Statistical Estimation Research Articles

System identification-based tuning of PID algorithm parameters by using PSO and genetic algorithms

The PID control algorithm is the most used industrial control method. This is due to its simplicity, ease of use, and because it yields stable results. PID parameters vary for each controller; therefore, finding the optimal parameters is crucial for obtaining good results. However, tuning PID parameters for complex systems is not a trivial task and is also somewhat difficult as conventional techniques rely on time and effort manual tuning or rely on simplified statistical estimation techniques of the system’s model yielding sub- optimal results. In this project, we propose to use machine learning for PID parameter tuning on proprietary historical time series operating process control data. The data is processed with the help of computational and machine-learning techniques to better identify the process model and predict the optimal PID parameters. The research methodology consists of three main steps. First, process-model identification is done by using a Radial Basis Function (RBF) neural network. Secondly, Particle Swarm Optimization (PSO) hybrid with Genetic Algorithms (GA) is used for finding the optimal PID parameters. The PID values predicted by PSO, will be fed to GA optimization process as an initial starting point. The final step consists of integrating the identified process model with the PID optimization algorithm in a computer-based simulation environment (Simulink). The experimental simulations are done for various study cases. Results showed that the predicted PID parameters error rate and standard deviation for PID control and process are decreased, which enhances the process controlling and stability.

Alternative Solution to Estimate Cucumber Crop Evapotranspiration in Shade Nets for the Valle de Culiacán, Mexico

Objective: This work aimed to estimate the evapotranspiration of cucumber crop grown in a shade house in Valle de Culiacán, México. Design/methodology/approach: The FAO56 method was used with a variation of the FAO Penman-Monteith equation, and a non-conventional evaporimeter to measure evaporation inside the shade house. Using the estimated reference evapotranspiration and the measured evaporation, pan coefficients were calculated, and a mathematical model was proposed to calculate this coefficient based on the meteorological parameters: air temperature, relative humidity, and net solar radiation. Results: The estimated crop evapotranspiration was 417.6 mm. The linear regression between the reference evapotranspiration estimated with FAO56 and calculated with evaporation and adjusted evaporimeter pan coefficient yielded excellent statistical estimators (R2>0.9). Findings/conclusions: The analysis of the evaporimeter pan coefficient's dependence on meteorological parameters indicates a strong dependence on air temperature, net solar radiation, and vapor pressure deficit, but not on relative humidity.

Consumption Dynamics in Mixed-Income Neighborhoods with Connected Households

AbstractWe investigate the dynamics of household consumption in a setting in which households are connected across income classes. Low- and high-income households form preferences endogenously, conditional on their own and their neighbor’s past consumption. The modeling effort relies on a stochastic dynamic model of interdependent consumer choice in which the demand for commodities evolves according to a non-linear difference equation with stochastic initial states. The analysis targets a region of the parameter space that corresponds to salient features of a mixed-income neighborhood in which households are connected. Standard methods of asymptotic analysis of dynamic systems (e.g. bifurcation analysis) are combined with numerical simulation, statistical modelling of extreme events and statistical estimation techniques to investigate the dynamics. From the mathematical point of view, our analysis reveals the existence of intricate bifurcation pattern, coexistence of multiple attractors, complex basins and long transients. The essential economic finding states that key features of household consumption vary significantly in the influence the high-income households exert on the preference formation of the low-income households. In particular, we find that the prevalence of long transients, i.e. long waiting times before convergence to asymptotic states occur, is inversely related to the type of connectedness considered. We demonstrate that the dynamics of the consumption trajectory evolving over an extended time period before it settles on long-run simple consumption pattern, may not at all be captured by an asymptotic state. Thus, policies targeting the economies in mixed-income neighborhoods that are solely based on information about long-run consumption states, might trigger unwanted, unanticipated effects.

Estimation of Motion Statistics From Statistics of Received Power in Low-Power IoT Sensing Nodes

Estimation of Motion Statistics From Statistics of Received Power in Low-Power IoT Sensing Nodes

Novel Uncertainty Quantification Through Perturbation-Assisted Sample Synthesis.

