Precision Of Parameter Estimates Research Articles

Estimation of the disorder degree of the classical static noise using three entangled qubits as quantum probes

The paper investigates the estimation of the disorder degree of the classical static noise using three entangled qubits as quantum probes together with the tools of local quantum estimation theory. Three probing schemes namely common environment (CE), independent environments (IEs) and mixed environments (MEs) are investigated and the optimal initial state preparation of the probes taken as a partially depolarized GHZ state. The results show that: (i) the IEs probing scheme allows one to achieve better estimation precision compared to both MEs and CE schemes respectively; (ii) the higher is the initial amount of entanglement of the probes, the larger is the estimation precision, independently of the scheme considered; (iii) both small and large values of the disorder parameter are uniformly estimable at the optimal interaction time; (iv) entangled qubits probes quickly encode information about the disorder parameter than single-qubit probe; (v) there is an improvement in the estimation of the disorder parameter when entangled probes interacting either in IEs or MEs are used instead of a single probe, demonstrating that a single probe is not sufficient to optimally estimate the disorder parameter of the static noise. On the other hand, we have also investigated the relationship between the residual amount of entanglement present in the probes at the optimal interaction time and the estimation precision of the disorder parameter. We show that the higher the residual amount of entanglement at the optimal interaction time, the smaller the estimation precision.

SA26 - SPARSE CANONICAL CORRELATION IN APPLICATION TO BIPOLAR PSYCHOTIC PHENOTYPES AND SCHIZOPHRENIA GENOME-WIDE SIGNIFICANT GENETIC LOCI

Background The aetiology of Bipolar Disorder (BD) and Schizophrenia (SZ) involves a complex gene-environment interplay and this involves common risk alleles that are shared across the disorders. Bipolar disorder is heterogeneous in presentation and we and others have postulated that the particular clinical presentation is in part determined by the particular risk alleles carried. To investigate this, we have employed sparse Canonical Correlation Analysis (sCCA), to seek patterns of correlation between psychotic symptoms and schizophrenia risk alleles in a large (N=3903) deeply phenotyped sample of subjects with BD. Methods Canonical Correlation Analysis (CCA) seeks linear relationships between two sets of multi-dimensional variables. In the psychiatric genetics field, this approach can be adapted to enable the analysis of both phenotype and genetic variables in one framework. This has the advantage of minimizing the number of statistical tests required. A recent extension of CCA to sparse canonical correlation analysis (sCCA) allows application of the general approach to high dimensional genomic data (Witten et al., 2009). sCCA has advantages compared to CCA in terms of precision of parameter estimates and statistical power. We employed sCCA to analyse 30 psychotic symptoms assessed with the OPerational CRITeria checklist (OPCRIT) and 82 independent genome-wide significant SNPs that were identified by the SZ PGC2 study (The Psychiatric Genomics Consortium, 2014) for which we had data in our BD sample. We applied the sCCA as a purely data driven approach to individual OPCRIT psychotic symptoms and also to groups of OPCRIT psychotic symptoms (“positive”, “negative”, “disorganised”) defined by a previously published factor analysis study of schizophrenia. Results sCCA analysis of the individual OPCRIT items with the set of significantly associated with SZ 82 sCCA analysis based on individual psychotic symptoms revealed a significant association (p=0.045) with the largest weights attributed to delusions of influence, bizarre behaviour and grandiose delusions and an indel SNP on chromosome 3 (3:180594593, build 37). sCCA analysis on the same set of SNPs and OPCRIT symptom groups confirmed association with the same SNP and the “disorganised” group of OPCRIT symptoms (p=0.01). The results also show significant association when we use less stringent p-value thresholds in SZ. In this case the most heavily weighted SNP remains 3:180594593, but other SNPs also contribute to the analysis. Discussion Our results suggest the CCA canonical correlation approach might be a useful tool to explore phenotype-genotype relationships. It can be applied to generate data-driven hypotheses with the potential to provide further insights into the complex architecture of psychiatric disorders. To the best of our knowledge, this is the first study to apply this approach in analysing phenotypes and genotypes together. sCCA offers the potential to be extended to include a larger number of fine grained systematic descriptors of BD, and for testing for correlation with genetic profiles from other co-morbid disorders.

