Multiple hypothesis testing and clustering with mixtures of non-central t-distributions applied in microarray data analysis

Multiple testing analysis, based on clustering methodologies, is usually applied in Microarray Data Analysis for comparisons between pair of groups. In this paper, we generalize this methodology to deal with multiple comparisons among more than two groups obtained from microarray expressions of genes. Assuming normal data, we define a statistic which depends on sample means and sample variances, distributed as a non-central t-distribution. As we consider multiple comparisons among groups, a mixture of non-central t-distributions is derived. The estimation of the components of mixtures is obtained via a Bayesian approach, and the model is applied in a multiple comparison problem from a microarray experiment obtained from gorilla, bonobo and human cultured fibroblasts.Clustering, MCMC computation, Microarray analysis, Mixture distributions, Multiple hypothesis testing, Non-central t-distribution

Why using a general model in Solvency II is not a good idea : an explanation from a Bayesian point of view

The passing of Directive 2009/138/CE (Solvency II) has opened a new era in the European insurance market. According to this new regulatory environment, the volume of own resources will be determined depending on the risks that any insurer would be holding. So, nowadays, the model to estimate the amount of economic capital is one of the most important elements. The Directive establishes that the European entities can use a general model to perform these tasks. However, this situation is far from being optimal because the calibration of the general model has been made using figures that reflects and average behaviour. This paper shows that not all the companies operating in a specific market has the same risk profile. For this reason, it is unsatisfactory to use a general model for all of them. We use the PAM clustering method and afterwards some Bayesian tools to check the results previously obtained. Analysed data (public information belonging to Spanish insurance companies about balance sheets and income statements from 1998 to 2007) comes from the DGSFP (Spanish insurance regulator).Solvency II, PAM, Longitudinal multinomial model

A Comparative Study of Turbulence Methods Applied to the Design of a 3D-Printed Scaffold and the Selection of the Appropriate Numerical Scheme to Simulate the Scaffold for Tissue Engineering

Current commercial software tools implement turbulence models on computational fluid dynamics (CFD) techniques and combine them with fluid-structural interaction (FSI) techniques. There are currently a great variety of turbulence methods that are worth investigating through a comparative study in order to delineate their behavior on scaffolds used in tissue engineering and bone regeneration. Additive manufacturing (AM) offers the opportunity to obtain three-dimensional printed scaffolds (3D scaffolds) that are designed respecting morphologies and that are typically used for the fused deposition model (FDM). These are typically made using biocompatible and biodegradable materials, such as polyetherimide (PEI), ULTEM 1010 biocompatible and polylactic acid (PLA). Starting from our own geometric model, simulations were carried out applying a series of turbulence models which have been proposed due to a variety of properties, such as permeability, speed regime, pressures, depressions and stiffness, that in turn are subject to boundary conditions based on a blood torrent. The obtained results revealed that the detached eddy simulation (DES) model shows better performance for the use of 3D scaffolds in its normal operating regime. Finally, although the results do not present relevant differences between the two materials used in the comparison, the prototypes simulated in PEI ULTEM 1010 do not allow their manufacture in FDM for the required pore size. The printed 3D scaffolds of PLA reveal an elastic behavior and a rigidity that are similar to other prototypes of ceramic composition. Prototypes made of PLA reveal unpredictable variability in pore and layer size which are very similar to cell growth itself and difficult to keep constant

A subordinated stochastic process model

We introduce a new stochastic model for non-decreasing processes which can be used to include stochastic variability into any deterministic growth function via subordination. This model is useful in many applications such as growth curves (children’s height, fish length, diameter of trees, etc.) and degradation processes (crack size, wheel degradation, laser light, etc.). One advantage of our approach is the ability to easily deal with data that are irregularly spaced in time or different curves that are observed at different moments of time. With the use of simulations and applications, we examine two approaches to Bayesian inference for our model: the first based on a Gibbs sampler and the second based on approximate Bayesian computation (ABC)

UVPAR: fast detection of functional shifts in duplicate genes

BACKGROUND: The imprint of natural selection on gene sequences is often difficult to detect. A plethora of methods have been devised to detect genetic changes due to selective processes. However, many of those methods depend heavily on underlying assumptions regarding the mode of change of DNA sequences and often require sophisticated mathematical treatments that made them computationally slow. The development of fast and effective methods to detect modifications in the selective constraints of genes is therefore of great interest. RESULTS: We describe UVPAR, a program designed to quickly test for changes in the functional constraints of duplicate genes. Starting with alignments of the proteins encoded by couples of duplicate genes in two different species, UVPAR detects the regions in which modifications of the functional constraints in the paralogs occurred since both species diverged. Sequences can be analyzed with UVPAR in just a few minutes on a standard PC computer. To demonstrate the power of the program, we first show how the results obtained with UVPAR compare to those based on other approaches, using data for vertebrate Hox genes. We then describe a comprehensive study of the RBR family of ubiquitin ligases in which we have performed 529 analyses involving 14 duplicate genes in seven model species. A significant increase in the number of functional shifts was observed for the species Danio rerio and for the gene Ariadne-2. CONCLUSION: These results show that UVPAR can be used to generate sensitive analyses to detect changes in the selection constraints acting on paralogs. The high speed of the program allows its application to genome-scale analyses

