Low Variance Estimates Research Articles

Optimized Parameter Estimation and Integrating Neural Network Forecasting of Dynamic Plant-Livestock Model for Early Warning in Agro-Environment Control Systems

The research utilizes the Lotka-Volterra prey-predator model to study Plant-Herbivore dynamics, focusing on the relationship between traditional livestock farming and vegetation conditions. Advanced methods are developed to improve the precision and efficiency of parameter estimation in these models. Neural networks are incorporated to enhance forecasting abilities, and an extension of the Plant-Herbivore models includes Botswana's climate and livestock variables. Efficient parameter space exploration is achieved using the Runge-Kutta method along with Multistart and the local solver $fmincon$ in MATLAB. This method improves parameter estimation accuracy. To address the impact of homogeneity assumptions in the data, estimate aggregation through weighting and time conversion is applied. Furthermore, the study investigates the use of nonlinear least squares to further refine the process, allowing for the identification of parameters that best fit observed livestock data, even with non-linearity. By using optimized parameter estimation techniques along with normalized nonlinear least squares, the cumulative error was reduced from an initial 1563.4521 to a final value of 0.0038, well within the specified thresholds (1.0, 0.1, and 0.01). Comparisons between Autoregressive Integrated Moving Average (ARIMA) and Neural Network Auto-Regressive (NNAR) models showed that NNAR models outperformed ARIMA models, with lower variance estimates (0.000004 - 0.000562) compared to ARIMA (0.103 - 0.155). NNAR models displayed Mean Error (ME) values ranging from -0.0012 to 0.0140, indicating a close match between forecasts and actual values with minor deviations. As a result, NNAR forecasting was used for predicting soil moisture, death, and harvest rates, which were integrated into the extended Plant-Herbivore model. This integration enabled the estimation of livestock production trajectories for 2021-2022, along with corresponding interpretations. The study also assessed the uncertainty propagation from NNAR forecasts onto the Plant-Herbivore dynamic model, revealing an increase in uncertainty with longer lead times.

Bias-free estimation of the covariance function and the power spectral density from data with missing samples including extended data gaps

Nonparametric estimation of the covariance function and the power spectral density of uniformly spaced data from stationary stochastic processes with missing samples is investigated. Several common methods are tested for their systematic and random errors under the condition of variations in the distribution of the missing samples. In addition to random and independent outliers, the influence of longer and hence correlated data gaps on the performance of the various estimators is also investigated. The aim is to construct a bias-free estimation routine for the covariance function and the power spectral density from stationary stochastic processes under the condition of missing samples with an optimum use of the available information in terms of low estimation variance and mean square error, and that independent of the spectral composition of the data gaps. The proposed procedure is a combination of three methods that allow bias-free estimation of the desired statistical functions with efficient use of the available information: weighted averaging over valid samples, derivation of the covariance estimate for the entire data set and restriction of the domain of the covariance function in a post-processing step, and appropriate correction of the covariance estimate after removal of the estimated mean value. The procedures abstain from interpolation of missing samples as well as block subdivision. Spectral estimates are obtained from covariance functions and vice versa using Wiener–Khinchin’s theorem.

Investigating the impact of non-additive genetic effects in the estimation of variance components and genomic predictions for heat tolerance and performance traits in crossbred and purebred pig populations

BackgroundNon-additive genetic effects are often ignored in livestock genetic evaluations. However, fitting them in the models could improve the accuracy of genomic breeding values. Furthermore, non-additive genetic effects contribute to heterosis, which could be optimized through mating designs. Traits related to fitness and adaptation, such as heat tolerance, tend to be more influenced by non-additive genetic effects. In this context, the primary objectives of this study were to estimate variance components and assess the predictive performance of genomic prediction of breeding values based on alternative models and two independent datasets, including performance records from a purebred pig population and heat tolerance indicators recorded in crossbred lactating sows.ResultsIncluding non-additive genetic effects when modelling performance traits in purebred pigs had no effect on the residual variance estimates for most of the traits, but lower additive genetic variances were observed, especially when additive-by-additive epistasis was included in the models. Furthermore, including non-additive genetic effects did not improve the prediction accuracy of genomic breeding values, but there was animal re-ranking across the models. For the heat tolerance indicators recorded in a crossbred population, most traits had small non-additive genetic variance with large standard error estimates. Nevertheless, panting score and hair density presented substantial additive-by-additive epistatic variance. Panting score had an epistatic variance estimate of 0.1379, which accounted for 82.22% of the total genetic variance. For hair density, the epistatic variance estimates ranged from 0.1745 to 0.1845, which represent 64.95–69.59% of the total genetic variance.ConclusionsIncluding non-additive genetic effects in the models did not improve the accuracy of genomic breeding values for performance traits in purebred pigs, but there was substantial re-ranking of selection candidates depending on the model fitted. Except for panting score and hair density, low non-additive genetic variance estimates were observed for heat tolerance indicators in crossbred pigs.