Estimation precision of full polarimetric parameters in the presence of additive and Poisson noise.

The final product of polarimetric measurements is often such polarimetric parameters as degree of polarization (DOP), angle of polarization (AOP) and ellipticity (EOP). Since these parameters are nonlinear functions of the Stokes vector, it is difficult to derive closed-form expressions of their variances. We derive approximate but accurate expressions of the estimation variances of DOP, AOP, and EOP in the presence of both additive and Poisson noise for optimal spherical design-based Stokes polarimeters. These original closed-from expressions provide a clear insight into the physical parameters that govern the estimation precision of each polarimetric parameter. They are validated through optical experiments on a real-world polarimeter. These expressions are important for designing and sizing polarimeters or polarimetric imagers aimed at different types of applications, and for assessing their performance.

Spatial partial least squares autoregression: Algorithm and applications

Partial least squares (PLS) is an efficient multivariate statistical data analysis method and has shown to be particularly useful to deal with knotty problems in practical applications, e.g., the ill-conditioned regression issues where the predictor variables are highly collinear or the sample size is much smaller than the number of covariates. Various works on PLS and its extension have been developed under the assumption that all the observations are mutually independent. However, this independence assumption may be violated in practice, especially when we collect data with network dependence structure among observations from some scientific disciplines, such as sociology and spatial economics. Yet relatively few works are available for PLS with network dependence structure. Here, we propose an spatial partial least squares autoregression (SPLSAR) to solve this problem, incorporating a spatial autoregressive parameter and a spatial weight matrix into PLS to accommodate dependence structure between individuals. Thus, the proposed method is more flexible as it can not only inherit the advantages of PLS, but also have the ability to deal with the network dependence. Moreover, we propose an efficient algorithm for the implementation of parameter estimation in SPLSAR regression. The finite sample performance of the proposed method is evaluated via extensive simulation study and a real data analysis, where results show that SPLSAR can achieve a better and more robust performance in terms of parameter estimation precision and out-of-sample prediction accuracy, when compared to classical PLS and SAR.

Evaluation of the precision of parameters of the Schaefer production model applied to South Atlantic swordfish (Xiphias gladius)

Standardized catch rates calculated from commercial fishery data have been used for many years to inform production models, which are usually the basis of stock assessments whenever data are limited. Statistical theory implies that precision should increase as we gather more informative data about the process. It is therefore expected that the precision of population parameter estimates should increase as catch rate series increase in length. Does this actually occur? We explore whether new catch rate data, added each year improve the ability to assess stocks using a Bayesian state-space version of the production model. One can assess how much we have “learned” about the parameters of interest by comparing estimates calculated from shorter time series with those from longer time series. That line of reasoning is applied to datasets for swordfish of South Atlantic. Most of the results suggest that standardized catch rates added during the last two or three decades did not result in a significant gain of knowledge regarding model parameters.

Quantum metrology with a non-Markovian qubit system**Projects supported by the Natural Science Foundation of Guangdong Province, China (Grant No. 2015A030310354), the Science Foundation for Enhancing School with Innovation of Guangdong Ocean University (Grant Nos. GDOU2017052504 and GDOU2015050207), the Foundation of Excellent-Young-Backbone Teacher of Guangdong Ocean University (Grant No. HDYQ2017005), and the Fund of University Student Innovation and Entrepreneurship Team of

The dynamics of the quantum Fisher information (QFI) of phase parameter estimation in a non-Markovian dissipative qubit system is investigated within the structure of single and double Lorentzian spectra. We use the time-convolutionless method with fourth-order perturbation expansion to obtain the general forms of QFI for the qubit system in terms of a non-Markovian master equation. We find that the phase parameter estimation can be enhanced in our model within both single and double Lorentzian spectra. What is more, the detuning and spectral width are two significant factors affecting the enhancement of parameter-estimation precision.

