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The paper proposes and examines a calibration method for inexact models. The method produces a confidence set on the parameters that includes the best parameter with a desired probability under any sample size. Additionally, this confidence set is shown to be consistent in that it excludes suboptimal parameters in large sample environments. The method works and the results hold with few assumptions; the ideas are maintained even with discrete input spaces or parameter spaces. Computation of the confidence sets and approximate confidence sets is discussed. The performance is illustrated in a simulation example as well as two real data examples.

Compressive strength is one of the important property of concrete and depends on many factors. Most of the concrete compressive strength predictive models mainly rely on available literature data, which are too simple to consider all the contributing factors. This study adopted a new approach to predict the compressive strength of sugarcane bagasse ash concrete (SCBAC). A vast amount of data from the literature study and fifteen laboratory tested concrete samples with different dosage of bagasse ash, were respectively used to calibrate and validate the models. The novel Gene Expression Programming, Multiple Linear Regression and Multiple Non-Linear Regression were used to model SCBAC compressive strength. The water cement ratio, bagasse ash percent replacement, quantity of fine and coarse aggregate and cement content were used as an input for models development. Various statistical indicators, i.e., NSE, R2 and RMSE were used to assess the performance of the models. The results indicated a strong correlation between observed and predicted values with NSE and R2 both above 0.8 during calibration and validation for the Gene Expression Programming (GEP). The outcomes from GEP outclassed all the models to predict SCBAC compressive strength. The validity of the model is further verified using data of fifteen tests conducted in the laboratory. Moreover, the cement content in the mix was revealed as the most sensitive parameter followed by water cement ratio form sensitivity analysis. The GEP fulfilled all the criteria for external validity. The simple formulae derived in this study could be used reliably for the prediction of SCBAC compressive strength.

A new empirical equation for the sigmoid pattern of determinate growth, 'the beta growth function', is presented. It calculates weight (w) in dependence of time, using the following three parameters: t(m), the time at which the maximum growth rate is obtained; t(e), the time at the end of growth; and w(max), the maximal value for w, which is achieved at t(e). The beta growth function was compared with four classical (logistic, Richards, Gompertz and Weibull) growth equations, and two expolinear equations. All equations described successfully the sigmoid dynamics of seed filling, plant growth and crop biomass production. However, differences were found in estimating w(max). Features of the beta function are: (1) like the Richards equation it is flexible in describing various asymmetrical sigmoid patterns (its symmetrical form is a cubic polynomial); (2) like the logistic and the Gompertz equations its parameters are numerically stable in statistical estimation; (3) like the Weibull function it predicts zero mass at time zero, but its extension to deal with various initial conditions can be easily obtained; (4) relative to the truncated expolinear equation it provides more reasonable estimates of final quantity and duration of a growth process. In addition, the new function predicts a zero growth rate at both the start and end of a precisely defined growth period. Therefore, it is unique for dealing with determinate growth, and is more suitable than other functions for embedding in process-based crop simulation models to describe the dynamics of organs as sinks to absorb assimilates. Because its parameters correspond to growth traits of interest to crop scientists, the beta growth function is suitable for characterization of environmental and genotypic influences on growth processes. However, it is not suitable for estimating maximum relative growth rate to characterize early growth that is expected to be close to exponential.

The determination of the saturated hydraulic conductivity Ks on a field scale presents a challenge in which several variables have to be considered. As there is no benchmark or reference method for the Ks determination, the suitability of each available method has to be evaluated. This study is aimed at the functional evaluation of three publicly available types of pedotransfer functions (PTFs) with different levels of utilised predictors. In total, ten PTF models were applied to the 56 data sets including the measured Ks value and the required predictors (% sand, silt and clay particles, dry bulk density, and organic matter/organic carbon content). A single agricultural field with a relatively homogenous particle size distribution was selected for the study to evaluate the ability of the PTF to reflect the variability of Ks. The correlation coefficient, coefficient of determination, mean error, and root mean square error were determined to evaluate the Ks prediction quality. The results showed a high variability in Ks within the field; the measured Ks values ranged between 10 and 1261 cm/day. Although the tested PTF models are based on a robust background of soil databases, they could not provide estimates with satisfactory accuracy unless local soil data were incorporated into the PTF development.

Iron concentration in drinking water higher than the recommended value imposes different health problems. There are advanced chemical-based iron extraction techniques, in spite of having certain limitations in developing countries. Due to this, iron removal by using locally available plants is a paramount sustainable option. Therefore, the current study was intended to explore the iron removal efficiency of the powder of Ocimum sanctum Linn. (OSL) leaves from water and investigate its capability by assessing various conditions of operation. The bioadsorption equilibrium isotherm and kinetics of iron extraction onto OSL leaf powder were studied and modelled. The experimental adsorption equilibrium observations served as the basis for a comparison of linear and nonlinear regression techniques for predicting the optimal isotherms and kinetics. The optimum conditions for the extraction of iron were observed to be pH of 5, biomass concentration of 0.2 g, contact time of 2 h, speed of agitation of 150 rpm at 25 °C temperature, while maximum bioadsorption capacity was 123.26 mg/g. The batch bioadsorption of iron obeys the Fritz–Schlunde isotherm and the pseudo-first-order-kinetic model. The isotherm and kinetics parameters obtained using the nonlinear regression method outperformed the linear approach. Moreover, the potential applicability of OSL leaves-based bioadsorbent could be further examined on a large-scale for industrial application.

