Disequilibrium Coefficient: A Bayesian Perspective

Hardy-Weinberg Equilibrium (HWE) is an important genetic property that populations should have whenever they are not observing adverse situations as complete lack of panmixia, excess of mutations, excess of selection pressure, etc. HWE for decades has been evaluated; both frequentist and Bayesian methods are in use today. While historically the HWE formula was developed to examine the transmission of alleles in a population from one generation to the next, use of HWE concepts has expanded in human diseases studies to detect genotyping error and disease susceptibility (association); Ryckman and Williams (2008). Most analyses focus on trying to answer the question of whether a population is in HWE. They do not try to quantify how far from the equilibrium the population is. In this paper, we propose the use of a simple disequilibrium coefficient to a locus with two alleles. Based on the posterior density of this disequilibrium coefficient, we show how one can conduct a Bayesian analysis to verify how far from HWE a population is. There are other coefficients introduced in the literature and the advantage of the one introduced in this paper is the fact that, just like the standard correlation coefficients, its range is bounded and it is symmetric around zero (equilibrium) when comparing the positive and the negative values. To test the hypothesis of equilibrium, we use a simple Bayesian significance test, the Full Bayesian Significance Test (FBST); see Pereira, Stern andWechsler (2008) for a complete review. The disequilibrium coefficient proposed provides an easy and efficient way to make the analyses, especially if one uses Bayesian statistics. A routine in R programs (R Development Core Team, 2009) that implements the calculations is provided for the readers.

Bayesian online algorithms for learning in discrete Hidden Markov Models

We propose and analyze two different Bayesian online algorithms for learning in discrete Hidden Markov Models and compare their performance with the already known Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalization we draw learning curves in simplified situations for these algorithms and compare their performances.

Haplotype distribution of five nuclear genes based on network genealogies and Bayesian inference indicates that Trypanosoma cruzi hybrid strains are polyphyletic

Chagas disease is still a major public health problem in Latin America. Its causative agent, Trypanosoma cruzi, can be typed into three major groups, T. cruzi I, T. cruzi II and hybrids. These groups each have specific genetic characteristics and epidemiological distributions. Several highly virulent strains are found in the hybrid group; their origin is still a matter of debate. The null hypothesis is that the hybrids are of polyphyletic origin, evolving independently from various hybridization events. The alternative hypothesis is that all extant hybrid strains originated from a single hybridization event. We sequenced both alleles of genes encoding EF-1 alpha, actin and SSU rDNA of 26 T. cruzi strains and DHFR-TS and TR of 12 strains. This information was used for network genealogy analysis and Bayesian phylogenies. We found T. cruzi I and T. cruzi II to be monophyletic and that all hybrids had different combinations of T. cruzi I and T. cruzi II haplotypes plus hybrid-specific haplotypes. Bootstrap values (networks) and posterior probabilities (Bayesian phylogenies) of clades supporting the monophyly of hybrids were far below the 95% confidence interval, indicating that the hybrid group is polyphyletic. We hypothesize that T. cruzi I and T. cruzi II are two different species and that the hybrids are extant representatives of independent events of genome hybridization, which sporadically have sufficient fitness to impact on the epidemiology of Chagas disease.

Chronostratigraphy and radiocarbon age inversion in the Holocene regressive barrier of Parana, southern Brazil

Twenty-two (14)C datings were performed at the central sector of the Parana coast to define Holocene regressive barrier evolution. The barrier Pleistocene substratum was ascribed an age between 40400 and 30000 yr BP, but it can also represent the penultimate sea level highstand during marine isotope stage 5e. The Holocene barrier samples provided ages between 8542-8279 and 2987-2751 cal yr BP, and showed at least six age inversions that were related to age differences between in situ or low-distance transported shells or trunk fragments, and high-distance transported vegetal debris, wood fragments and organic matter samples. The regressive Holocene barrier age was 4402-4135 cal yr BP near the base, and 2987-2751 cal yr BP near the top. Most of the vegetal remains were transported by ebb tidal currents from the estuaries to the inner shelf below wave base level during the mid-Holocene highstand; they were transported onshore by storm waves and littoral currents during the sea level lowering after the sea level maximum, and were deposited mainly as middle shoreface swaley cross-stratification facies. (C) 2008 Published by Elsevier B.V.

Bayesian updating rules in continuous opinion dynamics models

Here, I investigate the use of Bayesian updating rules applied to modeling how social agents change their minds in the case of continuous opinion models. Given another agent statement about the continuous value of a variable, we will see that interesting dynamics emerge when an agent assigns a likelihood to that value that is a mixture of a Gaussian and a uniform distribution. This represents the idea that the other agent might have no idea about what is being talked about. The effect of updating only the first moments of the distribution will be studied, and we will see that this generates results similar to those of the bounded confidence models. On also updating the second moment, several different opinions always survive in the long run, as agents become more stubborn with time. However, depending on the probability of error and initial uncertainty, those opinions might be clustered around a central value.

Modeling associations between genetic markers using Bayesian networks

Motivation: Understanding the patterns of association between polymorphisms at different loci in a population ( linkage disequilibrium, LD) is of fundamental importance in various genetic studies. Many coefficients were proposed for measuring the degree of LD, but they provide only a static view of the current LD structure. Generative models (GMs) were proposed to go beyond these measures, giving not only a description of the actual LD structure but also a tool to help understanding the process that generated such structure. GMs based in coalescent theory have been the most appealing because they link LD to evolutionary factors. Nevertheless, the inference and parameter estimation of such models is still computationally challenging. Results: We present a more practical method to build GM that describe LD. The method is based on learning weighted Bayesian network structures from haplotype data, extracting equivalence structure classes and using them to model LD. The results obtained in public data from the HapMap database showed that the method is a promising tool for modeling LD. The associations represented by the learned models are correlated with the traditional measure of LD D`. The method was able to represent LD blocks found by standard tools. The granularity of the association blocks and the readability of the models can be controlled in the method. The results suggest that the causality information gained by our method can be useful to tell about the conservability of the genetic markers and to guide the selection of subset of representative markers.

