True Parameters Research Articles

Scenario based optimisation over uncertain system identification models

Models of dynamical systems are often built from observed data using system identification techniques, and the uncertainty in the model parameters is commonly described using confidence regions to which the true model parameters belong with a certain probability. In this paper we propose methods which use the scenario approach to solve robust optimisation problems for model based design where there is uncertainty in the model parameters. The methods draw samples (scenarios) of the uncertain model parameters and solve an optimisation problem only involving the drawn scenarios. Both a Bayesian system identification setting where the model parameters are stochastic, and a non-Bayesian system identification setting where the model parameters are treated as being deterministic are considered. The Bayesian and non-Bayesian settings require different treatment, and whereas standard scenario optimisation theory can be directly utilised in the Bayesian setting, this is not the case in the non-Bayesian setting. For that reason the model class is restricted to linear regression models with deterministic regressors in the non-Bayesian case. Algorithms are proposed for drawing samples of the parameters such that the uncertainties in the system identification models are reflected in the samples. Theoretical results are given bounding the probability that the found solution to the scenario optimisation problem will give a worse performance when applied to the true system than seen on the drawn scenarios. The methods are illustrated in simulation examples showing good performance.

Evolution of fundamental mechanical properties with aliovalent Co/Cu partial substitution and preparation method for Y-123 system

This study investigates the effect of aliovalent Co/Cu replacement and preparation method on fundamental mechanical performance features of YBa2Cu3−xCoxO7−δ (Y-123) ceramic system depending on the crack propagation mechanism by Vickers hardness measurements (Hv) and mechanical investigation models for the first time. All the findings are verified by the scanning electron microscopy (SEM) examinations. Besides, the electron-dispersive X-ray (EDX) technique verifies the successful substitution mechanism. Besides, the Vickers hardness parameters improve systematically with the increment in the Co/Cu partial substitution (serving as a barrier) level due to formation of operable slip systems, ionic bond formations, and decrement of stress-amplified strain fields. Moreover, the Y-123 ceramic produced by solid-state reaction method and molecular weight of 0.20% presents the densest and smoothest surface morphology with the largest particle distributions and well-linked cobblestone-like grains. On the other hand, the Y-123 ceramic compounds produced by the sol–gel method are more sensitive and responsive to the indentation test loads. All the findings are wholly supported by the mechanical performance properties, including the shear modulus, resilience, and degree of granularity. Furthermore, the mechanical models indicate that every compound prepared exhibits the untypical reverse indentation size effect (RISE). Additionally, the modeling studies display that the induced cracking (IIC) approach is found to be the most appropriate method to examine true Vickers hardness parameters in the plateau limit regions. All in all, this comprehensive study reports efficiently exploiting the process–structure–property relationships in Y-123 ceramic material design for physical science and mechanical application fields using the aliovalent partial substitution and preparation condition.

Supervisory adaptive safety control for uncertain nonlinear systems

This paper investigates the supervisory adaptive safety control problem for uncertain nonlinear systems with unmeasurable states. In order to estimate unknown parameters and unmeasurable states, a supervisory observer framework consisting of a multi-observer bank and a supervisor unit, is proposed based on a dividing rectangles (DIRECT) algorithm. Under a desired accuracy, the parameter estimates converge to near the true parameters within finite-time while the estimation error of the system state converges to a small neighborhood near the origin. Also, an observer robust adaptive control barrier function is constructed to ensure safety for uncertain nonlinear systems by guaranteeing controlled invariance of a time-varying auxiliary set. By adjusting some parameters in the DIRECT algorithm, the time-varying auxiliary set approaches the original safe set, which reduces the conservatism generated by the compression of the safe set. Finally, two examples, including an adaptive cruise control system, are given to demonstrate the effectiveness of the proposed method.