Ambient Data-Driven Online Tracking of Electromechanical Modes Using Recursive Subspace Dynamic Mode Decomposition

The extraction of electromechanical modal parameters from ambient data is a useful and practical method that can monitor the modal properties of power system oscillations online. This paper proposes a recursive subspace dynamic mode decomposition (RSub-DMD) algorithm for online monitoring power system modes using wide-area synchronized ambient data. By introducing Givens rotation to the recursion process, the computational capability of subspace dynamic mode decomposition has been significantly improved without compromising accuracy. The shorter sliding data window enables the proposed RSub-DMD to quickly track the electromechanical modal parameters and participation factors (PFs), with low estimation variance. IEEE 16 generator 68 bus test system and measurement data from real system are used to verify the performance of the proposed RSub-DMD algorithm. The tracking results in different operating environments verify the effectiveness of the proposed algorithm.

Robust real-time optimization and parameter estimation of post-combustion CO2 capture under economic uncertainty

The operational cost of post-combustion carbon capture remains the principal factor impeding its uptake, thus real-time optimization has been proposed for economic operation. This requires that uncertainties be estimated, subjecting its solutions to estimation error. Herein, we propose uncertainty estimation and real-time optimization for post-combustion carbon capture plants. Model parameters are estimated using noisy measurements to address model uncertainty; accordingly, we deploy a low-variance scheme to address noise propagation. Our approach is implemented in a pilot-scale carbon capture plant through uncertain flue gas compositions and thermodynamic activities. The proposed method results in operating points closer to the true optima, with up to 25% improvement in economics compared to alternative operational approaches. Moreover, a robust real-time optimization strategy is proposed for cases in which model parameters and economic factors are simultaneously uncertain. The robust update strategy is deployed jointly with the low-variance estimation scheme to quantify the uncertainty in each model parameter, resulting in economic improvements and a notable reduction (80%) in the set point variability over the standard update approach. Through the schemes proposed, the carbon capture plant was able to operate at set points with high capture rates, low energy consumption, and low cost. This suggests that the proposed approach is suitable for the economic optimization of other energy and carbon capture systems.

Entropy Regularization for Population Estimation

Entropy regularization is known to improve exploration in sequential decision-making problems. We show that this same mechanism can also lead to nearly unbiased and lower-variance estimates of the mean reward in the optimize-and-estimate structured bandit setting. Mean reward estimation (i.e., population estimation) tasks have recently been shown to be essential for public policy settings where legal constraints often require precise estimates of population metrics. We show that leveraging entropy and KL divergence can yield a better trade-off between reward and estimator variance than existing baselines, all while remaining nearly unbiased. These properties of entropy regularization illustrate an exciting potential for bringing together the optimal exploration and estimation literature.

Backward Importance Sampling for Online Estimation of State Space Models

This article proposes a new Sequential Monte Carlo algorithm to perform online estimation in the context of state space models when either the transition density of the latent state or the conditional likelihood of an observation given a state is intractable. In this setting, obtaining low variance estimators of expectations under the posterior distributions of the unobserved states given the observations is a challenging task. Following recent theoretical results for pseudo-marginal sequential Monte Carlo smoothers, a pseudo-marginal backward importance sampling step is introduced to estimate such expectations. This new step allows to reduce very significantly the computational time of the existing numerical solutions based on an acceptance–rejection procedure for similar performance, and to broaden the class of eligible models for such methods. For instance, in the context of multivariate stochastic differential equations, the proposed algorithm makes use of unbiased estimates of the unknown transition densities under much weaker assumptions than most standard alternatives. The performance of this estimator is assessed for high-dimensional discrete-time latent data models, for recursive maximum likelihood estimation in the context of Partially Observed Diffusion process (POD), and in the case of a bidimensional partially observed stochastic Lotka-Volterra model. Supplementary materials for this article are available online.

