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On small sample inference for common mean in heteroscedastic one-way model

Viktor Witkovský, Alexander Savin, Gejza Wimmer (2003)

Discussiones Mathematicae Probability and Statistics

In this paper we consider and compare several approximate methods for making small-sample statistical inference on the common mean in the heteroscedastic one-way random effects model. The topic of the paper was motivated by the problem of interlaboratory comparisons and is also known as the (traditional) common mean problem. It is also closely related to the problem of multicenter clinical trials and meta-analysis. Based on our simulation study we suggest to use the approach proposed by Kenward...

Parametric inference for mixed models defined by stochastic differential equations

Sophie Donnet, Adeline Samson (2008)

ESAIM: Probability and Statistics

Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants. A tuned...

Pattern-mixture models

Geert Molenberghs, Herbert Thijs, Bart Michiels, Geert Verbeke, Michael G. Kenward (2004)

Journal de la société française de statistique

Population genetics models for the statistics of DNA samples under different demographic scenarios - Maximum likelihood versus approximate methods

Andrzej Polański, Marek Kimmel (2003)

International Journal of Applied Mathematics and Computer Science

The paper reviews the basic mathematical methodology of modeling neutral genetic evolution, including the statistics of the Fisher-Wright process, models of mutation and the coalescence method under various demographic scenarios. The basic approach is the use of maximum likelihood techniques. However, due to computational problems, intuitive or approximate methods are also of great importance.

Pre-symptomatic Influenza Transmission, Surveillance, and School Closings: Implications for Novel Influenza A (H1N1)

G. F. Webb, Y-H. Hsieh, J. Wu, M. J. Blaser (2010)

Mathematical Modelling of Natural Phenomena

Early studies of the novel swine-origin 2009 influenza A (H1N1) epidemic indicate clinical attack rates in children much higher than in adults. Non-medical interventions such as school closings are constrained by their large socio-economic costs. Here we develop a mathematical model to ascertain the roles of pre-symptomatic influenza transmission as well as symptoms surveillance of children to assess the utility of school closures. Our model analysis...

Quality improvement of rule-based gene group descriptions using information about GO terms importance occurring in premises of determined rules

Marek Sikora, Aleksandra Gruca (2010)

International Journal of Applied Mathematics and Computer Science

In this paper we present a method for evaluating the importance of GO terms which compose multi-attribute rules. The rules are generated for the purpose of biological interpretation of gene groups. Each multi-attribute rule is a combination of GO terms and, based on relationships among them, one can obtain a functional description of gene groups. We present a method which allows evaluating the influence of a given GO term on the quality of a rule and the quality of a whole set of rules. For each...

Quantitative Analysis of Melanocyte Migration in vitro Based on Automated Cell Tracking under Phase Contrast Microscopy Considering the Combined Influence of Cell Division and Cell-Matrix Interactions

V. Letort, S. Fouliard, G. Letort, I. Adanja, M. Kumasaka, S. Gallagher, O. Debeir, L. Larue, F. Xavier (2010)

Mathematical Modelling of Natural Phenomena

The aim of this study was to describe and analyze the regulation and spatio-temporal dynamics of melanocyte migration in vitro and its coupling to cell division and interaction with the matrix. The melanocyte lineage is particularly interesting because it is involved in both embryonic development and oncogenesis/metastasis (melanoma). Biological experiments were performed on two melanocyte cell lines established from wild-type and β-catenin-transgenic...

Rapid Emergence of Co-colonization with Community-acquired and Hospital-Acquired Methicillin-Resistant Staphylococcus aureus Strains in the Hospital Setting

E. M. C. D’Agata, G. F. Webb, J. Pressley (2010)

Mathematical Modelling of Natural Phenomena

Background: Community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA), a novel strain of MRSA, has recently emerged and rapidly spread in the community. Invasion into the hospital setting with replacement of the hospital-acquired MRSA (HA-MRSA) has also been documented. Co-colonization with both CA-MRSA and HA-MRSA would have important clinical implications given differences in antimicrobial susceptibility profiles and the potential...

Recursive estimates of quantile based on 0-1 observations

Pavel Charamza (1992)

Applications of Mathematics

The objective of this paper is to introduce some recursive methods that can be used for estimating an L D - 50 value. These methods can be used more generally for the estimation of the γ -quantile of an unknown distribution provided we have 0-1 observations at our disposal. Standard methods based on the Robbins-Monro procedure are introduced together with different approaches of Wu or Mukerjee. Several examples are also mentioned in order to demonstrate the usefulness of the methods presented.

Representación canónica simultánea de poblaciones y variables: una aplicación al estudio de enfermedades renales.

Martín Ríos, Angel Villarroya, Esteban Vegas, Josep M. Oller (1991)

Qüestiió

En este trabajo se describe una metodología que nos permite representar simultáneamente poblaciones estadísticas y variables aleatorias, así como transformaciones admisibles de las mismas. Para ello se representan las variables aleatorias, o sus transformadas, en el espacio tangente a la variedad de las poblaciones estadísticas, a continuación se proyectan en dicha variedad y, finalmente, se aplica un análisis canónico de poblaciones para su representación en un espacio de dimensión reducida. Los...

Sampling properties of estimators of nucleotide diversity at discovered SNP sites

Alexander Renwick, Penelope Bonnen, Dimitra Trikka, David Nelson, Ranajit Chakraborty, Marek Kimmel (2003)

International Journal of Applied Mathematics and Computer Science

SNP sites are generally discovered by sequencing regions of the human genome in a limited number of individuals. This may leave SNP sites present in the region, but containing rare mutant nucleotides, undetected. Consequently, estimates of nucleotide diversity obtained from assays of detected SNP sites are biased. In this research we present a statistical model of the SNP discovery process, which is used to evaluate the extent of this bias. This model involves the symmetric Beta distribution of...

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