LINEAR REGRESSION WITH DATA MISSING NOT AT RANDOM: BOOTSTRAP APPROACH

OLS regressions have a set of assumption in order to have its point and interval estimates to be unbiased and efficient. Data missing not at random (MNAR) can pose serious estimations issues in the linear regression. In this study we evaluate the performance of OLS confidence interval estimates with MNAR data. We also suggest bootstrapping as a remedy for such data cases and compare the traditional confidence intervals against bootstrap ones. As we need to know the true parameters, we carry out a simulations study. Research results indicate that both approaches show similar results having similar intervals size. Given that bootstrap required a lot of computations, traditional methods is still recommended to be used even in case of MNAR

Compare Some Shrinkage Bayesian Estimation Method forGumbel-Max Distribution with Simulation

The Gumbel max distribution is one of the most important statistical distributions because it has many applications, especially in the field of water research and the prediction of earthquakes and volcanoes. This work includes a comparison of several Shrinkage Bayesian methods, namely the Shrinkage Bayesian Square Loss Function, Shrinkage Bayesian Lenix Function, and Shrinkage Bayesian Unix Function to estimate the distribution parameter. The research also includes several simulated experiments according to the sample size change and the real value of the distribution parameter. The number of experiments is 15 simulated experiments based on the difference sample size and true distribution parameter values. The results of the simulation experiments are compared depending on each of the absolute least difference criteria ( and the mean squared error (). The comparison results show that the estimation method is affected by the sample size, and the real value of the distribution parameter. The best estimation method is the Shrinkage Bayesian Lenix Function. The Bayesian methods can be applied to other statistical distributions such that the Lindley Weibull distribution and logistics distribution.

Distributed statistical estimation in quantile regression over a network

In this paper, we consider distributed quantile regression over a decentralized network, which is an example of a popularly used non-smooth statistical model. Somewhat different from the viewpoint of the optimization literature, we jointly consider numerical convergence and statistical convergence when the objective function is the loss function constructed from i.i.d. data, and the convergence to the true population parameter (instead of the minimizer of the empirical risk) is emphasized. Distributed sub-gradient methods with and without gradient tracking are considered, with an emphasis on the former. With gradient tracking, the estimate linearly converges to the true parameter up to the statistical precision based on all data, when the local sample size is sufficiently large. The distinction of our result compared to the existing optimization literature is that linear convergence can be established despite the fact that the function is not strongly convex. Numerical illustrations are given to compare with distributed descent algorithm without gradient tracking, and compare the ATC (adapt-then-combine) version with the non-ATC one.

Salinity distribution in agricultural land by geophysical, hydrochemical and geostatistical approaches: a pilot area located in Qelabshowah–Belqas, East Nile Delta region, Egypt

The study area is situated in the Qelabshowah–Belqas region, known for its Quaternary deposits. This research aims to demonstrate the two-dimensional (2D) variation of subsurface layers and salinity distribution using geoelectrical data, hydrochemical analysis, and geostatistical analysis. DC resistivity measurements were taken at fifteen vertical electrical sounding (VES) survey points using a Schlumberger array (AB/2 = 100 m) along three profiles. In addition, an electrical resistivity tomography (ERT) survey was conducted with a dipole–dipole array across one profile. Seven surface water samples were collected in the area. From the 1D and 2D inversion of VES and ERT data sets, three-to-four geoelectric layers were identified, including unconsolidated surface deposits, saturated clayey sand, saturated sand, and a salt-rich layer. The 2D inversion of VES data revealed an ancient salt-rich layer deposited in swampy conditions over a conductive wet sand layer along profile one due to salt mineral infiltration and dissolution. The 2D inversion of ERT data showed accurate lateral geometric accuracy compared to the 2D inversion of VES data, highlighting geological features, such as caves in the second layer and a buried water canal on the ground surface. Surface water samples showed high salinity levels with sodium hazards, indicating an Na–Cl composition. Geoelectric and hydrochemical data sets were geostatistically analyzed using spherical variogram supported ordinary Kriging interpolation. The analysis indicated weak to moderate spatial dependency for true resistivity parameters, while sodium content (SC) and permeability index (PI) showed strong spatial correlation. The 2D spatial distribution resistivity maps based on the 1D inversion of VES data displayed a general decrease in resistivity with depth, likely due to clay minerals or moist soil in the second layer and saline irrigation water infiltration in the third layer. The 2D spatial distribution of SC and PI showed a high concentration zone, posing a potential risk to agricultural crops regardless of soil permeability. It is recommended to use these maps when cultivating plants that can tolerate high sodium levels during the reclamation process.