Spectral proper orthogonal decomposition using multitaper estimates

The use of multitaper estimates for spectral proper orthogonal decomposition (SPOD) is explored. Multitaper and multitaper-Welch estimators that use discrete prolate spheroidal sequences (DPSS) as orthogonal data windows are compared to the standard SPOD algorithm that exclusively relies on weighted overlapped segment averaging, or Welch’s method, to estimate the cross-spectral density matrix. Two sets of turbulent flow data, one experimental and the other numerical, are used to discuss the choice of resolution bandwidth and the bias-variance tradeoff. Multitaper-Welch estimators that combine both approaches by applying orthogonal tapers to overlapping segments allow for flexible control of resolution, variance, and bias. At additional computational cost but for the same data, multitaper-Welch estimators provide lower variance estimates at fixed frequency resolution or higher frequency resolution at similar variance compared to the standard algorithm.

Spectral estimator effects on accuracy of speed-over-ground radar

<p>Spectral estimation is a critical signal processing step in speed-over-ground (SoG) radar. It is argued that, for accurate speed estimation, spectral estimation should use low bias and variance estimator. However, there is no evaluation on spectral estimation techniques in terms of estimating mean Doppler frequency to date. In this paper, we evaluate two common spectral estimation techniques, namely periodogram based on Fourier transformation and the autoregressive (AR) based on burg algorithm. These spectral estimators are evaluated in terms of their bias and variance in estimating a mean frequency. For this purpose, the spectral estimators are evaluated with different Doppler signals that varied in mean frequency and signal-to-noise ratio (SNR). Results in this study indicates that the periodogram method performs well in most of the tests while the AR method did not perform as well as these but offered a slight improvement over the periodogram in terms of variance.</p>

Ship Collision Avoidance Utilizing the Cross-Entropy Method for Collision Risk Assessment

In this article, a new approach for ship-ship collision probability estimation based on the Cross-Entropy (CE) method is introduced, which can be treated as an adaptive importance sampler. It has the advantage of attaining low variance estimates of small collision probabilities, which will most often be the case in realistic scenarios. Furthermore, a risk-based Collision Avoidance (COLAV) system being able to take obstacle kinematic uncertainty and intention uncertainty into account is presented, namely the Probabilistic Scenario-Based Model Predictive Control (PSB-MPC). The collision probability estimator (CPE) is used in the risk assessment of the PSB-MPC, and tested in a simulation study, where the total system is validated. Simulation results show that the MPC is able to utilize the CPE for better risk assessment than the original version, in order to make safer decisions in close quarter situations and cases where nearby obstacles make unexpected maneuvers. It is also shown that when all vessels involved use the PSB-MPC, situations are resolved according to the traffic rules in a safe manner.

Quantum Rényi entropy by optimal thermodynamic integration paths

Despite being a well-established operational approach to quantify entanglement, Rényi entropy calculations have been plagued by their computational complexity. We introduce here a theoretical framework based on an optimal thermodynamic integration scheme, where the Rényi entropy can be efficiently evaluated using regularizing paths. This approach avoids slowly convergent fluctuating contributions and leads to low-variance estimates. In this way, large system sizes and high levels of entanglement in model or first-principles Hamiltonians are within our reach. We demonstrate this approach in the one-dimensional quantum Ising model and perform an evaluation of entanglement entropy in the formic acid dimer, by discovering that its two shared protons are entangled even above room temperature.Received 29 December 2021Accepted 9 June 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L032002Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasChemical Physics & Physical ChemistryEntanglement entropyPath integralsQuantum phase transitionsTechniquesMonte Carlo methodsCondensed Matter, Materials & Applied PhysicsQuantum InformationStatistical Physics

On bias, variance, overfitting, gold standard and consensus in single-particle analysis by cryo-electron microscopy.

Cryo-electron microscopy (cryoEM) has become a well established technique to elucidate the 3D structures of biological macromolecules. Projection images from thousands of macromolecules that are assumed to be structurally identical are combined into a single 3D map representing the Coulomb potential of the macromolecule under study. This article discusses possible caveats along the image-processing path and how to avoid them to obtain a reliable 3D structure. Some of these problems are very well known in the community. These may be referred to as sample-related (such as specimen denaturation at interfaces or non-uniform projection geometry leading to underrepresented projection directions). The rest are related to the algorithms used. While some have been discussed in depth in the literature, such as the use of an incorrect initial volume, others have received much less attention. However, they are fundamental in any data-analysis approach. Chiefly among them, instabilities in estimating many of the key parameters that are required for a correct 3D reconstruction that occur all along the processing workflow are referred to, which may significantly affect the reliability of the whole process. In the field, the term overfitting has been coined to refer to some particular kinds of artifacts. It is argued that overfitting is a statistical bias in key parameter-estimation steps in the 3D reconstruction process, including intrinsic algorithmic bias. It is also shown that common tools (Fourier shell correlation) and strategies (gold standard) that are normally used to detect or prevent overfitting do not fully protect against it. Alternatively, it is proposed that detecting the bias that leads to overfitting is much easier when addressed at the level of parameter estimation, rather than detecting it once the particle images have been combined into a 3D map. Comparing the results from multiple algorithms (or at least, independent executions of the same algorithm) can detect parameter bias. These multiple executions could then be averaged to give a lower variance estimate of the underlying parameters.