This paper introduces a novel Perturbation-Assisted Inference (PAI) framework utilizing synthetic data generated by the Perturbation-Assisted Sample Synthesis (PASS) method. The framework focuses on uncertainty quantification in complex data scenarios, particularly involving unstructured data while utilizing deep learning models. On one hand, PASS employs a generative model to create synthetic data that closely mirrors raw data while preserving its rank properties through data perturbation, thereby enhancing data diversity and bolstering privacy. By incorporating knowledge transfer from large pre-trained generative models, PASS enhances estimation accuracy, yielding refined distributional estimates of various statistics via Monte Carlo experiments. On the other hand, PAI boasts its statistically guaranteed validity. In pivotal inference, it enables precise conclusions even without prior knowledge of the pivotal's distribution. In non-pivotal situations, we enhance the reliability of synthetic data generation by training it with an independent holdout sample. We demonstrate the effectiveness of PAI in advancing uncertainty quantification in complex, data-driven tasks by applying it to diverse areas such as image synthesis, sentiment word analysis, multimodal inference, and the construction of prediction intervals.

Statistical Estimation of Production and Costs Functions of Cucumber Crop under greenhouse system: A Field Study

Statistical Estimation of Production and Costs Functions of Cucumber Crop under greenhouse system: A Field Study

Tracing gaseous filaments connected to galaxy clusters: The case study of Abell 2744

Filaments connected to galaxy clusters are crucial environments for studying the build up of cosmic structures as they funnel matter towards the clusters' deep gravitational potentials. Identifying gas in filaments is a challenge, due to their lower density contrast, which produces faint signals. Therefore, the best opportunity to detect these signals is in the outskirts of galaxy clusters. We revisited the X-ray observation of the cluster Abell 2744, using statistical estimators of the anisotropic matter distribution to identify filamentary patterns around it. We report, for the first time, the blind detection of filaments connected to a galaxy cluster from X-ray emission using a filament-finder technique and a multipole decomposition technique. We compare this result with filaments extracted from the distribution of spectroscopic galaxies using the same two approaches. This allowed us to demonstrate the robustness and reliability of our techniques in tracing the filamentary structure of three and five filaments connected to Abell 2744, in two and three dimensions, respectively.

A saddlepoint approximation for the smoothed periodogram

Poor variance properties of the periodogram often limit its practical applicability to a wide range of modern spectral estimation and detection applications. The smoothed periodogram, a refined periodogram-based method, is one such nonparametric approach to reducing variance. Neighboring spectral samples are averaged across a spectral window, as opposed to the more common temporal or lag window. Tapered spectral windows and other modifications needed to address the time-bandwidth product and resolution-variance trade-offs complicate the statistical analysis, making it difficult to quantify statistical performance. In addition, approximate distributions for the smoothed periodogram require a priori normalization along with simplifying assumptions to yield computationally tractable results. Here, under mild asymptotic conditions, the distribution derived prior to normalization is shown to be computationally intractable in most cases. First-order statistical approximations are computationally stable but result in sizeable inaccuracies, particularly in the tails. We use a saddlepoint approximation, a second-order asymptotic method, that allows for accurate statistical characterization but is also numerically stable. Monte Carlo simulations are used to validate the results and to illustrate the robustness of the approach. Finally, its utility is demonstrated on a real-world dataset relevant to the side-channel and hardware cybersecurity communities.

Semiparametric Inference for Two-Phase Studies with Ordinal Outcomes

Background: The two-phase design is an increasingly used approach in health research. In Phase 1, broad data are collected on a large sample size, and in Phase 2, the correlation of auxiliary variables with an expensive variable is used to select a small but more informative sample. Objectives: Previous research on two-phase design has primarily focused on binary, continuous, and time-to-event outcomes. Recognizing the lack of research on ordinal outcomes, we propose a novel approach for three logit models with proportional odds: cumulative logit (CL), adjacent category (AC), and stopping ratio (SR). Additionally, we examine the validity of our method through four simulation scenarios with various outcome distributions. Methods: We have developed a semiparametric maximum likelihood model to incorporate Phase 1 data. An expectation-maximization (EM) algorithm was used to obtain the estimates while the Louis method was employed to calculate the covariance matrix. We compare the results estimated by our method with those obtained using only Phase 2 data under both simple random sampling and balanced outcome-dependent sampling (ODS). Results: In all experiments, balanced ODS led to reduced bias and higher relative efficiency, and the advantage was more noticeable with higher variability in sampling probability between the outcome categories. The EM method led to improved results in balanced ODS for the CL and SR models, but it was not as effective for the AC model. Conclusions: These findings suggest the efficacy of our method in incorporating Phase 1 data to enhance the quality of statistical estimates when used with balanced ODS.

