rss_2.0Biometrical Letters FeedSciendo RSS Feed for Biometrical Letters Letters Feed on parametric functions in the linear model<abstract> <title style='display:none'>Summary</title> <p>Starting from a simple Gauss–Markov model, this paper presents notes about criteria for the estimability of parametric functions of the vector of interest in linear models. The results obtained for the transformed models are compared with known results from the literature.</p> </abstract>ARTICLEtrue’s inequality for synchronous functions and its consequences<abstract> <title style='display:none'>Summary</title> <p>The theory of inequalities is an essential tool in all fields of the theoretical and practical sciences, especially in statistics and biometrics. Fujiwara’s inequality provides relationships between expected values of products of random variables. Special cases of this inequality include important classical inequalities such as the Cauchy–Schwarz and Chebyshev inequalities.</p> <p>The purpose of this article is to prove Fujiwara’s inequality in abstract probability spaces with more general assumptions for random variables than those associated with monotonicity as found in the literature. This newly introduced property of random variables will be called synchronicity. As a consequence, we obtain inequalities originated by Chebyshev, Hardy–Littlewood–Pólya and Jensen–Mercer under new conditions.</p> <p>The results are illustrated by some examples constructed for specific probability measures and specific random variables. In biometrics, the obtained inequalities can be used wherever there is a need to compare the characteristics of experimental data based on means or moments, and the data can be modeled using functions that are synchronous or convex.</p> </abstract>ARTICLEtrue learning methods in the detection of brain tumors<abstract> <title style='display:none'>Summary</title> <p>Brain tumor is a very serious disease from which many people die every day. Appropriate early diagnosis is extremely important in treatment. In recent years, machine learning methods have come to the aid of doctors, allowing them to automate the process of brain tumor detection. It is a useful tool that can support doctors in their daily work. We consider here the use of machine learning methods to detect brain tumors based on magnetic resonance images. We use artificial neural networks to classify the images into those containing and those without a brain tumor. More specifically, we apply convolutional neural networks on appropriately transformed input data. The three proposed convolutional neural network models were created based on the pre-trained VGG19, DenseNet-121, and InceptionV3 networks, which achieved an accuracy of 92.59%, with areas under the ROC curve ranging from 0.95 to 0.96. The precision, sensitivity, and F1-score are also satisfactory and promising. These results are better than those for the models presented on the Kaggle platform.</p> </abstract>ARTICLEtrue identification for a linearly structured covariance matrix: part II<abstract> <title style='display:none'>Summary</title> <p>Covariance matrices with a linear structure are widely used in multivariate analysis. The choice of covariance structure can be made from a set of possible linear structures. As a result, the most appropriate structure is determined by minimizing the discrepancy function. This paper is a continuation of previous work on identifying linear structures with an entropy loss function as a discrepancy function. We present extensive simulation studies on the correctness of identification with the assumed pentagonal banded Toeplitz structure.</p> </abstract>ARTICLEtrue relationships between yield of maize ( L.) and its components<abstract> <title style='display:none'>Summary</title> <p>A field experiment was carried out in the years 2017–2019 on the fields of the Experimental Station in Chrząstowo, belonging to the Research Centre for Cultivar Testing in Słupia Wielka. It was carried out for 3 years in the same split-plot design with 2 experimental factors in 3 field replicates. The following factors were studied: A – 1st order factor – maize variety: A1 – ES Bombastic (FAO 230-240) – single cross hybrid (SC), A2 – ES Abakus (FAO 230-240) – three-way cross hybrid (TC, stay-green), A3 – ES Metronom (FAO 240) – single cross hybrid (SC, stay-green + roots power). B – 2nd order factor – type of nitrogen fertilizer: B1 – control (without N application), B2 – ammonium nitrate, B3 – urea, B4 – ammonium nitrate + N-Lock, B5 – urea + N-Lock, B6 – Super N-46, B7 – UltraGran stabilo. In this study, we investigated whether there was a functional relationship between maize grain yield and ear number, TSW (thousand-seed weight), and seed number per ear. Additionally, we investigated whether there was a functional relationship between maize grain yield and ear number, TSW, and seed number per ear for each type of fertilization in a given study year, as well as for each type of fertilization regardless of year.