Wind parameters measurement method based on co-prime array signal processing

In this paper, a co-prime arc array structure with ultrasonic sensors is proposed, and the PM (propagator method) is applied in the field of wind parameters measurement. Two sub-arrays with co-prime properties are stacked to form a co-prime arc array. The array aperture is enlarged which avoids angle blur, improves the measurement accuracy of wind parameters. The propagator method is introduced to keep away from eigenvalue decomposition and estimate wind parameters directly. The estimation variance and CRB (Cramer Rao Bound) of wind parameters are obtained through theoretical analysis and simulation calculation. Simulation results show that the wind parameters measurement method based on co-prime array has lower estimation variance and higher measurement accuracy. A wind parameters measurement system with co-prime arc array was built, and the wind tunnel experiments validated the feasibility of the proposed method.

Using a Chen-Stein identity to obtain low variance simulation estimators

AbstractThis paper is concerned with developing low variance simulation estimators of probabilities related to the sum of Bernoulli random variables. It shows how to utilize an identity used in the Chen-Stein approach to bounding Poisson approximations to obtain low variance estimators. Applications and numerical examples in such areas as pattern occurrences, generalized coupon collecting, system reliability, and multivariate normals are presented. We also consider the problem of estimating the probability that a positive linear combination of Bernoulli random variables is greater than some specified value, and present a simulation estimator that is always less than the Markov inequality bound on that probability.

PSXIV-19 Heritability for growth and resistance to gastrointestinal parasitism in meat goats and hair sheep

Abstract Genetic selection for resistance to internal parasitism is of great research interest. Heritabilities were determined for average daily gain (ADG), logarithmic transformed fecal egg count (FEC), packed cell volume (PCV), and serum immunoglobin (Ig) levels of growing male meat goats and hair sheep from different farms in the southcentral USA during three consecutive central performance tests (CPT). Tests entailed 7–10 wk of data collection after artificial infection with Haemonchus contortus. In year 1, animals evaluated were selected randomly and in years 2 and 3 progeny of CPT sires classified as highly or moderately resistant, which included 46, 50, and 51 Boer, Kiko, and Spanish and 59, 61, 34, and 46 Dorper, Katahdin-farm A, Katahdin-farm B, and St. Croix, respectively. Females were classified accordingly on-farm based on FEC and FAMACHA. Pedigree records consisted of 32 and 57 known sires, 95 and 152 known dams including 4 and 10 full-sibs and 97 and 149 half-sibs for goats and sheep, respectively. Variance components and heritabilities were estimated by AIREML using WOMBAT with a multivariate animal model. Heritability estimates were 0.48 ± 0.214 and 0.85 ± 0.157 of ADG, 0.31 ± 0.237 and 0.20 ± 0.172 of FEC, 0.60 ± 0.206 and 0.24 ± 0.185 of PCV, 0.26 ± 0.172 and 0.51 ± 0.167 of IgA, 0.335 and 0.543 of IgM, and 0.14 ± 0.192 and 0.31 ± 0.190 of IgG for goats and sheep, respectively. Reasons for relatively high heritabilities for all traits include the low residual variance estimates due primarily to a standardized environment in the performance test. In conclusion, moderate to high heritabilities were found for growth performance and response to parasite infection for growing meat goat and hair sheep males under a standardized environment that suggests considerable for genetic improvement through selection.

Tiered Sampling

We introduce Tiered Sampling , a novel technique for estimating the count of sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size M , which can be magnitudes smaller than the number of edges. Our methods address the challenging task of counting sparse motifs—sub-graph patterns—that have a low probability of appearing in a sample of M edges in the graph, which is the maximum amount of data available to the algorithms in each step. To obtain an unbiased and low variance estimate of the count, we partition the available memory into tiers (layers) of reservoir samples. While the base layer is a standard reservoir sample of edges, other layers are reservoir samples of sub-structures of the desired motif. By storing more frequent sub-structures of the motif, we increase the probability of detecting an occurrence of the sparse motif we are counting, thus decreasing the variance and error of the estimate. While we focus on the designing and analysis of algorithms for counting 4-cliques, we present a method which allows generalizing Tiered Sampling to obtain high-quality estimates for the number of occurrence of any sub-graph of interest, while reducing the analysis effort due to specific properties of the pattern of interest. We present a complete analytical analysis and extensive experimental evaluation of our proposed method using both synthetic and real-world data. Our results demonstrate the advantage of our method in obtaining high-quality approximations for the number of 4 and 5-cliques for large graphs using a very limited amount of memory, significantly outperforming the single edge sample approach for counting sparse motifs in large scale graphs.

