Approximate Estimation Research Articles

Approximate Cross-Validated Mean Estimates for Bayesian Hierarchical Regression Models

We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). BHRMs are popular for modeling complex dependence structures (e.g., Gaussian processes and Gaussian Markov random fields) but can be computationally expensive to run. Cross-validation (CV) is, therefore, not a common practice to evaluate the predictive performance of BHRMs. Our method circumvents the need to rerun computationally costly estimation methods for each cross-validation fold and makes CV more feasible for large BHRMs. We shift the CV problem from probability-based sampling to a familiar and straightforward optimization problem by conditioning on the variance-covariance parameters. Our approximation applies to leave-one-out CV and leave-one-cluster-out CV, the latter of which is more appropriate for models with complex dependencies. In many cases, this produces estimates equivalent to full CV. We provide theoretical results, demonstrate the efficacy of our method on publicly available data and in simulations, and compare the model performance with several competing methods for CV approximation. Code and other supplementary materials available online.

Shape Preserving Approximation of Periodic Functions: Conclusion

AbstractWe give here the final results about the validity of Jackson-type estimates in comonotone approximation of $$2\pi $$ 2 π -periodic functions by trigonometric polynomials ($$q=1$$ q = 1 ). For coconvex ($$q=2$$ q = 2 ) and the so called co-q-monotone, $$q>2$$ q > 2 , approximations, everything is known by now. Thus, this paper concludes the research on Jackson type estimates of Shape Preserving Approximation of periodic functions by trigonometric polynomials. It is interesting to point out that the results for comonotone approximation of a periodic function are substantially different than the analogous results for comonotone approximation of a continuous function on a finite interval, by algebraic polynomials.

Modeling of the interaction of stressful components agricultural production

There is a completely natural, organic nonlinear relationship between crop production and animal husbandry, which are crucial components of agricultural production in Ukraine. Timely and appropriate management of these subsystems contributes to the stable growth of the country’s agriculture with minimal risk. This approach requires improvements in terms of the digitalization of the economy, particularly in the context of applying computer modeling to the nonlinear processes of interaction between these components. The article develops a modern methodology for computer modeling of an economic management object—a thorough study of a nonlinear dynamic model of the VolterraLotka class, featuring a component that characterizes the increase in livestock profitability due to feed supply. The model takes into account various influencing factors, allowing for the assessment of the efficiency of the interaction between crop production and animal husbandry at different stages of agricultural production. The study examines the behavior of the dynamic model in the vicinity of the leverage point, analyzing the modeled trend dependencies and statistical components: in the vicinity of the equilibrium point, there are oscillatory movements with a certain defined period, and the solutions of the mathematical model, i.e., integral curves, over time reflect the seasonal nature of the interaction between crop production and animal husbandry. The behavior of virtual scenarios—integral curves and phase portraits based on the mathematical model of nonlinear interaction of agricultural production components—wasstudied, showing the location of the equilibrium point, extreme points, and other critical points for the respective curves in a specific coordinate system. A transition to a dimensionless dynamic model and an economic interpretation of its implicit solution were indicated. Additionally, the impact of external economic factors on the stability of the system was analyzed, allowing for better forecasting of potential risks and the preparation of appropriate strategies to minimize them. For the first time, an approximate numerical estimate of the economic risk measure of the evolution of the interaction and interplay of agricultural subsystems over time was carried out in the study of the nonlinear dynamic model of the economic management object. The obtained results can be used to improve management strategies in the agricultural sector, particularly to enhance the stability of production processes and reduce economic risks in the context of market instability and climate change. This research provides new opportunities for effective planning and the implementation of innovations in Ukraine’s agricultural sector.

Rationalised experiment design for parameter estimation with sensitivity clustering

Quantitative experiments are essential for investigating, uncovering, and confirming our understanding of complex systems, necessitating the use of effective and robust experimental designs. Despite generally outperforming other approaches, the broader adoption of model-based design of experiments (MBDoE) has been hindered by oversimplified assumptions and computational overhead. To address this, we present PARameter SEnsitivity Clustering (PARSEC), an MBDoE framework that identifies informative measurable combinations through parameter sensitivity (PS) clustering. We combined PARSEC with a new variant of Approximate Bayesian Computation-based parameter estimation for rapid, automated assessment and ranking of experiment designs. Using two kinetic model systems with distinct dynamical features, we show that PARSEC-based experiments improve the parameter estimation of a complex system. By its inherent formulation, PARSEC can account for experimental restrictions and parameter variability. Moreover, we demonstrate that there is a strong correlation between sample size and the optimal number of PS clusters in PARSEC, offering a novel method to determine the ideal sampling for experiments. This validates our argument for employing parameter sensitivity in experiment design and illustrates the potential to leverage both model architecture and system dynamics to effectively explore the experimental design space.