</p> </abstract>ARTICLEtrue methods for a linearly structured covariance matrix<abstract> <title style='display:none'>Summary</title> <p>Covariance matrices with a linear structure are widely used in multivariate analysis. The choice of the most appropriate covariance structure can be made from a class of possible linear structures. Once we have made the choice, an important question is how we can estimate the covariance matrix for a given covariance structure. This article describes methods used to estimate the structured covariance matrix, and indicates the advantages and disadvantages of the selected methods.</p> </abstract>ARTICLEtrue Poisson Regression Modeling of Plant Protein Consumption<abstract> <title style='display:none'>Summary</title> <p>This research fitted a discrete distribution for modeling count data. Specifically, Zero-Inflated Poisson (ZIP) regression was used to model plant protein consumption by 400 randomly sampled individuals in Wukari. The data was collected by questionnaire. The ZIP regression model was used based on its ability to model data with excess zeros present in the collected data. Variables considered and used for the analysis are Age, Body Mass Index, Blood Pressure, Occupation, Gender, Weight, Height, Body Reaction, and Consumption Class. The parameters of the ZIP model were estimated using the maximum likelihood estimation technique. The model was tested for Goodness of Fit (GoF) using deviance, scaled deviance, Pearson–<italic>χ</italic><sup>2</sup> and scaled Pearson–<italic>χ</italic><sup>2</sup> statistics. The results obtained showed that Age, Gender, and Reaction were significant at 5%, and the GoF tests revealed that the Zero-Inflated Poisson regression produces a good fit and is a good model for overcoming the overdispersion effect.</p> </abstract>ARTICLEtrue chemical balance weighing designs with positively correlated errors: part II<abstract> <title style='display:none'>Summary</title> <p>Some questions related to the problem of determining a chemical balance weighing design satisfying the criterion of D-optimality are considered. The theory is based on the assumption that the measurements are equally positively correlated and have the same variances. In this paper, we present a method of adding three measurements to a regular D-optimal chemical balance weighing designs to obtain a highly D-efficient chemical balance weighing design. The problem formulated in this way is an extension of results contained in a paper previously published in <italic>Biometrical Letters</italic>.</p> </abstract>ARTICLEtrue, uniqueness, boundedness and stability of periodic solutions of a certain second-order nonlinear differential equation with damping and resonance effects<abstract> <title style='display:none'>Summary</title> <p>In this paper, some qualitative behaviors of solutions for certain second-order nonlinear differential equation with damping and resonance effects are considered. By employing Lyapunov’s direct method, a complete Lyapunov function was used to investigate the stability of the system. Krasnoselskii’s fixed point theorem was used to establish sufficient conditions that guaranteed the existence and boundedness of a unique solution. The results show that the equilibrium point was asymptotically stable. Furthermore, a test for periodicity was conducted using the Bendixson criterion, and the results showed that the solution of the second-order nonlinear differential equation is aperiodic, which extends some results from the literature.</p> </abstract>ARTICLEtrue analysis of spring oat genotypes in south-west Poland<abstract> <title style='display:none'>Summary</title> <p>Oat is a grain in high demand, due to its physiological and nutritional attributes as a functional food. Oat is rich in <italic>β−</italic>glucans, and high in tocopherol and other dietary fibre components. It is also used for forage, fodder, chaff and as a major component of infant foods. In the present study, oat yields from six experimental stations in south-western Poland, obtained in 2019–2022, were analysed using three different linear mixed models that can be associated with three different stabilities. It is shown that the genotype Perun had the highest mean yield among the tested genotypes, while the genotype Armani was the most stable. Armani and Pablo had the lowest values of the GSI index, making them the most favourable genotypes for cultivation in that region.