The plausibility of alternative data-generating mechanisms: Comment on and attempt at replication of Dishop (2022).

Dishop (see record 2022-78260-001) identifies the consensus emergence model (CEM) as a useful tool for future research on emergence but argues that autoregressive models with positive autoregressive effects are an important alternative data-generating mechanism that researchers need to rule out. Here, we acknowledge that alternative data-generating mechanisms are possibility for most, if not all, nonexperimental designs and appreciate Dishop's attempts to identify cases where the CEM could provide misleading results. However, in a series of independent simulations, we were unable to replicate two of three key analyses, and the results for the third analysis did not support the earlier conclusions. The discrepancies appear to originate from Dishop's simulation code and what appear to be inconsistent model specifications that neither simulate the models described in the article nor include notable positive autoregressive effects. We contribute to the wider literature by suggesting four key criteria that researchers can apply to evaluate the possibility of alternative data-generating mechanisms: Theory, parameter recovery, fit to real data, and context. Applied to autoregressive effects and emergence data, these criteria reveal that (a) theory in psychology would generally suggest negative instead of positive autoregressive effects for behavior, (b) it is challenging to recover true autoregressive parameters from simulated data, and (c) that real data sets across a number of different contexts show little to no evidence for autoregressive effects. Instead, our analyses suggest that CEM results are congruent with the temporal changes occurring within groups and that autoregressive effects do not lead to spurious CEM results. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Quantifying uncertainty in carbon emission estimation: Metrics and methodologies

Carbon emissions are a significant driver of global climate change in today's world. A central concern in discussing carbon emissions is the level of uncertainty associated with them. This study aims to assess the feasibility of using the Mean Squared Error (MSE) as a point estimation measure and confidence interval (CI) as an interval estimation measure to quantify the uncertainty surrounding carbon emissions. To achieve this goal, the bootstrap and Markov Chain Monte Carlo (MCMC) sampling methods were used, utilizing both classical and Bayesian inference methods to uncover the true parameter value.In the context of Bayesian inference, a 2-chain MCMC method proved to be the optimal choice for generating posterior distributions and accurately estimating the true parameter of the distribution θ. The analysis also shows that, while a CI is valuable as an evaluative measure, it does not inherently provide a quantified form of uncertainty and should not be used for quantitative uncertainty assessment. Instead, the Relative Standard Error (RSE) emerges as a promising quantitative measure for capturing the uncertainty of θ, while the percentage uncertainty offers a qualitative perspective. These combined measures provide a comprehensive toolkit for computing and communicating the uncertainty in carbon emission and emission factor values. This reinforces a move towards incorporating transparent uncertainty metrics, ensuring that stakeholders have access to reliable and accurate carbon emission values.

Analysis of the Influence of Polarization Measurement Errors on the Parameter and Characteristics Measurement of the Fully Polarized Entomological Radar

Measuring the orientation, mass and body length of migratory insects through entomological radar is crucial for early warnings of migratory pests. The fully polarized entomological radar is an efficient device for observing migratory insects by calculating insect parameters through the scattering matrix obtained from the target. However, the measured target scattering matrix will be affected by system polarization measurement errors, leading to errors in insect parameter calculation, while the related analysis is currently relatively limited. Therefore, the scattering matrix measurement process is modeled, followed by an analysis of the effects of different errors on orientation, mass and body length estimation. The influence of polarization measurement errors on insect scattering characteristics is also analyzed. The results present that for fixed polarization measurement errors, the measurement errors of insect orientation, mass and body length will vary with insect orientation in specific patterns, and the distribution of measured insect parameters will be drastically distorted compared to the true parameter distribution. In addition, polarization measurement errors could seriously disrupt the reciprocity and bilateral symmetry of the measured insect scattering matrix. These analyses and conclusions provide a good basis for eliminating the effects of polarization measurement errors and improving the accuracy of insect parameter measurement.

