Candidate models and the direct estimate based on plot measurements alone were compared using coefficient of variation (CV). On average, the FH model reduced the CV by 52.3% compared to the direct estimate. Incorporating spatial structure via the FHCAR model reduced the CV by 56.9% and 10.8% relative to the direct and the FH model estimates, respectively. Overall, these results illustrate the applicability and utility of using a SAE framework for linking LiDAR with typical forest inventory data.

Fitting diameter distribution models to data from forest inventories with concentric plot design

Aim: Several national forest inventories use a complex plot design based on multiple concentric subplots where smaller diameter trees are inventoried when lying in the smaller-radius subplots and ignored otherwise. Data from these plots are truncated with threshold (truncation) diameters varying according to the distance from the plot centre. In this paper we designed a maximum likelihood method to fit the Weibull diameter distribution to data from concentric plots.Material and methods: Our method (M1) was based on multiple truncated probability density functions to build the likelihood. In addition, we used an alternative method (M2) presented recently. We used methods M1 and M2 as well as two other reference methods to estimate the Weibull parameters in 40000 simulated plots. The spatial tree pattern of the simulated plots was generated using four models of spatial point patterns. Two error indices were used to assess the relative performance of M1 and M2 in estimating relevant stand-level variables. In addition, we estimated the Quadratic Mean plot Diameter (QMD) using Expansion Factors (EFs).Main results: Methods M1 and M2 produced comparable estimation errors in random and cluster tree spatial patterns. Method M2 produced biased parameter estimates in plots with inhomogeneous Poisson patterns. Estimation of QMD using EFs produced biased results in plots within inhomogeneous intensity Poisson patterns.Research highlights:We designed a new method to fit the Weibull distribution to forest inventory data from concentric plots that achieves high accuracy and precision in parameter estimates regardless of the within-plot spatial tree pattern.

Improving Markov switching models using realized variance

SummaryThis paper proposes a class of models that jointly model returns and ex post variance measures under a Markov switching framework. Both univariate and multivariate return versions of the model are introduced. Estimation can be conducted under a fixed dimension state space or an infinite one. The proposed models can be seen as nonlinear common factor models subject to Markov switching and are able to exploit the information content in both returns and ex post volatility measures. Applications to equity returns compare the proposed models to existing alternatives. The empirical results show that the joint models improve density forecasts for returns and point predictions of return variance. Using the information in ex post volatility measures can increase the precision of parameter estimates, sharpen the inference on the latent state variable, and improve portfolio decisions.