</p> </abstract>ARTICLEtrue in plant tolerance to the fungal disease Sclerotinia in breeding experiments on winter oilseed rape<abstract> <title style='display:none'>Summary</title> <p><italic>Sclerotinia sclerotiorum</italic> is a pathogen which causes a disease of oilseed rape. Severe plant infection contributes to a decrease in the quality of the crop. It is therefore important to pay attention to whether hybrids are highly tolerant to this fungal disease at the early stages of breeding. In this study, the question of interest is whether there has been progress in increasing the tolerance of new hybrids to this pathogen. Three years of breeding experiments (2014, 2015, 2017) are included in the analysis. Each year, three to five experiments were carried out, with several dozen varieties and three standards. Each series of experiments was repeated in several locations. Because the degree of infection was assessed on a scale (from 1 – the highest infection – to 9 – the least infection), the analysis is carried out using an ordinal logistic model. It is noted that in earlier years the standard varieties’ probability of infection with this disease had a smaller range (empirical probability 0.5–0.83) than in the last analyzed year (empirical probability 0.33–1.00). The results of the analysis show that in 2014 and 2015 several hybrids exhibited a significantly higher tolerance to Sclerotinia, but in 2017 none of the hybrids were significantly better than the standard. Perhaps breeding selection of hybrids has eliminated the less tolerant varieties. However, to be able to draw more general conclusions, it would be necessary to repeat the study in controlled conditions (a greenhouse), where the level of fungal spores and their effect on plants could be controlled. Obtaining tolerant hybrids will enable a reduction in production costs, since there will be no need to monitor whether disease infestation occurs and no need to use corresponding plant protection products.</p> </abstract>ARTICLEtrue model for the transmission of mumps and its optimal control<abstract> <title style='display:none'>Summary</title> <p>Mumps is a viral contagious disease associated with puffy cheeks and tender and swollen jaw. It spreads through direct contact with saliva or respiratory droplets from the mouth, nose or throat of infected persons. In this work, we present a mathematical model which describes the dynamics of the disease in a human population. The model incorporates isolation and treatment of infected individuals as a control measure. It is shown that the disease-free equilibrium (DFE) is locally and globally asymptotically stable when the control reproduction number R<sub>c</sub> is less than one. It is also shown that the model has a unique endemic equilibrium which exists when R<sub>c</sub> &gt; 1. The existence of a unique endemic equilibrium confirms the global stability of the DFE, and the absence of backward bifurcation in the model. Optimal control analysis is performed on the model to obtain the proportion of infected humans to be isolated for optimal control of the disease. Plots are presented to show the dynamics of the disease in the presence of the control measures.</p> </abstract>ARTICLEtrue chemical balance weighing designs with positively correlated errors: part I<abstract> <title style='display:none'>Summary</title> <p>In this paper, the problem of indicating chemical balance weighing designs satisfying the criterion of D-optimality is considered. Moreover, we study such designs under the assumption that the measurements are equally positively correlated and they have the same variances. We formulate a method to add at most four runs to a regular D-optimal chemical balance weighing design to obtain a highly D-efficient chemical balance weighing deign.</p> </abstract>ARTICLEtrue–Schumacher Split-Plot Design Modelling of Rice Yield<abstract> <title style='display:none'>Summary</title> <p>In this research, an intrinsically nonlinear split-plot design model (INSPDM) is formulated and studied. It was formulated by fitting a Johnson–Schumacher (JS) function to the split-plot model mean function. The fitted model parameters are estimated using the estimated generalized least squares (EGLS) technique based on a Gauss–Newton procedure with Taylor series expansion, by minimizing the objective function of the model. The variance components for the whole plot and subplot random effects are estimated using restricted maximum likelihood estimation (REML) techniques. The adequacy of the fitted INSPDM was tested using four median adequacy measures: resistant coefficient of determination, resistant prediction coefficient of determination, the resistant modeling efficiency statistic, and the median square error prediction statistic based on the residuals of the fitted model. Akaike’s Information Criterion (AIC), Corrected Akaike’s Information Criterion (AICC) and Bayesian Information Criterion (BIC) statistics are used to select the best parameter estimation technique. The results obtained are compared with the techniques of ordinary least squares (OLS) and EGLS via maximum likelihood estimation (MLE). The results showed the model to be adequate, reliable, stable, and a good fit based on EGLS-REML when compared with OLS and EGLS-MLE fitted model parameter estimates.</p> </abstract>ARTICLEtrue and Multiple Regression Analyses in Medical Research<abstract> <title style='display:none'>Summary</title> <p>Regression analysis methods, such as linear regression for continuous outcomes and logistic regression for binary outcomes, have been widely used in medical research data analysis for many years. However, there have been instances of misconceptions and misinterpretations of regression results within the medical community. Univariate and multiple regression analyses are commonly used by medical publications to identify factors that are significantly correlated with the outcome. In this manuscript, we critically evaluate the validity of this approach. Our findings indicate that this method is invalid and should be completely disregarded by medical researchers.