Bridging theory and data: A computational workflow for cultural evolution

Cultural evolution applies evolutionary concepts and tools to explain the change of culture over time. Despite advances in both theoretical and empirical methods, the connections between cultural evolutionary theory and evidence are often vague, limiting progress. Theoretical models influence empirical research but rarely guide data collection and analysis in logical and transparent ways. Theoretical models themselves are often too abstract to apply to specific empirical contexts and guide statistical inference. To help bridge this gap, we outline a quality-assurance computational workflow that starts from generative models of empirical phenomena and logically connects statistical estimates to both theory and real-world explanatory goals. We emphasize and demonstrate validation of the workflow using synthetic data. Using the interplay between conformity, migration, and cultural diversity as a case study, we present coded and repeatable examples of directed acyclic graphs, tailored agent-based simulations, a probabilistic transmission model for longitudinal data, and an approximate Bayesian computation model for cross-sectional data. We discuss the assumptions, opportunities, and pitfalls of different approaches to generative modeling and show how each can be used to improve data analysis depending on the structure of available data and the depth of theoretical understanding. Throughout, we highlight the significance of ethnography and of collecting basic cultural and demographic information about study populations and call for more emphasis on logical and theory-driven workflows as part of science reform.

An analysis of estimation strategies for knock control

Since knock behaves as a random process, all knock controllers regulate some statistical property of this process which must be estimated from the data. The choice of the statistical metric used for feedback, its target value, and the method used for its estimation all have a strong impact on the performance of the closed loop system. In this work, expressions for the asymptotic variance of the estimates of different test statistics are derived and used to compare empirical versus parametric estimation methods. The variance of different metrics and the slope of their response curves (e.g. knock probability vs knock percentile intensity feedback) are also used to compute and compare the efficacy of these different measures for knock control purposes. The efficacy is seen to vary as a function of the chosen knock probability target, and lower knock thresholds/higher knock rate targets are recommended. Finally, the estimator dynamics are shown to dominate the dynamics of the closed loop response, and estimates obtained using a sliding window versus an exponentially weighted moving average are compared and contrasted. In each case, the results are illustrated using closed loop simulations of controller response subject to disturbances.

Turbulence statistics estimation across a step change in roughness via interpretable network-based modelling

Abstract This study proposes a data-driven methodology to complement existing time-series measurement tools for turbulent flows. Specifically, a cluster-based transition network model is employed for the estimation of velocity time traces and their corresponding statistics. The method is tested on a laboratory-modelled turbulent boundary layer over a step change in surface roughness, where velocity time series are recorded for training and validation purposes via Laser Doppler Anemometry. Results show that our approach can estimate velocity and momentum flux statistics within experimental uncertainty over a rough surface through an unsupervised approach, and across the step change in roughness through a semi-supervised variant. The friction velocity across the domain is also estimated with 10\% relative error compared to the measured value. The proposed methodology is interpretable robust against the main methodological parameters. A reliable data-driven framework is hence provided that can be integrated within existing laboratory setups to supplement or partially replace measurement systems, as well as to reduce wind tunnel running times.

Bibliometric analysis of scientific literature on the use of suppositories in the treatment of prostate cancer patients

Nowadays, cancer remains one of the main causes of death worldwide. Statistical data from various literary sources indicate that more than 130,000 people in Ukraine receive this diagnosis as a sentence every year. Cancer can affect any organs of the human body and, over time, the entire organism. In 2024, the agency of the World Health Organization on cancer and the International Agency of Cancer Research published the latest statistical estimates of this pathology in a global format, where prostate cancer is among the five most common oncological pathologies and takes the fourth place. Oncological diseases are one of the priority areas of healthcare development in accordance with the Order of the Ministry of Health of Ukraine No. 1832 dated 07.10.2022 “On Approval of Priority Areas of Healthcare Development for 2023–2025”. It was this fact that determined the choice of the direction of this research in the matter of finding information on the provision of pharmaceutical care, namely the use of a drug – a rectal suppository for the treatment of prostate cancer. The aim of the work is to carry out a bibliometric analysis and further generalize the data of the scientific literature to study the prognostic value and features of the prescription of suppositories in the treatment of prostate cancer. Materials and methods. The data search was conducted in the PubMed electronic database using the following key terms: “prostate cancer and suppositories”, “prostate cancer”. To monitor and analyze international scientific research, with the help of visualization tools and modern SciVal citation metrics using the online platform, bibliometric analysis can be performed. Using the VOSviewer functional program, bibliometric networks were constructed and visualized. Results. A map of the relationships between the most used keywords on the topics of “prostate cancer” and “prostate cancer and suppositories”, grouped into clusters for the period from 1986 to 2024, was built. The clustering of the most used keywords on the subject of “prostate cancer” for the specified period is summarized. According to the bibliographic analysis, interest in the above topic was highest in 2014 and 2021. Conclusions. According to the bibliographic analysis, the interest in the subject of the patients’ treatment with prostate cancer disease continues to grow from 1998 up to the present. The analysis of publication activity using the visualization tool of bibliometric networks VOSviewer for the period from 2014 to 2024 for the key words “prostate cancer” has shown the presence of 14 clusters. The largest cluster is devoted to modern methods of prostate cancer treatment, studies of gene rearrangement, target therapy, carcinogenesis.