Bayesian information fusion for degradation analysis of deteriorating products with individual heterogeneity

Degradation analysis is a popular and effective method for reliability analysis of long-life and high-reliability products. However, for newly developed products, especially for highly customized products with small sample size, the challenge of sparse degradation observations with product heterogeneity is still an open issue deserving further research. In this article, Bayesian degradation analysis is presented for reliability analysis of products with heterogeneity. The degradation process is modeled by a Gamma process. Random effects are incorporated in the Gamma process model for characterizing the individual heterogeneity. To improve the precision of parameter estimation and degradation analysis, a Bayesian information fusion is presented to leverage degradation information from multiple sources. The proposed model is demonstrated through degradation-based reliability analysis of heavy-duty machine tool’s spindle system, which is characterized as degradation analysis with individual heterogeneity and information fusion.

Towards a 'resolution limit' for DW-MRI tumor microstructural models: A simulation study investigating the feasibility of distinguishing between microstructural changes.

Purpose To determine the feasibility of extracting sufficiently precise estimates of cell radius, R, and intracellular volume fraction, f i, from DW‐MRI data in order to distinguish between specific microstructural changes tissue may undergo, specifically focusing on cell death in tumors. Methods Simulations with optimized and non‐optimized clinical acquisitions were performed for a range of microstructures, using a two‐compartment model. The ability to distinguish between (i) cell shrinkage with cell density constant, mimicking apoptosis, and (ii) cell size constant with cell density decreasing, mimicking loss of cells, was evaluated based on the precision of simulated parameter estimates. Relationships between parameter precision, SNR, and the magnitude of specific parameter changes, were used to infer SNR requirements for detecting changes. Results Accuracy and precision depended on microstructural properties, SNR, and the acquisition protocol. The main benefit of optimized acquisitions tended to be improved accuracy and precision of R, particularly for small cells. In most cases considered, higher SNR was required for detecting changes in R than for changes in f i. Conclusions Given the relative changes in R and f i due to apoptosis, simulations indicate that, for a range of microstructures, detecting changes in R require higher SNR than detecting changes in f i, and that such SNR is typically not achieved in clinical data. This suggests that if apoptotic cell size decreases are to be detected in clinical settings, improved SNR is required. Comparing measurement precision with the magnitude of expected biological changes should form part of the validation process for potential biomarkers.

Enhancing the Precision of Phase Estimation by Weak Measurement and Quantum Measurement Reversal in High Dimensional Quantum System

We investigate the effect of the weak measurement (WM) and quantum measurement reversal (QMR) on the improvement of the parameter-estimation precision for a qurit interacting with a zero-temperature reservoir with both spontaneous emission and dephasing. We derive the exact expressions of the optimal quantum Fisher information (QFI), show explicitly that the WM and QMR operation indeed helps for enhancing the precision of parameter estimation from spontaneous emission damping, but not for dephasing damping. In particular, we found that the enhancement effect is work in high dimensional quantum system, which extends the applicable scope of the WM and QMR approach.

Effect of Hidden Relatedness on Single-Step Genetic Evaluation in an Advanced Open-Pollinated Breeding Program.

Open-pollinated (OP) mating is frequently used in forest tree breeding due to the relative temporal and financial efficiency of the approach. The trade-off is the lower precision of the estimated genetic parameters. Pedigree/sib-ship reconstruction has been proven as a tool to correct and complete pedigree information and to improve the precision of genetic parameter estimates. Our study analyzed an advanced generation Eucalyptus population from an OP breeding program using single-step genetic evaluation. The relationship matrix inferred from sib-ship reconstruction was used to rescale the marker-based relationship matrix (G matrix). This was compared with a second scenario that used rescaling based on the documented pedigree. The proposed single-step model performed better with respect to both model fit and the theoretical accuracy of breeding values. We found that the prediction accuracy was superior when using the pedigree information only when compared with using a combination of the pedigree and genomic information. This pattern appeared to be mainly a result of accumulated unrecognized relatedness over several breeding cycles, resulting in breeding values being shrunk toward the population mean. Using biased, pedigree-based breeding values as the base with which to correlate predicted GEBVs, resulted in the underestimation of prediction accuracies. Using breeding values estimated on the basis of sib-ship reconstruction resulted in increased prediction accuracies of the genotyped individuals. Therefore, selection of the correct base for estimation of prediction accuracy is critical. The beneficial impact of sib-ship reconstruction using G matrix rescaling was profound, especially in traits with inbreeding depression, such as stem diameter.