</p> </abstract>ARTICLEtrue analytic Bayes factors from summary statistics in repeated-measures designs<abstract> <title style='display:none'>Summary</title> <p>Bayes factors are an increasingly popular tool for indexing evidence from experiments. For two competing population models, the Bayes factor reflects the relative likelihood of observing some data under one model compared to the other. Computing Bayes factors can be difficult, requiring one to integrate the product of the likelihood and a prior distribution on the population parameter(s) for both competing models. Previous work has obviated this difficulty for independent-groups designs. In this paper, we develop a new analytic formula for computing Bayes factors directly from minimal summary statistics in repeated-measures designs. This work is an improvement on previous methods for computing Bayes factors from summary statistics (e.g., the BIC method), which produce Bayes factors that violate the Sellke upper bound of evidence for smaller sample sizes. The new approach taken in this paper requires knowing only the <italic>F</italic> -statistic and degrees of freedom, both of which are commonly reported in most empirical work. In addition to providing computational examples, we report a simulation study that benchmarks the new formula against other methods for computing Bayes factors in repeated-measures designs. Our new method provides an easy way for researchers to compute Bayes factors directly from a minimal set of summary statistics, allowing users to index the evidential value of their own data, as well as data reported in published studies.</p> </abstract>ARTICLEtrue of the covariance matrix: An overview<abstract> <title style='display:none'>Summary</title> <p>In this paper, some multivariate and double multivariate modelling approaches are presented. Moreover, this article provides an overview of the modelling of the structure of the covariance matrix. Furthermore, some methods of covariance structure identification are given.</p> </abstract>ARTICLEtrue of edgeR and DESeq2 methods in plant experiments based on RNA-seq technology<abstract> <title style='display:none'>Summary</title> <p>We compared two of the most common methods for differential expression analysis in the RNA-seq field: edgeR and DESeq2. We evaluated these methods based on four real RNA-seq plant datasets. The results indicate that there is a large number of joint differentially expressed genes between the two methods. However, depending on the research goal and the preparation of an experiment, different approaches to statistical analysis and interpretation of the results can be suggested. We focus on answering the question: what workflow should be used in the statistical analysis of the datasets under consideration to minimize the number of falsely identified differentially expressed genes?</p> </abstract>ARTICLEtrue of the Effect of Prognostic Variables on the Survival Analysis of Prostate Cancer<abstract> <title style='display:none'>Summary</title> <p>Prostate cancer is a severe threat to human lives. Approximately 1 in 7 men will be diagnosed with prostate cancer throughout their lifetimes, and 1 in 39 men will die from prostate cancer. There are many factors which increase or decrease the survival time of prostate cancer patients. Data is used here from a randomised clinical trial for the choice of treatment for prostate cancer patients in stages 3 and 4. This study is done to identify probable variables that influence the survival time of patients only for these two stages. The AFT and the Cox-PH models determine how variables affect prostate cancer patients' survival time.</p> </abstract>ARTICLEtrue role of maize variety ( L.) in shaping the grain vitamin content<abstract> <title style='display:none'>Summary</title> <p>The Faculty of Agronomy at the University of Life Sciences in Poznań conducted laboratory tests on the content of B vitamins in the grain of three varieties of yellow-colored fodder maize. The grains of the variety ES Metronom had the statistically significantly highest content of vitamins B1 and B9. In the case of vitamin B3, the significantly highest concentration was recorded in the grain of the variety ES Abakus, while the lowest concentration was found for the variety ES Metronom. In contrast, the grain of the variety ES Bombastic had significantly higher vitamin B6 content than that of the varieties ES Abakus and ES Metronom. The grain of the variety ES Metronom had significantly higher vitamin B9 content than the other two varieties tested. In general, it should be concluded that the content of B vitamins in maize grain is not determined by the type of maize hybrid.</p> </abstract>ARTICLEtrue