Many model-free dimension reduction methods have been developed for high-dimensional regression data but have not paid much attention on problems with non-linear confounding. In this paper, we propose an inverse-regression method of dependent variable transformation for detecting the presence of non-linear confounding. The benefit of using geometrical information from our method is highlighted. A ratio estimation strategy is incorporated in our approach to enhance the interpretation of variable selection. This approach can be implemented not only in principal Hessian directions (PHD) but also in other recently developed dimension reduction methods. Several simulation examples that are reported for illustration and comparisons are made with sliced inverse regression and PHD in ignorance of non-linear confounding. An illustrative application to one real data is also presented.

The small island effect (SIE), i.e. the hypothesis that species richness below a certain threshold area varies independently of island size, has become a widely accepted part of the theory of island biogeography. However, there are doubts whether the findings of SIEs were based on appropriate methods. The aim of this study was thus to provide a statistically sound methodology for the detection of SIEs and to show this by re-analysing data in which an SIE has recently been claimed ( Sfenthourakis & Triantis, 2009 , Diversity and Distributions, 15, 131-140). Ninety islands of the Aegean Sea (Greece). First, I reviewed publications on SIEs and evaluated their methodology. Then, I fitted different species-area models to the published data of area (A) and species richness (S) of terrestrial isopods (Oniscidea), with log A as predictor and both S (logarithm function) and log S (power function) as response variables: (i) linear; (ii) quadratic; (iii) cubic; (iv) breakpoint with zero slope to the left (SIE model); (v) breakpoint with zero slope to the right; (vi) two-slope model. I used non-linear regression with R²adj., AICc and BIC as goodness-of-fit measures. Many different methods have been applied for detecting SIEs, all of them with serious shortcomings. Contrary to the claim of the original study, no SIE occurs in this particular dataset as the two-slope variants performed better than the SIE variants for both the logarithm and power functions. For the unambiguous detection of SIEs, one needs to (i) include islands with no species; (ii) compare all relevant models; and (iii) account for different model complexities. As none of the reviewed SIE studies met all these criteria, their findings are dubious and SIEs may be less common than reported. Thus, conservation-related predictions based on the assumption of SIEs may be unreliable.

In the quantitative analysis of dynamic contrast-enhanced magnetic resonance imaging compartment models allow the uptake of contrast medium to be described with biologically meaningful kinetic parameters. As simple models often fail to describe adequately the observed uptake behaviour, more complex compartment models have been proposed. However, the non-linear regression problem arising from more complex compartment models often suffers from parameter redundancy. We incorporate spatial smoothness on the kinetic parameters of a two-tissue compartment model by imposing Gaussian Markov random-field priors on them. We analyse to what extent this spatial regularization helps to avoid parameter redundancy and to obtain stable parameter point estimates per voxel. Choosing a full Bayesian approach, we obtain posteriors and point estimates by running Markov chain Monte Carlo simulations. The approach proposed is evaluated for simulated concentration time curves as well as for in vivo data from a breast cancer study.

The usable floor area is one of the key parameters when appraising residential property. In Poland, valuers have to base their analysis on data from the Real Estate Price Register (RCN) in order to value a property. Unfortunately, these data often turn out to be incomplete, especially with regard to floor area, which makes the selection of reference properties difficult and can lead to erroneous valuation results. To address this problem, a study was conducted that used linear models, non-linear models and machine learning algorithms to calculate the floor area of buildings with complex multi-pitched roofs. The analysis was conducted using data sourced from the Database of Topographic Objects (BDOT10k). Three key factors were identified to provide a reliable estimate of usable floor area: the covered area, the height of the building and, optionally, the number of storeys. The results show that the linear model based on the design data achieved an accuracy of 88%, the non-linear model achieved 89% and the machine learning algorithms achieved 93%. For the existing building data from the city of Koszalin, the best model achieved an accuracy of 90%. The estimated values of the usable area of the building designs for the best model on the test set differed on average from the true ones by 8.7 m2, while for the existing buildings, the difference was 9.9 m2 on average (in both cases, the average relative error was about 7%).

To explore a robust tool for advancing digital breeding practices through an artificial intelligence-driven phenotype prediction expert system, we undertook a thorough analysis of 11 non-linear regression models. Our investigation specifically emphasized the significance of Support Vector Regression (SVR) and SHapley Additive exPlanations (SHAP) in predicting soybean branching. By using branching data (phenotype) of 1918 soybean accessions and 42 k SNP (Single Nucleotide Polymorphism) polymorphic data (genotype), this study systematically compared 11 non-linear regression AI models, including four deep learning models (DBN (deep belief network) regression, ANN (artificial neural network) regression, Autoencoders regression, and MLP (multilayer perceptron) regression) and seven machine learning models (e.g., SVR (support vector regression), XGBoost (eXtreme Gradient Boosting) regression, Random Forest regression, LightGBM regression, GPs (Gaussian processes) regression, Decision Tree regression, and Polynomial regression). After being evaluated by four valuation metrics: R 2 (R-squared), MAE (Mean Absolute Error), MSE (Mean Squared Error), and MAPE (Mean Absolute Percentage Error), it was found that the SVR, Polynomial Regression, DBN, and Autoencoder outperformed other models and could obtain a better prediction accuracy when they were used for phenotype prediction. In the assessment of deep learning approaches, we exemplified the SVR model, conducting analyses on feature importance and gene ontology (GO) enrichment to provide comprehensive support. After comprehensively comparing four feature importance algorithms, no notable distinction was observed in the feature importance ranking scores across the four algorithms, namely Variable Ranking, Permutation, SHAP, and Correlation Matrix, but the SHAP value could provide rich information on genes with negative contributions, and SHAP importance was chosen for feature selection. The results of this study offer valuable insights into AI-mediated plant breeding, addressing challenges faced by traditional breeding programs. The method developed has broad applicability in phenotype prediction, minor QTL (quantitative trait loci) mining, and plant smart-breeding systems, contributing significantly to the advancement of AI-based breeding practices and transitioning from experience-based to data-based breeding.