Causal Strategic Learning with Competitive Selection

We study the problem of agent selection in causal strategic learning under multiple decision makers and address two key challenges that come with it. Firstly, while much of prior work focuses on studying a fixed pool of agents that remains static regardless of their evaluations, we consider the impact of selection procedure by which agents are not only evaluated, but also selected. When each decision maker unilaterally selects agents by maximising their own utility, we show that the optimal selection rule is a trade-off between selecting the best agents and providing incentives to maximise the agents' improvement. Furthermore, this optimal selection rule relies on incorrect predictions of agents' outcomes. Hence, we study the conditions under which a decision maker's optimal selection rule will not lead to deterioration of agents' outcome nor cause unjust reduction in agents' selection chance. To that end, we provide an analytical form of the optimal selection rule and a mechanism to retrieve the causal parameters from observational data, under certain assumptions on agents' behaviour. Secondly, when there are multiple decision makers, the interference between selection rules introduces another source of biases in estimating the underlying causal parameters. To address this problem, we provide a cooperative protocol which all decision makers must collectively adopt to recover the true causal parameters. Lastly, we complement our theoretical results with simulation studies. Our results highlight not only the importance of causal modeling as a strategy to mitigate the effect of gaming, as suggested by previous work, but also the need of a benevolent regulator to enable it.

CHEX-MATE: CLUster Multi-Probes in Three Dimensions (CLUMP-3D). I. Gas analysis method using X-ray and Sunyaev–Zel’dovich effect data

Galaxy clusters are the products of structure formation through myriad physical processes that affect their growth and evolution throughout cosmic history. As a result, the matter distribution within galaxy clusters, or their shape, is influenced by cosmology and astrophysical processes, in particular the accretion of new material due to gravity. We introduce an analysis method for investigating the three-dimensional triaxial shapes of galaxy clusters from the Cluster HEritage project with -- Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE). In this paper, the first in a CHEX-MATE triaxial analysis series, we focus on utilizing X-ray data from and Sunyaev-Zel'dovich (SZ) effect maps from and the Atacama Cosmology Telescope to obtain a three-dimensional triaxial description of the intracluster medium (ICM) gas. We present the forward modeling formalism of our technique, which projects a triaxial ellipsoidal model for the gas density and pressure, to be compared directly with the observed two-dimensional distributions in X-rays and the SZ effect. A Markov chain Monte Carlo is used to estimate the posterior distributions of the model parameters. Using mock X-ray and SZ observations of a smooth model, we demonstrate that the method can reliably recover the true parameter values. In addition, we applied the analysis to reconstruct the gas shape from the observed data of one CHEX-MATE galaxy cluster, PSZ2 G313.33+61.13 (Abell 1689), to illustrate the technique. The inferred parameters are in agreement with previous analyses for the cluster, and our results indicate that the geometrical properties, including the axial ratios of the ICM distribution, are constrained to within a few percent. With a much better precision than previous studies, we thus further establish that Abell 1689 is significantly elongated along the line of sight, resulting in its exceptional gravitational lensing properties.

A new automatic geo-electric self-potential imaging technique for diverse sustainable development scenarios