MethylCallR : a comprehensive analysis framework for Illumina Methylation Beadchip

DNA methylation is a molecular process that mediates gene-environment interactions. Epigenome-wide association studies (EWAS) using the Illumina Human Methylation BeadChip are powerful tools for quantifying the relationship between DNA methylation and phenotypes. Recently, the Illumina Methylation EPICv2 BeadChip (EPICv2) was released, which includes new features, such as duplicated probes and changed probe names. Several published algorithms have been updated to address these features in EPICv2. However, appropriate EPICv2 preprocessing and integration with previous microarray versions remain complex. Therefore, MethylCallR, an open-source R package designed to provide standard procedures for performing EWAS using Illumina methylation microarrays including EPICv2, was developed. MethylCallR can be used to control duplicated probes in EPICv2, by using pre-set data implemented in MethylCallR or new customized data. MethylCallR includes a straightforward conversion function between different types of Illumina Human Methylation BeadChips. Using MethylCallR, potential outlier sample detection and statistical power estimation were conducted and used to select meaningful probes. Publicly available data was analyzed using MethylCallR and the findings were compared to that of a previous study.

Quantification and Sensitivity Analysis of the Model Uncertainty in the Projectile-Barrel Coupled Artillery Dynamics System Based on Random Matrix Theory

Simplifications in the engineering of artillery firing dynamics modeling introduce model uncertainty, which seriously affects the model’s predictive performance. To this end, a typical variable-section hollow cylindrical cantilever beam structure in artillery firing dynamics is investigated in this paper. The statistical approximation methods quantify parameter and model uncertainty separately, and their respective confidence intervals were calculated and compared. The results show that the traditional parameter uncertainty approach overestimates the parameter uncertainty ranges, and introducing the model uncertainty approach dramatically improves the model prediction performance. Additionally, a projectile-barrel coupled artillery dynamics model considering model uncertainty is established, and its effectiveness is validated through the actual launch experiments. The sensitivity of the dynamic responses to the system matrix, namely model uncertainty, is further analyzed. This paper provides theoretical references for the study of uncertainty in artillery launch dynamics and proposes effective methods to enhance the predictability of computational models for complex structural systems.

Foraging strategy as a route for sexual size dimorphism evolution.

Female-biased sexual size dimorphism stands as a widespread evolutionary pattern. Fecundity selection, favouring larger females with greater reproductive output, is a leading explanation. However, larger body sizes demand greater energy intake, potentially hindering the evolution of extreme female sizes. Thus, the evolution of more lucrative foraging tactics may allow for an increase in size. Hence, coupled with selection against larger males, fecundity selection should result in larger SSD in species with more lucrative foraging strategies. Crab spiders are sit-and-wait predators that hunt in several plant substrata. Species that forage on flowers or employ prey-luring strategies likely have access to higher food intake than other species. We extracted body size measurements of 614 crab spider species from 43 genera and classified them based on their foraging strategy. Our findings show that foraging strategies that provide higher energy input (EFS) result in larger SSD. Statistical estimates indicate that females have a cephalothorax width 91% larger than males in EFS species, compared to 26% larger females than males in non-EFS species. These differences possibly arise due to larger females and smaller males. The effects on male size reduction might result from scramble competition, whereas the increase in female size is likely due to fecundity selection. These results suggest that the shift towards more lucrative foraging strategies may have been a key event in body size and SSD evolution in crab spiders.

