Bivariate covariance functions of Pólya type

Bivariate extreme value modeling for road safety estimation

Data comprising 7211 lactation records of 2894 cows were used to estimate genetic and phenotypic parameters for milk production (lactation milk yield, LMY and lactation length, LL) and fertility (calving interval, CI; number of services per conception, NSC and age at first calving, AFC) traits. Genetic, environmental and phenotypic trends were also estimated. Variance components were estimated using univariate, bivariate and trivariate animal models on based restricted maximum likelihood procedures. Univariate models were used for each trait, while bivariate models were used to estimate genetic and phenotypic correlations between milk production and fertility traits and between LMY, LL, CI and NSC within each lactation. Trivariate models were used in the analysis of LMY, LL, CI and NSC in the first three lactations. Heritability estimates from the univariate model were 0.16, 0.07, 0.03, 0.04 and 0.01 for LMY, LL, CI, AFC and NSC, respectively. The heritability estimates from trivariate analysis were higher for milk production traits than those from univariate analyses. Genetic correlations were high and undesirable between milk production and fertility traits, while phenotypic correlations were correspondingly low. Genetic trends were close to zero for all traits, while environmental and phenotypic trends fluctuated over the study period.

A study on estimation and prediction in bivariate geostatistical models Bivariate geostatistical models dene random functions for two stochastic processes with known spatial locations. Existence of a Gaussian random elds can be assumed for each latent random variable. This Gaussianity assumption for the latent process is a convenient one for the inferences on the model parameters and for spatial predictions once the joint distribution for a set of points is multivariate normal. The covariance matrix of this distribution should be positivedenite and to have the spatial variability structure between and among the attributes. Gelfand et al. (2004) and Diggle e Ribeiro Jr. ( This work reports on a simulation study of bivariate models together with maximum likelihood estimators and spatial prediction under dierent sets of sampling locations space. Soil sample data from a eld with 51.8 hectares is also analyzed with the two soil attributes observed at 67 spatial locations. Data on pH and base saturation were submitted to spatial descriptive analysis, univariate and bivariate modeling and spatial prediction. To check for advantages of the adoption of univariate or bivariate models, the sample of the more expensive variable was divided into a modeling and testing subsamples. The rst was used to t geostatistical models, and the second was used to compare the spatial prediction precisions in the locations not used in the modeling process.

To identify the genetic determinants of obesity using univariate and bivariate models in a genome scan. We evaluated the genetic and environmental effects and performed a genome-wide linkage analysis of obesity-related traits in 478 subjects from 105 Mexican-American nuclear families ascertained through a proband with documented coronary artery disease. The available obesity traits include BMI, body surface area (BSA), waist-to-hip ratio (WHR), and trunk fat mass as percentage of body weight. Heritability estimates and multipoint linkage analysis were performed using a variance components procedure implemented in SOLAR software. The heritability estimates were 0.62 for BMI, 0.73 for BSA, 0.40 for WHR, and 0.38 for trunk fat mass as percentage of body weight. Using a bivariate genetic model, we observed significant genetic correlations between BMI and other obesity-related traits (all p < 0.01). Evidence for univariate linkage was observed at 252 to approximately 267 cM on chromosome 2 for three obesity-related traits (except for WHR) and at 163 to approximately 167 cM on chromosome 5 for BMI and BSA, with the maximum logarithm of the odds ratio score of 3.12 (empirical p value, 0.002) for BSA on chromosome 2. Use of the bivariate linkage model yielded an additional peak (logarithm of the odds ratio = 3.25, empirical p value, 0.002) at 25 cM on chromosome 7 for the pair of BMI and BSA. The evidence for linkage on chromosomes 2q36-37 and 5q36 is supported both by univariate and bivariate analysis, and an additional linkage peak at 7p15 was identified by the bivariate model. This suggests that use of the bivariate model provides additional information to identify linkage of genes responsible for obesity-related traits.

Indonesia Composite Index (IHSG) is an indicator of stock price changes in Indonesia Stock Exchange. IHSG is time series data that can be modeled with parametric models. But there are some assumptions for parametric model, while the fluctuated IHSG data usually doesn’t occupy these assumptions. Another alternative for this study is nonparametric regression. Penalized spline regression is one of nonparametric regression method that can be used. The optimal penalized spline models depends on the determination of the optimal smoothing parameter λ and the optimal number of knots, that has a minimum value of Generalized Cross Validation (GCV). The best model in this study is penalized spline degree 1 (linear) with 1 knot, that is 5120,625, smoothing parameter λ value is 41590, and GCV value is 1567,203. R 2 value for in sample data is 83,2694% and R 2 value for out sample data is 96,4976% show that the model have a very good performance. MAPE values for in sample data is 0,5983% and MAPE values for out sample data is 0,4974%. Because the value of MAPE in sample and out sample is less than 10%, it means that the performance of the model and forecasting are very accurate. Keywords: Indonesia Composite Index, Nonparametric Regression, Penalized Spline Regression, GCV, MAPE

