General Parametric Model Research Articles

ForLion: a new algorithm for D-optimal designs under general parametric statistical models with mixed factors

ForLion: a new algorithm for D-optimal designs under general parametric statistical models with mixed factors

Semiparametric efficiency gains from parametric restrictions on propensity scores

Abstract We explore how much knowing a parametric restriction on propensity scores improves semiparametric efficiency bounds in the potential outcome framework. For stratified propensity scores, considered as a parametric model, we derive explicit formulas for the efficiency gain from knowing how the covariate space is split. Based on these, we find that the efficiency gain decreases as the partition of the stratification becomes finer. For general parametric models, where it is hard to obtain explicit representations of efficiency bounds, we propose a novel framework that enables us to see whether knowing a parametric model is valuable in terms of efficiency even when it is high dimensional. In addition to the intuitive fact that knowing the parametric model does not help much if it is sufficiently flexible, we discover that the efficiency gain can be nearly zero even though the parametric assumption significantly restricts the space of possible propensity scores.

Minimizing robust density power-based divergences for general parametric density models

Minimizing robust density power-based divergences for general parametric density models

Recurrence and transience of a Markov chain on $\mathbb Z$ + and evaluation of prior distributions for a Poisson mean

AbstractEaton (1992) considered a general parametric statistical model paired with an improper prior distribution for the parameter and proved that if a certain Markov chain, constructed using the model and the prior, is recurrent, then the improper prior is strongly admissible, which (roughly speaking) means that the generalized Bayes estimators derived from the corresponding posterior distribution are admissible. Hobert and Robert (1999) proved that Eaton’s Markov chain is recurrent if and only if its so-called conjugate Markov chain is recurrent. The focus of this paper is a family of Markov chains that contains all of the conjugate chains that arise in the context of a Poisson model paired with an arbitrary improper prior for the mean parameter. Sufficient conditions for recurrence and transience are developed and these are used to establish new results concerning the strong admissibility of non-conjugate improper priors for the Poisson mean.

Scalable quantum neural networks by few quantum resources

This paper focuses on the construction of a general parametric model that can be implemented executing multiple swap tests over few qubits and applying a suitable measurement protocol. The model turns out to be equivalent to a two-layer feedforward neural network which can be realized combining small quantum modules. The advantages and the perspectives of the proposed quantum method are discussed.

Characterizing the true descendants of the first stars

ABSTRACT The metal-poor stars in the Galactic halo are thought to show the imprints of the first (Pop III) stars, and thus provide a glance at the first episodes of star formation. In this work, we aim at understanding whether all very metal-poor stars formed in environments polluted by Pop III supernovae (SNe) and at what level. With a general parametric model for early metal enrichment, we study the chemical abundances (from C to Zn) of an environment imprinted by a single Pop III SN. We investigate how these abundances depend on the initial mass and internal mixing of Pop III stars, as well as on their SN explosion energy. We then study how subsequent generations of normal (Pop II) SNe affect the Pop III chemical signatures. By comparing the observed chemical abundances with our model predictions, we show that stars with [C/Fe] > +2.5 form in environments polluted purely by low-energy Pop III SNe (ESN < 2 × 1051 erg). At lower [C/Fe], stars can be imprinted either by Pop III only, or also by normal Pop II SNe. The probability of being enriched by Pop II SNe increases as [C/Fe] decreases. When Pop II stars contribute more to the pollution, they wash out the diverse chemical peculiarities left by the different Pop III SNe, and the chemical dispersion between their descendants decreases. We conclude that C-normal stars ($\rm [C/Fe] \le +0.7$) have likely been enriched by Pop II SNe at a $\ge 50~{{\ \rm per\ cent}}$ level and we identify in the abundance scatter a key diagnostic to pinpoint the signature of Pop III SNe.

An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer

System identification is an important methodology used in control theory and constitutes the first step of control design. It is known that many real systems can be better characterized by fractional-order models. However, it is often quite complex and difficult to apply classical control theory methods analytically for fractional-order models. For this reason, integer-order models are generally considered in classical control theory. In this study, an alternative approximation method is proposed for fractional-order models. The proposed method converts a fractional-order transfer function directly into an integer-order transfer function. The proposed method is based on curve fitting that uses a quadratic system model and Equilibrium Optimizer (EO) algorithm. The curve fitting is implemented based on the unit step response signal. The EO algorithm aims to determine the optimal coefficients of integer-order transfer functions by minimizing the error between general parametric quadratic model and objective data. The objective data are unit step response of fractional-order transfer functions and obtained by using the Grünwald-Letnikov (GL) method in the Fractional-Order Modeling and Control (FOMCON) toolbox. Thus, the coefficients of an integer-order transfer function most properly can be determined. Some examples are provided based on different fractional-order transfer functions to evaluate the performance of the proposed method. The proposed method is compared with studies from the literature in terms of time and frequency responses. It is seen that the proposed method exhibits better model approximation performance and provides a lower order model.