This study introduces a rapid and efficient inversion algorithm designed for the interpretation of self-potential responses originating from mineralized and ore sources and hydrothermal activity, specifically addressing spherical, vertical, and horizontal cylindrical structures. The algorithm leverages local wavenumber and correlation imaging techniques to enhance accuracy in modeling. The correlation factor (Cf value) is crucial in this approach, calculated as the correlation between the local wavenumber of the measured self-potential field and that of the computed field. The algorithm identifies the maximum correlation Cf value (CF-max) as indicative of the optimal true model parameters. To validate the proposed algorithm, it was applied to three theoretical examples—one with contamination from regional background and another with multiple sources with and without different types of noises (random Gaussian and white Gaussian noises). Additionally, the approach was tested on three distinct real field cases related to mining, ore investigation and hydrothermal activity in India, Germany and USA. Through a comprehensive analysis of results from theoretical and real-world scenarios, including comparisons with different available data and literature information, the study concludes that the method is effective, applicable to multiple sources, accurate, and does not necessitate prior knowledge of the source shape. This algorithm presents a promising advancement in the field of self-potential interpretation for mineral exploration and geothermal exploration.

Variable selection of Kolmogorov-Smirnov maximization with a penalized surrogate loss

Kolmogorov-Smirnov (KS) statistic is quite popular in many areas as the major performance evaluation criterion for binary classification due to its explicit business intension. Fang and Chen (2019) proposed a novel DMKS method that directly maximizes the KS statistic and compares favorably with the popular existing methods. However, DMKS did not consider the critical problem of variable selection since the special form of KS brings great challenge to establish the DMKS estimator's asymptotic distribution which is most likely to be nonstandard. This intractable issue is handled by introducing a surrogate loss function which leads to a n-consistent estimator for the true parameter up to a multiplicative scalar. Then a nonconcave penalty function is combined to achieve the variable selection consistency and asymptotical normality with the oracle property. Results of empirical studies confirm the theoretical results and show advantages of the proposed SKS (Surrogated Kolmogorov-Smirnov) method compared to the original DMKS method without variable selection.

GMM weighting matrices in cross-sectional asset pricing tests

When estimating misspecified linear factor models for the cross-section of expected returns using GMM, the explanatory power of these models can be spuriously high when the estimated factor means are allowed to deviate substantially from the sample averages. In fact, by shifting the weights on the moment conditions, any level of cross-sectional fit can be attained. The mathematically correct global minimum of the GMM objective function can be obtained at a parameter vector that is far from the true parameters of the data-generating process. This property is not restricted to small samples, but rather holds in population. It is a feature of the GMM estimation design and applies to both strong and weak factors, as well as to all types of test assets.

MAST: Phylogenetic Inference with Mixtures Across Sites and Trees.

Hundreds or thousands of loci are now routinely used in modern phylogenomic studies. Concatenation approaches to tree inference assume that there is a single topology for the entire dataset, but different loci may have different evolutionary histories due to incomplete lineage sorting (ILS), introgression, and/or horizontal gene transfer; even single loci may not be treelike due to recombination. To overcome this shortcoming, we introduce an implementation of a multi-tree mixture model that we call mixtures across sites and trees (MAST). This model extends a prior implementation by Boussau et al. (2009) by allowing users to estimate the weight of each of a set of pre-specified bifurcating trees in a single alignment. The MAST model allows each tree to have its own weight, topology, branch lengths, substitution model, nucleotide or amino acid frequencies, and model of rate heterogeneity across sites. We implemented the MAST model in a maximum-likelihood framework in the popular phylogenetic software, IQ-TREE. Simulations show that we can accurately recover the true model parameters, including branch lengths and tree weights for a given set of tree topologies, under a wide range of biologically realistic scenarios. We also show that we can use standard statistical inference approaches to reject a single-tree model when data are simulated under multiple trees (and vice versa). We applied the MAST model to multiple primate datasets and found that it can recover the signal of ILS in the Great Apes, as well as the asymmetry in minor trees caused by introgression among several macaque species. When applied to a dataset of 4 Platyrrhine species for which standard concatenated maximum likelihood (ML) and gene tree approaches disagree, we observe that MAST gives the highest weight (i.e., the largest proportion of sites) to the tree also supported by gene tree approaches. These results suggest that the MAST model is able to analyze a concatenated alignment using ML while avoiding some of the biases that come with assuming there is only a single tree. We discuss how the MAST model can be extended in the future.