In this paper, we present an edge detection method based on the thin-plate spline with tension. Under regularization theory, the image is represented in a convolution form between the original image data and a two-dimensional kernel. This convolution kernel is derived from a PDE, which is related to a second order (thin-plate or bending) term and a first order (membrane or tension) term. This image representation involves two parameters: a smoothing parameter (or scale parameter) and a weighted smoothness parameter (which controls the degrees of the continuity of the reconstruction by placing a different weighting on the thin-plate and tension terms). By tuning these parameters, the image can be represented at different scales and with different smoothness requirements. Based on this convolution representation, the edges can be detected by differentiating the image to look for the zero-crossings of the Laplacian. By tuning the values of these two parameters, the edges at the different scales will be extracted.KeywordsEdge DetectionCoarse ScaleModify Bessel FunctionNoise SuppressionConvolution KernelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The estimated probabilistic model of wind data based on the conventional approach may have high discrepancy compared with the true distribution because of the uncertainty caused by the instrument error and limited monitoring data. A sequential quadratic programming (SQP) algorithm-based finite mixture modeling method has been developed in the companion paper and is conducted to formulate the joint probability density function (PDF) of wind speed and direction using the wind monitoring data of the investigated bridge. The established bivariate model of wind speed and direction only represents the features of available wind monitoring data. To characterize the stochastic properties of the wind parameters with the subsequent wind monitoring data, in this study, Bayesian inference approach considering the uncertainty is proposed to update the wind parameters in the bivariate probabilistic model. The slice sampling algorithm of Markov chain Monte Carlo (MCMC) method is applied to establish the multi-dimensional and complex posterior distribution which is analytically intractable. The numerical simulation examples for univariate and bivariate models are carried out to verify the effectiveness of the proposed method. In addition, the proposed Bayesian inference approach is used to update and optimize the parameters in the bivariate model using the wind monitoring data from the investigated bridge. The results indicate that the proposed Bayesian inference approach is feasible and can be employed to predict the bivariate distribution of wind speed and direction with limited monitoring data.

The main purpose of this research is to evaluate the performance of a Bayesian approach for estimating unknown change points using Monte Carlo simulations. The univariate and bivariate unknown change point mixed models were presented and the basic idea of the Bayesian approach for estimating the models was discussed. The performance of Bayesian estimation was evaluated using simulation studies of longitudinal data with different sample sizes, varying change point values, different levels of Level-1 variances, and univariate versus bivariate outcomes. The numerical results compared the performance of the Bayesian methods with the first-order Taylor expansion method and the adaptive Gaussian quadrature method implemented in SAS PROC NLMIXED. These simulation results showed that the first-order Taylor expansion method and the adaptive Gaussian quadrature method were sensitive to the initial values, making the results somewhat unreliable. In contrast, these simulation results showed that Bayesian estimation was not sensitive to the initial values and the fixed-effects and Level-1 variance parameters can be accurately estimated in all of the conditions. One concern was that the estimates of the Level-2 covariance parameters were found to be biased when the Level-1 variance was large in the bivariate model. However, and in general, the new Bayesian approach to the estimation of turning points in longitudinal data proved to be quite robust and practically useful.

Heritability of scrotal circumference adjusted and unadjusted for body weight in nellore bulls, using univariate and bivariate animal models

BackgroundThe focus in dairy cattle breeding is gradually shifting from production to functional traits and genetic parameters of calving traits are estimated more frequently. However, across countries, various statistical models are used to estimate these parameters. This study evaluates different models for calving ease and stillbirth in United Kingdom Holstein-Friesian cattle.MethodsData from first and later parity records were used. Genetic parameters for calving ease, stillbirth and gestation length were estimated using the restricted maximum likelihood method, considering different models i.e. sire (−maternal grandsire), animal, univariate and bivariate models. Gestation length was fitted as a correlated indicator trait and, for all three traits, genetic correlations between first and later parities were estimated. Potential bias in estimates was avoided by acknowledging a possible environmental direct-maternal covariance. The total heritable variance was estimated for each trait to discuss its theoretical importance and practical value. Prediction error variances and accuracies were calculated to compare the models.Results and discussionOn average, direct and maternal heritabilities for calving traits were low, except for direct gestation length. Calving ease in first parity had a significant and negative direct-maternal genetic correlation. Gestation length was maternally correlated to stillbirth in first parity and directly correlated to calving ease in later parities. Multi-trait models had a slightly greater predictive ability than univariate models, especially for the lowly heritable traits. The computation time needed for sire (−maternal grandsire) models was much smaller than for animal models with only small differences in accuracy. The sire (−maternal grandsire) model was robust when additional genetic components were estimated, while the equivalent animal model had difficulties reaching convergence.ConclusionsFor the evaluation of calving traits, multi-trait models show a slight advantage over univariate models. Extended sire models (−maternal grandsire) are more practical and robust than animal models. Estimated genetic parameters for calving traits of UK Holstein cattle are consistent with literature. Calculating an aggregate estimated breeding value including direct and maternal values should encourage breeders to consider both direct and maternal effects in selection decisions.