A proxy learning curve for the Bayes classifier

In this paper, a theoretical learning curve is derived for the multi-class Bayes classifier. This curve fits general multivariate parametric models of the class-conditional probability density. The derivation uses a proxy approach based on analyzing the convergence of a statistic which is proportional to the posterior probability of the true class. By doing so, the curve depends only on the training set size and on the dimension of the feature vector; it does not depend on the model parameters. Essentially, the learning curve provides an estimate of the reduction in the excess of the probability of error that can be obtained by increasing the training set size. This makes it attractive in order to deal with the practical problems of defining appropriate training set sizes.

Extrapolation in parametric models with Laplace measurement error

For general parametric statistical models with some variables being contaminated with the Laplace measurement error, we propose an extrapolation algorithm to estimate the unknown parameters. By applying the conditional expectation directly to the target function, either the function to be optimized or an estimation equation, the proposed algorithm successfully bypasses the simulation step in the classical simulation extrapolation procedure and thus provides a viable alternative to the classical simulation extrapolation algorithm. Large sample properties of the resulting estimator are discussed. Finite sample performance of the proposed extrapolation estimation procedure is demonstrated by examples and numerical simulation studies.

Simplified models for predicting the environmental impacts of geothermal power generation

Geothermal energy is a renewable source of base-load power that could facilitate decarbonising the power generation sector. This work proposes novel simplified models based on Life Cycle Assessment (LCA) that enable rapid but accurate estimates of the environmental impacts of geothermal power. The proposed approach not only reduces the variability of LCA estimates due to methodological choices, but also substantially facilitates data collection by identifying the most important input parameters. These parameters are selected using Sobol’ total order indices from Global Sensitivity Analysis to a general parametric model. The models are applicable to both conventional and enhanced geothermal technologies, and cover numerous environmental impact categories. We determine the level of correlation between the simplified models and the general model. Our analysis shows that the simplified models correlate well with the general model, with correlation coefficients above 0.75 for both types of geothermal technologies and for all environmental categories. We also evaluate the performance of the simplified models by comparison with literature data. The results are positive, especially for conventional technologies where the relative difference with literature data on climate change impacts averages 14%. Finally, we identify the most appropriate model for each technology archetype and environmental category. • Simplified geothermal models rely on 1–5 influential parameters. • Influential parameters are obtained from Sobol’ total order indices. • Models cover conventional/enhanced technologies and multiple environmental categories. • Carbon footprint estimates are validated against literature data. • Open-source python script for easy updates or customisation.

Design of a Hybrid Electric Power-Split Transmission for Braking Energy Recovery in a Drilling Rig

Despite the promising potential of the hybrid electric power-split layout, its broader market penetration is prevented by the large number of feasible solutions and the constructive complexity, which overcomplicate the design process. Moreover, due to the lack of relevant literature references, the power-split transmissions design is even more difficult if concerning applications outside the automotive and agricultural sectors. In this paper, a general parametric model already available in the literature to design a single-mode power-split transmission with up to two planetary gear sets and six ordinary gear sets was applied to hybridize an oil drilling rig to recover energy braking during the gravity-driven lowering phases. This is the first power-split electric hybridization of a drilling rig. Two solutions differing in engine power size are presented. Thanks to the modularity of the model, the procedure enabled the optimization of the ICE, the electric machines, and the gear sets through decoupled design phases.

A flexible parametric accelerated failure time model and the extension to time-dependent acceleration factors.

Accelerated failure time (AFT) models are used widely in medical research, though to a much lesser extent than proportional hazards models. In an AFT model, the effect of covariates act to accelerate or decelerate the time to event of interest, that is, shorten or extend the time to event. Commonly used parametric AFT models are limited in the underlying shapes that they can capture. In this article, we propose a general parametric AFT model, and in particular concentrate on using restricted cubic splines to model the baseline to provide substantial flexibility. We then extend the model to accommodate time-dependent acceleration factors. Delayed entry is also allowed, and hence, time-dependent covariates. We evaluate the proposed model through simulation, showing substantial improvements compared to standard parametric AFT models. We also show analytically and through simulations that the AFT models are collapsible, suggesting that this model class will be well suited to causal inference. We illustrate the methods with a data set of patients with breast cancer. Finally, we provide highly efficient, user-friendly Stata, and R software packages.

