<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

Computing analytic Bayes factors from summary statistics in repeated-measures designs

<abstract xmlns="http://www.w3.org/1999/xhtml">

<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.
</abstract>

Department of Mathematical and Statistical Methods

Progress in plant tolerance to the fungal disease Sclerotinia in breeding experiments on winter oilseed rape

<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

Johnson–Schumacher Split-Plot Design Modelling of Rice Yield

<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

D-optimal chemical balance weighing designs with positively correlated errors: part I

<abstract xmlns="http://www.w3.org/1999/xhtml">

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.
</abstract>

Department of Biostatistics and Computational Biology

Univariate and Multiple Regression Analyses in Medical Research

<abstract xmlns="http://www.w3.org/1999/xhtml">

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 Rc is less than one. It is also shown that the model has a unique endemic equilibrium which exists when Rc > 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.
</abstract>

Mathematical model for the transmission of mumps and its optimal control

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Biometrical Letters

 Biometrical Letters is the official journal of the Polish Biometric Society, founded in 1964, now published with the financial support of the Ministry of Science and Higher Education. The anonymous double-blind peer review by the two independent reviewers is applied to all the papers.  The purposes of Biometrical Letters are:   publishing papers dealing with various aspects of the analysis and interpretation of results from biometrical experiments, using mathematical and statistical methods;  promoting and extending the use of statistical and mathematical methods in the principal disciplines of life sciences by reporting on the development and application of these methods;  presenting statistical and mathematical tools useful in biometry. Methodological developments should be motivated by interesting problems from life sciences, applied or applicable;  publishing review papers and papers presenting practical use of various methods of data analysis and statistical inference.   The core of most Biometrical Letters articles is statistical inference that sets scientific or policy objectives, motivates methodological development and demonstrates the operation of new methods.  The paper should include a description of the biometrical problem and a section detailing the application of the new methodology.  The Journal welcomes the submission of manuscripts from bioscience, mathematical and statistical theory, biology, genetics, medical statistics, agriculture, forestry, ecology, environmental sciences, biometrics and clinical trials. Case studies and articles on the use and development of statistical software are also welcome.  Rejection Rate   20%   Archiving  Sciendo archives the contents of this journal in Portico - digital long-term preservation service of scholarly books, journals and collections.  Plagiarism Policy  The editorial board is participating in a growing community of Similarity Check System's users in order to ensure that the content published is original and trustworthy. Similarity Check is a medium that allows for comprehensive manuscripts screening, aimed to eliminate plagiarism and provide a high standard and quality peer-review process. 