Recently several efforts have been made to model space–time covariance functions. The majority of covariance model structures are monotonic decreasing, typically remains non-negative. One class of spatially isotropic models proposed by Gneiting (J Am Stat Assoc 97(458):590–600, 2002) has been used as a building block to model various complicated non-separable models. Kent et al. (Biometrika 98(2):489–494, 2011) draw out attention on the counterintuitive presence of possible dimple property associated with these covariance models. In this paper, we first attempt to propose a simple approach to model potentially negative-value stationary space–time models. Second, we show that in certain circumstances such space–time models possess a reverse (pointing upward) dimple. To illustrate analytical findings, results of numerical calculations and numerous plots are presented.

Spatial data in the Earth and environmental sciences acquired by instrument collection or simulation are constrained to finite, discrete, (ir)regular grids whose geometry is delineated by a boundary within which missingness, either random or structured, may exist. We model (ir)regularly sampled Cartesian spatial data as realizations of discrete two- and three-dimensional random fields whose covariance structure we estimate parametrically with a spectral-domain maximum-likelihood estimation strategy using the debiased Whittle likelihood, which efficiently counters the effects of aliasing and spectral leakage that arise from finite sampling and boundary effects. We work with the general, flexible Matérn class of covariance functions, which characterizes the shape of a field through three parameters that quantify its amplitude, smoothness, and correlation length. We quantify parameter covariance analytically and asymptotically based on the parametric model and sampling grid alone, agnostic of observed data. Our uncertainty quantification allows us to study how sampling geometry imparts uncertainty on a covariance model and provides a path for optimizing the design of a sampling grid to reduce error for an anticipated model. We formulate several approaches for interrogating our model residuals to interpret where real Earth data depart from the null hypotheses of Gaussianity, stationarity, and isotropy. We explore select case studies that demonstrate the broad applicability of our models across Earth science disciplines and develop software in MATLAB and Python for implementation by domain scientists, in hydrology, and elsewhere.

Objective: Estimate (co)variance components and genetic parameters of live weight traits and examine the effect of selection culling when using bivariate analysis in registered Charolais beef cattle. Materials and methods: The effect of incomplete data over accuracies was compared, expected progeny differences (EPD) and standard errors of prediction (SEP) were obtained and evaluated by comparing univariate and bivariate models for birth (BW), weaning (WW) and yearling (YW) weights. Results: Bivariate models for WW and YW, improved accuracies of EPDs and reduced the SEPs. Joint analysis for BW and WW increased in a 38% the accuracies and reduced SEP estimators for YW (p&lt;0.001). Accuracies of EPD for BW obtained from univariate models were improved when BW was included in bivariate models. Conclusions: The results support the use of bivariate genetic analysis in limited or incomplete live weight indicators databases that were registered after birth, such as weaning and yearling weight.

Recently, neuro-transfer function (neuro-TF) has become a recognized method for electromagnetic (EM) parametric modeling. The existing neuro-TF methods use the vector fitting technique to perform transfer function (TF) parameter extraction, commonly encountering nonsmoothness and discontinuity issues for the extracted TF parameters with respect to geometrical parameters. This letter proposes an advanced autoencoder TF parameter extraction technique for neuro-TF parametric modeling of microwave components. In the proposed technique, the autoencoder is introduced to extract a set of TF parameters as TF parameters from the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$</tex-math> </inline-formula> -parameters with the encoder part and generate a decoder function as the TF in the original neuro-TF model. The TF parameters extracted using the proposed technique behave much smoother than the TF parameters extracted using traditional vector fitting. Meanwhile, the proposed technique avoids the discontinuity problem caused by vector fitting in the standard neuro-TF method. Parametric modeling using the smooth TF parameters can thus have higher accuracy than modeling with nonsmooth TF parameters. The proposed technique is demonstrated by two examples of EM parametric modeling of microwave components.

In the era of autonomous vehicles (AVs), accurately predicting extreme traffic conflicts is vital for improving road safety. This study leverages Extreme Value Theory (EVT) to analyse AV-generated conflict data, focusing on Modified Time-to-Collision (MTTC) and Post-Encroachment Time (PET) indicators. We compare univariate and bivariate EVT models using Peak-Over-Threshold (POT) and Block Maxima (BM) methods, addressing data’s spatiotemporal gaps. A novel model validation criterion is introduced, applicable across modeling approaches and sample sizes, independent of crash records. Results show bivariate POT models outperform univariate models by up to 20% lower Mean Absolute Error (MAE) and offer greater temporal stability. Univariate BM models are reliable only for short intervals (∼5–7 min), while POT models maintain or improve accuracy over time. Covariate selection significantly impacts model performance, varying by structure. Overall, bivariate POT models prove most effective, offering practical, adaptive tools for AV-based traffic conflict analysis in diverse urban environments.