Use of ambiguous detections to improve estimates from species distribution models.

As large carnivores recover throughout Europe, their distribution needs to be studied to determine their conservation status and assess the potential for human-carnivore conflicts. However, efficient monitoring of many large carnivore species is challenging due to their rarity, elusive behavior, and large home ranges. Their monitoring can include opportunistic sightings from citizens in addition to designed surveys. Two types of detection errors may occur in such monitoring schemes: false negatives and false positives. False-negative detections can be accounted for in species distribution models (SDMs) that deal with imperfect detection. False-positive detections, due to species misidentification, have rarely been accounted for in SDMs. Generally, researchers use ad hoc data-filtering methods to discard ambiguous observations prior to analysis. These practices may discard valuable ecological information on the distribution of a species. We investigated the costs and benefits of including data types that may include false positives rather than discarding them for SDMs of large carnivores. We used a dynamic occupancy model that simultaneously accounts for false negatives and positives to jointly analyze data that included both unambiguous detections and ambiguous detections. We used simulations to compare the performances of our model with a model fitted on unambiguous data only. We tested the 2 models in 4 scenarios in which parameters that control false-positive detections and true detections varied. We applied our model to data from the monitoring of the Eurasian lynx (Lynx lynx) in the European Alps. The addition of ambiguous detections increased the precision of parameter estimates. For the Eurasian lynx, incorporating ambiguous detections produced more precise estimates of the ecological parameters and revealed additional occupied sites in areas where the species is likely expanding. Overall, we found that ambiguous data should be considered when studying the distribution of large carnivores through the use of dynamic occupancy models that account for misidentification.

Modeling semicontinuous longitudinal data with order constraints.

Semicontinuous longitudinal data are characterized by within-subjects repeated measurements that either indicate absence of abnormality or reflect different amount of abnormality. Joint models for semicontinuous longitudinal data have been increasingly receiving attention in the literature. Such models permit flexible characterization of covariates-outcome associations. Order-restricted statistical inference has been well established in the literature but has not yet been applied to joint models for semicontinuous longitudinal data. We incorporate general order-restricted inference into the general joint models for semicontinuous longitudinal data previously proposed. We develop computational methods to address general order restrictions. Through simulations and a real-data example, we demonstrate the advantages of order-restricted inference in terms of increased power in hypothesis testing and increased precision in parameter estimation.

Estimating the flight parameters of a moving airborne source using one hydrophone

The low frequency tone noise of the turboprop aircrafts can be discovered more easily under water than the broadband continuum spectrum noise due to its higher intensity. Ferguson and Lo provided a method based on a single hydrophone for estimating the four flight parameters, including the source frequency, velocity, altitude and CPA time (the time when the source passes the closet point of approach), using the variation of the instantaneous frequency (IF) of a single tone over time [Ferguson and Lo, IEEE J. Oceanic Eng., 24(4):424–435 (1999)]. Therefore, the performance of their method is largely determined by the precision of the IF estimates, which were obtained by using the short-time Fourier transform (STFT). In this paper, the polynomial chirplet transform (PCT), which models the change of the IF over time as a polynomial, is used instead of STFT to provide more accurate IF estimates. Moreover, multiple tones are used to improve the precision of the flight parameter estimates. The performance improvement is demonstrated by simulations and an experiment carried out near the Sanya coast in May, 2018.