On the reliable estimation of sequential Monod kinetic parameters

While dozens of studies have attempted to estimate the Monod kinetic parameters of microbial reductive dechlorination, published values in the literature vary by 2–6 orders of magnitude. This lack of consensus can be attributed in part to limitations of both experimental design and parameter estimation techniques. To address these issues, Hamiltonian Monte Carlo was used to produce more than one million sets of realistic simulated microcosm data under a variety of experimental conditions. These data were then employed in model fitting experiments using a number of parameter estimation algorithms for determining Monod kinetic parameters. Analysis of data from conventional triplicate microcosms yielded parameter estimates characterized by high collinearity, resulting in poor estimation accuracy and precision. Additionally, confidence intervals computed by commonly used classical regression analysis techniques contained true parameter values much less frequently than their nominal confidence levels. Use of an alternative experimental design, requiring the same number of analyses as conventional experiments but comprised of microcosms with varying initial chlorinated ethene concentrations, is shown to result in order-of-magnitude decreases in parameter uncertainty. A Metropolis algorithm which can be run on a typical personal computer is demonstrated to return more reliable parameter interval estimates.

Grid-free algorithms for direction-of-arrival trajectory localization.

Direction-of-arrival (DOA) estimation algorithms are crucial in localizing acoustic sources. Traditional localization methods rely on block-level processing to extract the directional information from multiple measurements processed together. However, these methods assume that DOA remains constant throughout the block, which may not be true in practical scenarios. Also, the performance of localization methods is limited when the true parameters do not lie on the parameter search grid. In this paper, two trajectory models are proposed, namely the polynomial and harmonic trajectory models, to capture the DOA dynamics. To estimate trajectory parameters, two gridless algorithms are adopted: (i) Sliding Frank-Wolfe (SFW), which solves the Beurling LASSO problem, and (ii) Newtonized orthogonal matching pursuit (NOMP), which is improved over orthogonal matching pursuit (OMP) using cyclic refinement. Furthermore, our analysis is extended to include multi-frequency processing. The proposed models and algorithms are validated using both simulated and real-world data. The results indicate that the proposed trajectory localization algorithms exhibit improved performance compared to grid-based methods in terms of resolution, robustness to noise, and computational efficiency.

Ensuring Consistency between Noise and Detection in Hierarchical Bayesian Inference

Hierarchical Bayesian inference can simultaneously account for both measurement uncertainty and selection effects within astronomical catalogs. In particular, the imposed hierarchy encodes beliefs about the interdependence of the physical processes that generate the observed data. We show that several proposed approximations within the literature actually correspond to inferences that are incompatible with any physical detection process. This generically leads to biases and is associated with the assumption that detectability is independent of the observed data given the true source parameters. We show several examples of how this error can affect astrophysical inferences based on catalogs of coalescing binaries observed through gravitational waves, including misestimating the redshift evolution of the merger rate as well as incorrectly inferring that general relativity is the correct theory of gravity when it is not. In general, one cannot directly fit for the “detected distribution” and “divide out” the selection effects in post-processing. Similarly, when comparing theoretical predictions to observations, it is better to simulate detected data (including both measurement noise and selection effects) rather than comparing estimates of the detected distributions of event parameters (which include only selection effects). While the biases introduced by model misspecification from incorrect assumptions may be smaller than statistical uncertainty for moderate catalog sizes (O(100) events), they will nevertheless pose a significant barrier to precision measurements of astrophysical populations.

Contexts of Convenience: Generalizing from Published Evaluations of School Finance Policies.

Recent attention to the causal identification of spending impacts provides improved estimates of spending outcomes in a variety of circumstances, but the estimates are substantially different across studies. Half of the variation in estimated funding impact on test scores and over three-quarters of the variation of impacts on school attainment reflect differences in the true parameters across study contexts. Unfortunately, inability to describe the circumstances underlying effective school spending impedes any attempts to generalize from the extant results to new policy situations. The evidence indicates that how funds are used is crucial to the outcomes, but such factors as targeting of funds or court interventions fail to explain the existing pattern of results.