Statistical analysis for progressive stress accelerated life test with transmutation Weibull distribution

The Transmutation Weibull distribution is derived from the quadratic rank transmutation map of the Weibull distribution. This distribution integrates the high adaptability of the Weibull distribution in engineering and materials fields, and has great potential utility for modeling lifetime data. Therefore, the article explores the progressive stress accelerated life test model for components under the Transmutation Weibull distribution, conducts statistical analysis using the maximum likelihood estimation (MLE), Lindley’s approximation, and Markov Chain Monte Carlo (MCMC) algorithm to provide approximate estimates for the model. Finally, by comparing the results of numerical simulations, it is confirmed that the Bayesian estimation is more accurate and effective.

Spectral Galerkin Approximation and Error Analysis Based on a Mixed Scheme for Fourth‐Order Problems in Complex Regions

ABSTRACTIn this article, an efficient spectral Galerkin method, which is based on a mixed scheme, is proposed and studied for solving fourth‐order problems in complex regions. The fundamental idea behind this approach is to transform the initial problem into an equivalent form in cylindrical coordinates and to reshape the computational domain into a product‐type rectangular one, which facilitates the utilization of spectral methods. However, when considering the equivalent fourth‐order form directly in cylindrical coordinates, it introduces intricate pole conditions and variable coefficients, posing challenges to both theoretical analysis and algorithm implementation. To address this, we employ the orthogonality of Fourier series to further decompose it into a sequence of decoupled two‐dimensional fourth‐order eigenvalue problems. For each such problem, we introduce an auxiliary function to transform it into an equivalent second‐order coupled system. Building on this, we formulate a mixed variational formulation and discrete scheme, and prove the error estimates for eigenvalue and eigenfunction approximations. Furthermore, we extend this algorithm to the two‐dimensional complex domains. Finally, a series of numerical examples are presented, and the numerical results validate the effectiveness of the algorithm and the correctness of the theoretical results.

Modelling of the time to death of breast cancer patients at Hiwot Fana Specialized University Hospital

Breast cancer is the most common cause of cancer death and is a frequently diagnosed cancer among women worldwide. It is becoming a challenging health condition in Ethiopia with a high rate of morbidity and mortality. The main aim of this study was to model the time to death in breast cancer patients at Hiwot Fana Specialized University Hospital. A retrospective cohort study was carried out from April 1st, 2020, to April 1st, 2023, and 296 women were included in the study. We used nonparametric methods and Bayesian accelerated failure time models (with Laplace approximation) to identify risk factors and choose a model fitting breast cancer patient data. Model comparison was performed using the marginal likelihood, deviance information criterion and Watanabe Akaike information criterion. From the total of 296 patients in the study, 56 (18.9%) died. The estimated median survival time was 33 months. The log-rank test showed that age group, stage, alcohol consumption, smoking habit, and comorbidity were potential risk factors associated with the time to death in breast cancer patients at the 5% level of significance. The Bayesian Weibull accelerated failure time model was found to be the best fitted model for predicting the survival time of patients with minimum DIC (520.39) and WAIC (521.59) values. The final Bayesian Weibull AFT model with the integrated nested Laplace approximation estimation technique revealed that age group, stage, alcohol consumption, smoking habit, and comorbidity were significantly associated with the time to death in breast cancer patients. Individuals older than 65 years, with stage IV disease, drinking alcohol, smoking cigarettes and having comorbidities had shortened survival times in patients with breast cancer. Hence, Hiwot Fana Specialized University Hospital and related bodies should work on awareness creation to reduce smoking habits and alcohol use as well as give due attention to elderly and stage IV breast cancer patients during intervention.