Efficient Likelihood-based Estimation via Annealing for Dynamic Structural Macrofinance Models

Most solved dynamic structural macrofinance models are non-linear and/or non-Gaussian state-space models with high-dimensional and complex structures. We propose an annealed controlled sequential Monte Carlo method that delivers numerically stable and low variance estimators of the likelihood function. The method relies on an annealing procedure to gradually introduce information from observations and constructs globally optimal proposal distributions by solving associated optimal control problems that yield zero variance likelihood estimators. To perform parameter inference, we develop a new adaptive SMC$^2$ algorithm that employs likelihood estimators from annealed controlled sequential Monte Carlo. We provide a theoretical stability analysis that elucidates the advantages of our methodology and asymptotic results concerning the consistency and convergence rates of our SMC$^2$ estimators. We illustrate the strengths of our proposed methodology by estimating two popular macrofinance models: a non-linear new Keynesian dynamic stochastic general equilibrium model and a non-linear non-Gaussian consumption-based long-run risk model.

Sparse, Predictive, and Interpretable Functional Connectomics with UoILasso.

Network formation from neural activity is a foundational problem in systems neuroscience. Functional networks, after downstream analysis, can provide key insights into the nature of neurobiological structure and computation. The validity of such insights hinges on accurate selection and estimation of the edges connecting nodes. However, commonly used statistical inference procedures generally fail to identify the correct features, and further introduce consequential bias in the estimates. To address these issues, we developed Union of Intersections (UoI), a flexible, modular, and scalable framework for enhanced statistical feature selection and estimation. Methods based on UoI perform feature selection and feature estimation through intersection and union operations, respectively. In the context of linear regression (specifically UoILasso), we summarize extensive numerical investigation on synthetic data to demonstrate tight control of false-positives and false-negatives in feature selection with low-bias and low-variance estimates of selected parameters, while maintaining high-quality prediction accuracy. We demonstrate, with UoILasso, the extraction of sparse, predictive, and interpretable functional networks from human electrocorticography recordings during speech production and the inference of parsimonious coupling models from nonhuman primate single-unit recordings during reaching tasks. Our results establish that UoILasso generates interpretable and predictive functional connectivity networks.

Gaussian process regression for the estimation of generalized frequency response functions

Bayesian learning techniques have recently garnered significant attention in the system identification community. Originally introduced for low variance estimation of linear impulse response models, the concept has since been extended to the nonlinear setting for Volterra series estimation in the time domain. In this paper, we approach the estimation of nonlinear systems from a frequency domain perspective, where the Volterra series has a representation comprised of Generalized Frequency Response Functions (GFRFs). Inspired by techniques developed for the linear frequency domain case, the GFRFs are modelled as real/complex Gaussian processes with prior covariances related to the time domain characteristics of the corresponding Volterra series. A Gaussian process regression method is developed for the case of periodic excitations, and numerical examples demonstrate the efficacy of the proposed method, as well as its advantage over time domain methods in the case of band-limited excitations.

An improved instrumental variable method for industrial robot model identification

Industrial robots are electro-mechanical systems with double integrator behaviour, necessitating operation and model identification under closed-loop control conditions. The Inverse Dynamic Identification Model (IDIM) is a mechanical model based on Newton’s laws that has the advantage of being linear with respect to the parameters. Existing Instrumental Variable (IDIM-IV) estimation provides a robust solution to this estimation problem and the paper introduces an improved IDIM-PIV method that takes account of the additive noise characteristics by adding prefilters that provide lower variance estimates of the IDIM parameters. Inspired by the prefiltering approach used in optimal Refined Instrumental Variable (RIV) estimation, the IDIM-PIV method identifies the nonlinear physical model of the robot, as well as the noise model resulting from the feedback control system. It also has the advantage of providing a systematic prefiltering process, in contrast to that required for the previous IDIM-IV method. The issue of an unknown controller is also considered and resolved using existing parametric identification. The evaluation of the new estimation algorithms on a six degrees-of-freedom rigid robot shows that they improve statistical efficiency, with the controller either known or identified as an intrinsic part of the IDIM-PIV algorithm.