Maximal quantum Fisher information in the semi-classical Rabi model

To improve the precision of parameter estimation in semi-classical Rabi model, we study the maximal quantum Fisher information (MQFI) of the parameters in the system by the counter-rotating hybridized rotating-wave approximation (CHRWA). The validity of this approximation is discussed by the operator fidelity method, and the applicable effective parameter zone is found out. To get the MQFI of the system, we generalize the analytical expression of the MQFI for all unitary parametrization processes in two-level system. Then we apply our results to get the MQFI of the semi-classical Rabi model, and give the condition to reach the limit of parameter estimation’s precision. Finally, we discuss the relationship between the MQFI and the Bloch–Siegert (BS) shift in this model.

A general-threshold filtering method for improving intravoxel incoherent motion parameter estimates

In this study, we present an image denoising method for diffusion-weighted magnetic resonance imaging (DW-MRI) data. Our aim is to improve the estimation of intravoxel incoherent motion (IVIM) parameters using denoised DW-MRI data. A general-threshold filtering (GTF) reconstruction via total variation minimization has been proposed to improve image quality in few-view computed tomography. Here, we applied the combination of GTF and total difference to image denoising. Voxel-wise IVIM analysis was performed using both real and simulated DW-MRI data. Using an institutional review board-approved protocol with written informed consent, DW-MRI imaging was performed at a 3 T hybrid PET/MR system in 10 patients with Hodgkin lymphoma lesions. A simulated phantom consisting of four organs (liver, pancreas, spleen and kidney) was used to generate noisy DW-MRI data according to the IVIM model at different noise levels. DW-MRI data were denoised before IVIM parameter estimation. The proposed image denoising method was compared with the image denoising method using joint rank and edge constraints (JREC). The results of simulated data show that at the lower signal-to-noise ratios the proposed image denoising method outperformed the JREC method in terms of the accuracy and precision of the IVIM parameter estimates. The experimental results also show that the proposed image denoising method could yield better parametric images than the JREC method in terms of noise reduction and edge preservation.

Enhancement of parameter-estimation precision by weak measurement and quantum measurement reversal under various non-Markovian decoherence sources

We investigate the effect of the weak measurement (WM) and quantum measurement reversal (QMR) on the improvement of the precision of parameter estimation for a qubit interacting with various non-Markovian decoherence sources: amplitude damping, dephasing damping and random unitary damping, respectively. We derive the exact expressions of the optimal quantum Fisher information, show explicitly that the WM and QMR operation indeed helps for enhancing the precision of parameter estimation from amplitude damping and phase damping, but not for random unitary damping. In particular, we found that the enhancement effect is independent of the specific form of the spectral density of the reservoir, which extends the applicable scope of the WM and QMR approach.

Robustness of the covariance matrix for galaxy clustering measurements

We present a study on the robustness of the covariance matrix estimation for galaxy clustering measurements depending on the cosmological parameters and galaxy bias. To this end, we have produced 9000 galaxy mock catalogues relying on the effective Zel'dovich approximation implemented in the EZmocks computer code, using different input cosmological models and bias parameters. The reference catalogue has also been produced with this code making our study insensitive to the approximation at least on a relative-qualitative level. Our findings indicate that the covariance matrix is insensitive to the input power spectrum (including $\sigma_8$), as long as the 2- and 3-point galaxy clustering measurements agree with the given data. In fact, the covariance matrix shows a bias at small scales ($r\lesssim40 h^{-1}$Mpc) when the chosen galaxy bias parameters yield a 3-point statistics, which is not compatible with the reference one within the error bars, even though the 2-point statistics agree within 1%. Nevertheless, the error becomes negligible at large scales making the covariance matrix still reliable for data analysis using only measurements in that regime (e.g., measuring baryon acoustic oscillations). High precision in cosmological parameter estimation is expected for covariance matrices extracted from mock galaxy catalogues which take accurately into account both the 2- and the 3- point statistics. This is independent of whether this is achieved by using the right cosmology and galaxy bias (which are not a priori known) or just any combination of both fitting the net observed galaxy clustering.

Removal models accounting for temporary emigration.