A Cooperative Control Method for Wide-Range Maneuvering of Autonomous Aerial Refueling Controllable Drogue

In the realm of autonomous aerial refueling missions for unmanned aerial vehicles (UAVs), the controllable drogue represents a novel approach that significantly enhances both the safety and efficiency of aerial refueling operations. This paper delves into the issue of wide-range maneuverability control for the controllable drogue. Initially, a dynamic model for the variable-length hose–drogue system is presented. Based on this, a cooperative control framework that synergistically utilizes both the hose and the drogue is designed to achieve wide-range maneuverability of the drogue. To address the delay in hose retrieval and release, an open-loop control strategy based on neural networks is proposed. Furthermore, a closed-loop control method utilizing fuzzy approximation and adaptive error estimation is designed to tackle the challenges posed by modeling inaccuracies and uncertainties in aerodynamic parameters. Comparative simulation results show that the proposed control strategy can make the drogue maneuvering range reach more than 6 m. And it can accurately track the time-varying trajectory under the influence of model uncertainty and wind disturbance with an error of less than 0.1 m throughout. This method provides an effective means for achieving wide-range maneuverability control of the controllable drogue in autonomous aerial refueling missions.

Theoretical analysis for estimating laser integrated linewidth via frequency-noise power spectral density.

The measurement of a laser linewidth is significant in metrology, coherent optical communications, high-resolution sensing, and LIDAR. Firstly, in this study, we theoretically explain why estimating an integrated linewidth via a frequency-noise power spectral density (PSD) is valid. We find that the previous methods estimating the integrated linewidth via the frequency-noise PSD result from Gaussian approximation and obtain a more general consequence. Secondly, according to the theory, we propose the Voigt approximation method to improve the estimation performance. The simulation results show the Voigt approximation estimation error is lower than 5%. Finally, based on the Voigt approximation, the relationship between the interference visibility and laser linewidth is found, providing a possible convenient approach to measuring the linewidth.

Reliability Estimation of Scale Parameter in Type II Generalized Half-Logistic Distribution from Doubly Censored Samples Based on Monte Carlo Simulation

Objectives: This article deals with estimation of the reliability function for one-parameter Type II Generalized Half- Logistic distribution (Type II GHLD). Methods: The Maximum likelihood (ML) and Approximate Maximum likelihood (AML) methods provided by Jilani et.al. 1 . Findings: Comparisons between the estimators were made using Monte Carlo Simulation based on statistical indicter bias and mean squared error (MSE). We have generated 3000 random samples of size n=10(5)20 from a standard one-parameter Type II GHLD with = 0.5, 1.5 and 2.0. Each sample is then ordered and from this sample a doubly (including left and right) censored sample is considered, by censoring r smallest observations and s largest observations with all possible choices of r and s corresponding to this resultant sample we compute MLEs (using Newton-Raphson method), the LAMLE and unbiased LAMLE . Finally, the results are explained with tables. Novelty: This study has empirically proves that all the three reliability estimators have the same asymptotic variance. Hence, in this case, any one of the three estimators can be used but preferable estimator based unbiased estimator. Keywords: Maximum likelihood estimation, Approximate Maximum likelihood estimation, Bias, Mean squared error, Variances

A new invasive freshwater mussel: Discovery of a non-native population of Pilsbryoconcha exilis (Lea, 1838) in Myanmar (Bivalvia: Unionidae)

The present study reports on the first record of a non-native population of the freshwater mussel Pilsbryoconcha exilis (Lea, 1838) (Bivalvia: Unionidae) in Myanmar. It was discovered from irrigation canals that are situated in the Delta Region of the Ayeyarwady River. Based on approximate age estimates and information from local villagers, this population was probably established in 2019-2020. The DNA sequence data reveals that the Ayeyarwady population shares a single COI haplotype and that this haplotype was previously recorded from the Udon Thani Province of Thailand (Mekong River drainage). Based on this evidence, we could assume that P. exilis was introduced to Myanmar from Thailand. Our new findings expand the global checklist of invasive freshwater mussels that currently contains 17 species.

HTLV-1/2 infection in Italy: a narrative review of epidemiological studies.