Extrapolation estimation in parametric regression models with measurement error

For the general parametric regression models with covariates contaminated with normal measurement errors, an alternative method to the traditional simulation extrapolation algorithm is proposed to estimate the unknown parameters in the regression function. By applying the conditional expectation directly to the target function, the proposed algorithm successfully removes the simulation step, by generating an estimation equation either for immediate use or for extrapolating, thus providing a possibility of reducing the computational time or the Monte Carlo simulation error. Large sample properties of the resulting estimator, including the consistency and the asymptotic normality, are thoroughly discussed. Potential wide applications of the proposed estimation procedure are illustrated by examples, simulation studies, as well as a real data analysis.

Maximizing Multi‐Decadal Water Surface Elevation Estimates With Landsat Imagery and Elevation/Bathymetry Datasets

AbstractIdentifying patterns and trends in long‐term lake dynamics is essential to establish effective water management procedures and boost our understanding of inland water's role in the global water cycle. This research leverages Google Earth Engine to estimate multi‐decadal water surface elevations for 52 lakes and reservoirs with varying physical properties. Water surface elevation was estimated using the entire Landsat 4, 5, 7, and 8 Landsat Top‐of‐Atmosphere Tier‐1 Collection‐1 archive from August 1982 through December 2017 via shoreline boundary statistics extracted from the National Elevation Dataset merged with lake bathymetry. Image contamination was identified and removed to provide elevation estimates for images with varying levels of image contamination. To improve accuracy, data filtering techniques were identified which retained over 70% of images with detectable water boundaries producing 26 lakes with sub‐meter root‐mean‐square‐error accuracy and 40 lakes with sub‐meter mean‐absolute‐error‐accuracy using a general overall parameter model. Additionally, lake‐specific locally optimized models were also determined with 45 of the 52 lakes producing sub‐meter root‐mean‐square‐error accuracies and 49 with sub‐meter mean‐absolute‐errors with individual lake accuracy as low as 0.191 m RMSE CI95%[0.129, 0.243]. In general, individual lake accuracy is highly correlated with the mean slope of the surrounding terrain with low‐slope shorelines having greater accuracy than high‐slope shorelines. Seasonal patterns in estimate accuracy were also identified. This research extends our ability to track lake dynamics over long time periods to lakes lacking traditional in‐situ monitoring, enables rapid assessment of lake dynamics across large areas, and balances a need for both high‐accuracy measurements and maximum temporal resolution.

The KhAI-90 Light Civil Turboprop Airplane Pilot Project

Abstract The pilot project of new light civil turboprop aircraft, called the KhAI-90, featuring a cruising speed of 350km/h, payload of 600 kg at 500 km range, and equipped with two turboprop Rolls-Royce 250-B17F engines each with power of 420 hp (alternatively, two AI-450C engines each with power of 450 hp may be installed) is presented herein. Based on the developed technical task, the concept for creating the KhAI-90 new competitive light civil aircraft, and the analysis of prototypes’ aircraft parameters and characteristics, the main tactical and technical requirements are assigned. The take-off weight of the new aircraft is determined in three approximations at the preliminary design stage of light civil turboprop aircraft, using the iterative software “CLA-TOW”, studying the influence of the wing geometric parameters and lift devices on aerodynamic performance, the power-to-weight ratio and the airplane weight parameters. The following parameters are calculated for the design: minimum take-off weight WTO min = 3,600 kg, optimal wing loading p 0 opt = 130 daN/m2, optimal aspect ratio 9.6, taper ratio 2.25, sweep angle at leading edge 3 degrees, airfoil relative thickness 10.6%. A general view and three-dimensional parametric models of the master-geometry and passenger cabin space distribution are constructed for the KhAI-90 by means of the SIEMENS NX computer integrated system. More broadly, this pilot project has also demonstrated the viability of the method we developed and previously reported for determining light civil turboprop airplane parameters.

Competing risks survival data under middle censoring—An application to COVID-19 pandemic

Survival data is being analysed here under the middle censoring scheme, using specifically quantile function modelling under competing risks. The use of middle censoring scheme has been shown to be very appropriate under the COVID-19 pandemic scenario. Cause-specific quantile inference under middle censoring is employed. Such quantile inferences are obtained through cumulative incidence function based on cause-specific proportional hazards model. The baseline lifetime is assumed to follow a very general parametric model namely the Weibull distribution, and is independent of the censoring mechanism. We obtain estimates of the unknown parameters and cause specific quantile functions under classical as well as a Bayesian set-up. A Monte Carlo simulation study assesses the relative performance of the different estimators. Finally, a real life data analysis is given for illustration of the proposed methods.