A flexible approach for normal approximation of geometric and topological statistics

A flexible approach for normal approximation of geometric and topological statistics

Agricultural innovation for climate change: limited but positive impacts of commercialized drought-tolerant corn

Abstract The extent to which new technologies can countervail the risks posed by climate change is a critical element for designing adaptation strategies. This study uses new experimental data spanning 17 US states from 2008 to 2023 to examine the potential impact of recently commercialized drought tolerant (DT) traits on both yield and yield resilience in US corn production. We find that there is no yield advantage for DT hybrids under average weather conditions, but they improve yield resilience, particularly with respect to precipitation. These effects are spatially heterogeneous, such that DT has a positive yield impact in the droughty, western US, but a small, or even negative, impact in the central and eastern US. In addition, the presence of DT reduces yield variance and kurtosis, and increases skewness, all of which imply a reduction in yield risk. Using the statistical model estimates, we project the impact of DT on corn yields under future climate conditions obtained from 20 general circulation models with two representative concentration pathways. The projected ensemble means of yield gains are 6.34 bu/acre and 5.39 bu/acre under moderate and extreme warming scenarios, respectively, by the mid-twenty-first century. These gains compensate for 23% and 13.5% of total yield loss due to climate change. Our results indicate that current commercial DT hybrids reduce yield risk, improve resilience with respect to precipitation, and have the potential to offer moderate benefits under climate change warming scenarios.

Integration of fixed-frequency and FM-CW (frequency-modulated continuous-wave) reflectometers for coincident turbulence measurements on LTX-β (Lithium Tokamak eXperiment-β).

The fixed-frequency and frequency-modulated continuous-wave (FM-CW) reflectometers on LTX-β (Lithium Tokamak eXperiment-β) have been configured to use the same transmission lines and antenna arrays for coincident views of the core and edge plasma. The fixed-frequency channels (13.1-20.5 and 20-40GHz, tunable between discharges) provide time-resolved measurements of density fluctuations, while the FM-CW channels (13.1-20.2 and 19.5-33.5GHz) measure the density profile and fluctuations, with high spatial resolution and a sampling rate determined by the frequency sweep interval (5 μs). Data from both reflectometers are synchronously acquired to simultaneously leverage the wide bandwidth and high spatial resolution of the respective systems. Experiments showed that mutual crosstalk interference is momentary and does not diminish the capability of either system. Spectral analysis indicated broad power spectra (several hundreds of kHz) and suggests that the signals from the FM-CW system are consistent with under-sampled fixed-frequency signals. Radial correlations were explored using data from the two reflectometers, as well as from the FM-CW system alone. The core channels showed high levels of agreement between these two comparisons, suggesting that the data from the reflectometers are interchangeable for statistical estimates. For the edge channels, comparisons using data from the FM-CW reflectometer alone showed significant decorrelation due to time lag caused by the finite frequency up-sweep duration. Alternatively, this effect is eliminated when cross-correlating data from the different reflectometers. These results highlight the advantages of operating the fixed-frequency and FM-CW reflectometers in this manner, where the combined system can overcome the limitations of each separate system.

The joint effect of changes in urbanization and climate on trends in floods: A comparison of panel and single-station quantile regression approaches

Estimates of annual maximum (peak) flow quantiles are needed for basins undergoing changes in both urbanization and climate. Most previous work on the effect of urbanization on peak flows has considered urbanization alone and only the spatial variation in flood quantiles or its mean temporal effect, and most work on the effect of nonstationarity in climate has focused on single-station analyses, which give uncertain results for extreme quantiles. To address these gaps, three approaches to the statistical estimation of the joint effects of changes in impervious cover and climate on the estimation of peak-flow quantiles were compared: single-station quantile regression; a fixed effect panel-quantile regression (pQR) method using a location (mean) shift to homogenize the panel; and a location-scale panel regression model (pQRmom), which accounts for both scale (variance) and location effects. The different approaches were applied to a dataset consisting of instantaneous annual peak flows from 127 minimally nested basins in the midwestern United States with at least 4 % change in imperviousness. The annual maximum daily discharge from a water-balance model was selected as the primary climate predictor; in addition, to provide a comparison of climate predictors, precipitation was also considered. The coefficients from single-station regressions were usually sufficiently certain to determine the effects of climate variation but usually too uncertain to estimate the effects of urbanization. The panel-quantile regression approaches give much more certain results, but their estimates of quantile dependence differ: although both indicate urbanization effects decreasing with decreasing annual exceedance probability (AEP), the pQRmom urbanization coefficients are insignificantly different from zero for AEPs less than 0.10, whereas the pQR coefficients remain positive and are significant except for AEP = 0.01, the smallest AEP value considered. Although the location-scale structure of the pQRmom approach has less flexible quantile dependence than the pQR approach, the pQRmom approach has somewhat lower overall error, and it is found that by subsetting the dataset to homogenize the scale effects, the pQR and pQRmom results become similar, indicating the insignificant urbanization coefficients for small AEPs of the pQRmom results are likely correct for the study dataset.