The human T-cell leukemia virus type 1 (HTLV-1) was first described in 1980. It is spread in highly endemic regions in the world, such as the Southwestern part of Japan, sub-Saharan Africa and South America, Caribbean, Middle East, and Australo-Melanesia regions. HTLV-1 causes adult T cell leukemia and is associated with many inflammatory conditions, most notably HTLV-1-associated myelopathy/tropic spastic paraparesis. HTLV-2, first isolated in 1982, was recognized as a common infection in intravenous drug users, but a clear association with disease remains elusive. The first estimate of HTLV-1-positive individuals worldwide, in 1993, was around 10-20 millions. Due to the lack of global population-based prevalence studies, this is considered an underestimate at the moment. Furthermore, HTLV-1 prevalence in Europe is impacted by changing migration flows. Particularly, no data on HTLV-1 prevalence in the general population in Italy are available. Here, we report a systematic literature review of studies conducted in Italy on HTLV-1/2 from 1980 to 2023. Based on the criteria we adopted a total of 426 publications were found (64 reviews, 99 epidemiological, and 263 translational studies). The contents of some representative publications are summarized and discussed. Moreover, an approximate estimation of about 26,000 HTLV-1 positive foreigners living in Italy was obtained from updated data of foreigners from each single country officially registered as resident in Italy and from data on HTLV-1 prevalence among the general population in the corresponding countries.

Carleman estimates for space semi-discrete approximations of one-dimensional stochastic parabolic equation and its applications

Abstract In this paper, we study discrete Carleman estimates for space semi-discrete approximations of one-dimensional stochastic parabolic equation. We then apply these Carleman estimates to investigate two inverse problems for the space semi-discrete stochastic parabolic equations, including a discrete inverse random source problem and a discrete Cauchy problem. We firstly establish two Carleman estimates for a one-dimensional semi-discrete stochastic parabolic equation, one for homogeneous boundary and the other for non-homogeneous boundary. Then we apply these two estimates separately to derive two stability results. The first one is the Lipschitz stability for the discrete inverse random source problem. The second one is the H"{o}lder stability for the discrete Cauchy problem.

Arterial stiffness after 6 weeks postdelivery in women with a history of hypertensive disorders of pregnancy: a systematic review protocol

IntroductionHypertensive disorders of pregnancy (HDP) are one of the leading causes of maternal morbidity and mortality. The risk of developing cardiovascular diseases following HDP is high. Arterial stiffness is a...

Comparing Large-Eddy Simulation and Gaussian Plume Model to Sensor Measurements of an Urban Smoke Plume

The fast prediction of the extent and impact of accidental air pollution releases is important to enable a quick and informed response, especially in cities. Despite this importance, only a small number of case studies are available studying the dispersion of air pollutants from fires in a short distance (O(1 km)) in urban areas. While monitoring pollution levels in Southampton, UK, using low-cost sensors, a fire broke out from an outbuilding containing roughly 3000 reels of highly flammable cine nitrate film and movie equipment, which resulted in high values of PM2.5 being measured by the sensors approximately 1500 m downstream of the fire site. This provided a unique opportunity to evaluate urban air pollution dispersion models using observed data for PM2.5 and the meteorological conditions. Two numerical approaches were used to simulate the plume from the transient fire: a high-fidelity computational fluid dynamics model with large-eddy simulation (LES) embedded in the open-source package OpenFOAM, and a lower-fidelity Gaussian plume model implemented in a commercial software package: the Atmospheric Dispersion Modeling System (ADMS). Both numerical models were able to quantitatively reproduce consistent spatial and temporal profiles of the PM2.5 concentration at approximately 1500 m downstream of the fire site. Considering the unavoidable large uncertainties, a comparison between the sensor measurements and the numerical predictions was carried out, leading to an approximate estimation of the emission rate, temperature, and the start and duration of the fire. The estimation of the fire start time was consistent with the local authority report. The LES data showed that the fire lasted for at least 80 min at an emission rate of 50 g/s of PM2.5. The emission was significantly greater than a ‘normal’ house fire reported in the literature, suggesting the crucial importance of the emission estimation and monitoring of PM2.5 concentration in such incidents. Finally, we discuss the advantages and limitations of the two numerical approaches, aiming to suggest the selection of fast-response numerical models at various compromised levels of accuracy, efficiency and cost.