A General Model for Describing the Ovate Leaf Shape

Many plant species produce ovate leaves, but there is no general parametric model for describing this shape. Here, we used two empirical nonlinear equations, the beta and Lobry–Rosso–Flandrois (LRF) equations, and their modified forms (referred to as the Mbeta and MLRF equations for convenience), to generate bilaterally symmetrical curves along the x-axis to form ovate leaf shapes. In order to evaluate which of these four equations best describes the ovate leaf shape, we used 14 leaves from 7 Neocinnamomum species (Lauraceae) and 72 leaves from Chimonanthus praecox (Calycanthaceae). Using the AIC and adjusted root mean square error to compare the fitted results, the modified equations fitted the leaf shapes better than the unmodified equations. However, the MLRF equation provided the best overall fit. As the parameters of the MLRF equation represent leaf length, maximum leaf width, and the distance from leaf apex to the point associated with the maximum leaf width along the leaf length axis, these findings are potentially valuable for studying the influence of environmental factors on leaf shape, differences in leaf shape among closely related plant species with ovate leaf shapes, and the extent to which leaves are bilaterally symmetrical. This is the first work in which temperature-dependent developmental equations to describe the ovate leaf shape have been employed, as previous studies lacked similar leaf shape models. In addition, prior work seldom attempted to describe real ovate leaf shapes. Our work bridges the gap between theoretical leaf shape models and empirical leaf shape indices that cannot predict leaf shape profiles.

An improved online system identification method for tiltrotor aircraft

An online system identification method for tiltrotor aircraft flight dynamics modeling is developed in this paper. A general parametric flight dynamics model which can be used for online identification purpose in the three flight modes of tiltrotor aircraft (i.e., helicopter mode, conversion mode, and fixed-wing mode) is developed, and an unideal noise model is also introduced in order to minimize the parameter identification error caused by measurement noise. An adaptive model structure identification algorithm is established by introducing local accuracy criteria, so that a time variant optimal model structure is obtained in real time. A weighted recursive least squares algorithm is established for parameter identification, and a time variant weighting matrix is designed to provide best numerical performance in the identification procedure at any time. A comprehensive nonlinear flight dynamics model of a notional tiltrotor aircraft is used to generate simulation flight test data in all flight modes, and the identification results of the notional tiltrotor aircraft in fixed wing mode, helicopter model as well as conversion mode are obtained and verified. Finally, the flight dynamics model of an unmanned tiltrotor aircraft in helicopter mode is identified by using the real flight test data. The identification results show that the online system identification method for tiltrotor aircraft developed in this paper is effective, efficient and robust.

NONPARAMETRIC NONLINEARITY IDENTIFICATION WITH AN UPDATED EKF APPROACH USING DYNAMIC RESPONSE FUSION

Most parametric nonlinear behavior identification methods require an assumed mathematical model to describe the hysteretic behavior of structural members or substructures. Due to the individuality of various construction materials and structural systems, it is challenging to forecast the real nonlinear performance of a structure member or a substructure under dynamic loadings with a general parametric model in prior. In this paper, a nonparametric nonlinear restoring force (NRF) identification approach with limited output and unknown input is proposed by employing a double Chebyshev polynomial combined with an updated Extended Kalman filter (U-EKF) approach, where the observation equation is updated without using external excitation information. Moreover, data fusion is used to deal with the drift problem in dynamic response forecasting. The proposed approach is validated numerically with multi-degree-of-freedom (MDOF) structures equipped with various nonlinear members, including MR damper (damping-dominant) and SMA damper (stiffness-dominant) employed to mimic different structural nonlinear behavior. Moreover, a four-story shear frame model, including MR damper on the fourth floor, is employed to experimentally validate the approach. Identified results show that the proposed algorithm can identify structural nonlinear behavior in a nonparametric way without using excitation as an input, which is helpful for structural damage diagnosis where nonlinearity and loading profile should be considered.

Analyzing left-truncated and right-censored infectious disease cohort data with interval-censored infection onset.

In an infectious disease cohort study, individuals who have been infected with a pathogen are often recruited for follow up. The period between infection and the onset of symptomatic disease, referred to as the incubation period, is of interest because of its importance on disease surveillance and control. However, the incubation period is often difficult to ascertain due to the uncertainty associated with asymptomatic infection onset time. An additional complication is that the observed infected subjects are likely to have longer incubation periods due to the prevalent sampling. In this article, we demonstrate how to estimate the distribution of the incubation period with the uncertain infection onset, subject to left-truncation and right-censoring. We employ a family of sufficiently general parametric models, the generalized odds-rate class of regression models, for the underlying incubation period and its correlation with covariates. In simulation studies, we assess the finite sample performance of the model fitting and hazard function estimation. The proposed method is illustrated on data from the HIV/AIDS study on injection drug users admitted to a detoxification program in Badalona, Spain.