SummaryRemoval of protected species from sites scheduled for development is often a legal requirement in order to minimize the loss of biodiversity. The assumption of closure in the classic removal model will be violated if individuals become temporarily undetectable, a phenomenon commonly exhibited by reptiles and amphibians. Temporary emigration can be modeled using a multievent framework with a partial hidden process, where the underlying state process describes the movement pattern of animals between the survey area and an area outside of the study. We present a multievent removal model within a robust design framework which allows for individuals becoming temporarily unavailable for detection. We demonstrate how to investigate parameter redundancy in the model. Results suggest the use of the robust design and certain forms of constraints overcome issues of parameter redundancy. We show which combinations of parameters are estimable when the robust design reduces to a single secondary capture occasion within each primary sampling period. Additionally, we explore the benefit of the robust design on the precision of parameters using simulation. We demonstrate that the use of the robust design is highly recommended when sampling removal data. We apply our model to removal data of common lizards, Zootoca vivipara, and for this application precision of parameter estimates is further improved using an integrated model.

Evaluation of the accuracy and precision of the diffusion parameter EStImation with Gibbs and NoisE removal pipeline

This work evaluates the accuracy and precision of the Diffusion parameter EStImation with Gibbs and NoisE Removal (DESIGNER) pipeline, developed to identify and minimize common sources of methodological variability including: thermal noise, Gibbs ringing artifacts, Rician bias, EPI and eddy current induced spatial distortions, and motion-related artifacts. Following this processing pipeline, iterative parameter estimation techniques were used to derive diffusion parameters of interest based on the diffusion tensor and kurtosis tensor. We evaluated accuracy using a software phantom based on 36 diffusion datasets from the Human Connectome project and tested the precision by analyzing data from 30 healthy volunteers scanned three times within one week. Preprocessing with both DESIGNER or a standard pipeline based on smoothing (instead of noise removal) improved parameter precision by up to a factor of 2 compared to preprocessing with motion correction alone. When evaluating accuracy, we report average decreases in bias (deviation from simulated parameters) over all included regions for fractional anisotropy, mean diffusivity, mean kurtosis, and axonal water fraction of 9.7%, 8.7%, 4.2%, and 7.6% using DESIGNER compared to the standard pipeline, demonstrating that preprocessing with DESIGNER improves accuracy compared to other processing methods.

Gaia Data Release 2

Context. The Gaia Data Release 2 (DR2) contains the first release of radial velocities complementing the kinematic data of a sample of about 7 million relatively bright, late-type stars. Aims. This paper provides a detailed description of the Gaia spectroscopic data processing pipeline, and of the approach adopted to derive the radial velocities presented in DR2. Methods. The pipeline must perform four main tasks: (i) clean and reduce the spectra observed with the Radial Velocity Spectrometer (RVS); (ii) calibrate the RVS instrument, including wavelength, straylight, line-spread function, bias non-uniformity, and photometric zeropoint; (iii) extract the radial velocities; and (iv) verify the accuracy and precision of the results. The radial velocity of a star is obtained through a fit of the RVS spectrum relative to an appropriate synthetic template spectrum. An additional task of the spectroscopic pipeline was to provide first-order estimates of the stellar atmospheric parameters required to select such template spectra. We describe the pipeline features and present the detailed calibration algorithms and software solutions we used to produce the radial velocities published in DR2. Results. The spectroscopic processing pipeline produced median radial velocities for Gaia stars with narrow-band near-IR magnitude GRVS ≤ 12 (i.e. brighter than V ~ 13). Stars identified as double-lined spectroscopic binaries were removed from the pipeline, while variable stars, single-lined, and non-detected double-lined spectroscopic binaries were treated as single stars. The scatter in radial velocity among different observations of a same star, also published in Gaia DR2, provides information about radial velocity variability. For the hottest (Teff ≥ 7000 K) and coolest (Teff ≤ 3500 K) stars, the accuracy and precision of the stellar parameter estimates are not sufficient to allow selection of appropriate templates. The radial velocities obtained for these stars were removed from DR2. The pipeline also provides a first-order estimate of the performance obtained. The overall accuracy of radial velocity measurements is around ~200–300 m s−1, and the overall precision is ~1 km s−1; it reaches ~200 m s−1 for the brightest stars.