ESTIMATING THE SOLAR EXERGY POTENTIAL OF SURFACES WITH DIFFERENT TILT ANGLES

Solar energy, which is a clean, unlimited, and environmentally friendly energy source, has critical importance in sustainable energy management. The usable potential of energy is expressed in terms of exergy, and the determination of the exergy potential of solar energy ensures the correct utilization of this potential. Turkey has a very high solar energy potential, and this potential should be utilized in the most efficient way possible to achieve sustainable energy targets. The tilt angle of solar panels has a significant effect on efficiency. Efficient operation of solar panels can be achieved by determining the optimum tilt angle. In this study, Turkey's solar exergy potential was calculated for the horizontal plane and five different tilt angles (21°, 30°, 39°, 48°, and 57°). Thus, it was tried to determine the appropriate panel angle to get the highest efficiency from solar panels that can be used in different regions of Turkey. The calculations are based on 22-year average solar energy potential data obtained from NASA. The exergy potential was determined for the coordinates where Turkey is located, and the potential for the regions between the coordinates was determined by the interpolation method. With the interpolation method used, an approximate estimation for the areas where there is no measurement is also provided, and it is aimed at saving the time and cost required for long-term measurements. Among the tilt angles analyzed, the optimum angle for the whole year was determined to be 30 degrees. The exergy potential for 30° inclined surfaces in all coordinates of Turkey is given as a seasonal map. With the use of the maps, it is thought that the optimum angle and exergy potential for different regions and seasons of Turkey will be predicted, and thus it will be easier for new investors to determine the high-potential regions of Turkey.

Assessment of heat flow in the northern part of the Indigiro– Zyryansky trough (Yakutia)

An approximate estimation of the heat flow value was performed for three deep parametric wells drilled in the northern part of the Indigiro-Zyryansky trough. Boreholes have uncovered Paleogene and Upper Jurassic rocks. Geothermal gradients were calculated from the temperature values at the lower boundary of the cryolithozone (0 ºC) and at the downhole. The thermal conductivity of rocks was roughly estimated from published data. The calculated heat flow on the Indigirskaya area is on average 70 mW/m2 . The values of heat flow values were recorded in the previously studied neighboring areas. Thus, the heat flow estimate obtained by the authors in the Indigiro-Zyryansky trough correspond fully to the available data on the heat flow level in this region of East Yakutia.

Rectified Binary Network for Single-Image Super-Resolution.

Binary neural network (BNN) is an effective approach to reduce the memory usage and the computational complexity of full-precision convolutional neural networks (CNNs), which has been widely used in the field of deep learning. However, there are different properties between BNNs and real-valued models, making it difficult to draw on the experience of CNN composition to develop BNN. In this article, we study the application of binary network to the single-image super-resolution (SISR) task in which the network is trained for restoring original high-resolution (HR) images. Generally, the distribution of features in the network for SISR is more complex than those in recognition models for preserving the abundant image information, e.g., texture, color, and details. To enhance the representation ability of BNN, we explore a novel activation-rectified inference (ARI) module that achieves a more complete representation of features by combining observations from different quantitative perspectives. The activations are divided into several parts with different quantification intervals and are inferred independently. This allows the binary activations to retain more image detail and yield finer inference. In addition, we further propose an adaptive approximation estimator (AAE) for gradually learning the accurate gradient estimation interval in each layer to alleviate the optimization difficulty. Experiments conducted on several benchmarks show that our approach is able to learn a binary SISR model with superior performance over the state-of-the-art methods. The code will be released at https://github.com/jwxintt/Rectified-BSR.

Non-coercive Neumann Boundary Control Problems

The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both the state and adjoint state equations. The article establishes the existence and uniqueness of solutions for both equations, with minimal assumptions made about the problem’s data. Next, the regularity of these solutions is studied in three frameworks: Hilbert–Sobolev spaces, Sobolev–Slobodeckiĭ spaces, and weighted Sobolev spaces. These regularity results enable a numerical analysis of the finite element approximation of both the state and adjoint state equations. The results cover both convex and non-convex domains and quasi-uniform and graded meshes. Finally, the optimal control problem is analyzed and discretized. Existence and uniqueness of the solution, first-order optimality conditions, and error estimates for the finite element approximation of the control are obtained. Numerical experiments confirming these results are included.

An Algorithm for Finding the Exact Value of the Argument for the Modulus of Continuity in Estimate of Approximation of a Continuous Periodic Function by a Partial Sum of Its Fourier Series

An Algorithm for Finding the Exact Value of the Argument for the Modulus of Continuity in Estimate of Approximation of a Continuous Periodic Function by a Partial Sum of Its Fourier Series