Non-linear models of disability and age applied to census data

It is usually considered that the proportion of handicapped people grows with age. Namely, the older the man/woman is, the more level of disability he/she suffers. However, empirical evidence shows that this assessment is not always true, or at least, it is not true in the Spanish population. This study tries to assess the impact of age on disability in Spain. It is divided into three different parts. The first one is focused in describing the way disability is measured in this work. We used a former index defined by the authors that distinguishes between men and women. The second one is focused in a literature review about the methods used in this paper. This section emphasizes on local regression, feed forward neural networks and BARS. Finally, in the last section estimations are undertaken. Several methods are used and, therefore, there are fairly differences in the results, not only among the methodologies, but also between genders

Why using a general model in Solvency II is not a good idea : an explanation from a Bayesian point of view

The passing of Directive 2009/138/CE (Solvency II) has opened a new era in the European insurance market. According to this new regulatory environment, the volume of own resources will be determined depending on the risks that any insurer would be holding. So, nowadays, the model to estimate the amount of economic capital is one of the most important elements. The Directive establishes that the European entities can use a general model to perform these tasks. However, this situation is far from being optimal because the calibration of the general model has been made using figures that reflects and average behaviour. This paper shows that not all the companies operating in a specific market has the same risk profile. For this reason, it is unsatisfactory to use a general model for all of them. We use the PAM clustering method and afterwards some Bayesian tools to check the results previously obtained. Analysed data (public information belonging to Spanish insurance companies about balance sheets and income statements from 1998 to 2007) comes from the DGSFP (Spanish insurance regulator)

Bayesian modeling of bacterial growth for multiple populations

Bacterial growth models are commonly used for the prediction of microbial safety and the shelf life of perishable foods. Growth is affected by several environmental factors such as temperature, acidity level and salt concentration. In this study, we develop two models to describe bacterial growth for multiple populations under both equal and different environmental conditions. Firstly, a semi-parametric model based on the Gompertz equation is proposed. Assuming that the parameters of the Gompertz equation may vary in relation to the running conditions under which the experiment is performed, we use feed forward neural networks to model the influence of these environmental factors on the growth parameters. Secondly, we propose a more general model which does not assume any underlying parametric form for the growth function. Thus, we consider a neural network as a primary growth model which includes the influencing environmental factors as inputs to the network. One of the main disadvantages of neural networks models is that they are often very difficult to tune which complicates fitting procedures. Here, we show that a simple, Bayesian approach to fitting these models can be implemented via the software package WinBugs. Our approach is illustrated using real experimental Listeria Monocytogenes growth data

Bayesian modeling of two- and three-species bacterial competition in milk

Listeria monocytogenes is a well-known food-borne pathogen and is among the bacteria best adapted to grow at low temperatures. Psychrotrophic spoilage microorganisms present in milk and milk products are primarily in the genus Pseudomonas, and their numbers increase during cold storage leading to deterioration and/or spoilage. The nature of the competition in two- or three-species bacterial systems with L. monocytogenes, L. innocua, and P. fluorescens in skimmed milk at 7 or 14°C was studied. The Baranyi growth model was used to estimate the growth rate and the maximum population density of the three microorganisms for each strain in single cultures or in two- or three-strains co-cultures. The highest Listeria populations were achieved by pure cultures, decreasing in co-culture with P. fluorescens at both temperatures. A modified deterministic logistic model was applied which includes inhibition functions for single cultures, and two- or three-species cultures. A subsequent Bayesian approach was applied for modelling the bacterial interactions. There was not a direct correlation between the growth rate of P. fluorescens and its inhibitory effect on Listeria species. The use of some species from the natural food microflora to inhibit pathogen growth may be an important tool to enhance the safety of refrigerated foods such as milk and dairy products

Bayesian inference and data cloning in population projection matrices

Discrete time models are used in Ecology for describing the evolution of an agestructured population. Usually, they are considered from a deterministic viewpoint but, in practice, this is not very realistic. The statistical model we propose in this article is a reasonable model for the case in which the evolution of the population is described by means of a projection matrix. In this statistical model, fertility rates and survival rates are unknown parameters and they are estimated by using a Bayesian approach. Usual Bayesian and data cloning methods (based on Bayesian methodology) are applied to real data from the population of the Steller sea lions located in the Alaska coast since 1978 to 2004. The estimates obtained from these methods show a good behavior when they are compared to the actual value