Using Bayesian networks with rule extraction to infer the risk of weed infestation in a corn-crop

This paper describes the modeling of a weed infestation risk inference system that implements a collaborative inference scheme based on rules extracted from two Bayesian network classifiers. The first Bayesian classifier infers a categorical variable value for the weed-crop competitiveness using as input categorical variables for the total density of weeds and corresponding proportions of narrow and broad-leaved weeds. The inferred categorical variable values for the weed-crop competitiveness along with three other categorical variables extracted from estimated maps for the weed seed production and weed coverage are then used as input for a second Bayesian network classifier to infer categorical variables values for the risk of infestation. Weed biomass and yield loss data samples are used to learn the probability relationship among the nodes of the first and second Bayesian classifiers in a supervised fashion, respectively. For comparison purposes, two types of Bayesian network structures are considered, namely an expert-based Bayesian classifier and a naive Bayes classifier. The inference system focused on the knowledge interpretation by translating a Bayesian classifier into a set of classification rules. The results obtained for the risk inference in a corn-crop field are presented and discussed. (C) 2009 Elsevier Ltd. All rights reserved.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Pricing farm-level agricultural insurance: a Bayesian approach

This paper applies Hierarchical Bayesian Models to price farm-level yield insurance contracts. This methodology considers the temporal effect, the spatial dependence and spatio-temporal models. One of the major advantages of this framework is that an estimate of the premium rate is obtained directly from the posterior distribution. These methods were applied to a farm-level data set of soybean in the State of the Parana (Brazil), for the period between 1994 and 2003. The model selection was based on a posterior predictive criterion. This study improves considerably the estimation of the fair premium rates considering the small number of observations.

Bayesian ratemaking procedure of crop insurance contracts with skewed distribution

Over the years, crop insurance programs became the focus of agricultural policy in the USA, Spain, Mexico, and more recently in Brazil. Given the increasing interest in insurance, accurate calculation of the premium rate is of great importance. We address the crop-yield distribution issue and its implications in pricing an insurance contract considering the dynamic structure of the data and incorporating the spatial correlation in the Hierarchical Bayesian framework. Results show that empirical (insurers) rates are higher in low risk areas and lower in high risk areas. Such methodological improvement is primarily important in situations of limited data.

Leaf area index estimation with MODIS reflectance time series and model inversion during full rotations of Eucalyptus plantations

The leaf area index (LAI) of fast-growing Eucalyptus plantations is highly dynamic both seasonally and interannually, and is spatially variable depending on pedo-climatic conditions. LAI is very important in determining the carbon and water balance of a stand, but is difficult to measure during a complete stand rotation and at large scales. Remote-sensing methods allowing the retrieval of LAI time series with accuracy and precision are therefore necessary. Here, we tested two methods for LAI estimation from MODIS 250m resolution red and near-infrared (NIR) reflectance time series. The first method involved the inversion of a coupled model of leaf reflectance and transmittance (PROSPECT4), soil reflectance (SOILSPECT) and canopy radiative transfer (4SAIL2). Model parameters other than the LAI were either fixed to measured constant values, or allowed to vary seasonally and/or with stand age according to trends observed in field measurements. The LAI was assumed to vary throughout the rotation following a series of alternately increasing and decreasing sigmoid curves. The parameters of each sigmoid curve that allowed the best fit of simulated canopy reflectance to MODIS red and NIR reflectance data were obtained by minimization techniques. The second method was based on a linear relationship between the LAI and values of the GEneralized Soil Adjusted Vegetation Index (GESAVI), which was calibrated using destructive LAI measurements made at two seasons, on Eucalyptus stands of different ages and productivity levels. The ability of each approach to reproduce field-measured LAI values was assessed, and uncertainty on results and parameter sensitivities were examined. Both methods offered a good fit between measured and estimated LAI (R(2) = 0.80 and R(2) = 0.62 for model inversion and GESAVI-based methods, respectively), but the GESAVI-based method overestimated the LAI at young ages. (C) 2010 Elsevier Inc. All rights reserved.

Influence of Phase Inversion on the Formation and Stability of One-Step Multiple Emulsions

A novel method of preparation of water-in-oil-in-micelle-containing water (W/O/W(m)) Multiple emulsions using the one-step emulsification method is reported. These multiple emulsions were normal (not temporary) and stable over a 60 day test period. Previously, reported multiple emulsion by the one-step method were abnormal systems that formed at the inversion point of simple emulsion (where there is an incompatibility in the Ostwald and Bancroft theories, and typically these are O/W/O systems). Pseudoternary phase diagrams and bidimensional process-composition (phase inversion) maps were constructed to assist in process and composition optimization. The surfactants used were PEG40 hydrogenated castor oil and sorbitan oleate, and mineral and vegetables oils were investigated. Physicochemical characterization studies showed experimentally, for the First time, the significance of the ultralow surface tension point oil multiple emulsion formation by one-step via phase inversion processes. Although the significance of ultralow surface tension has been speculated previously, to the best of our knowledge, this is the first experimental confirmation. The multiple emulsion system reported here was dependent not only upon the emulsification temperature, but also upon the component ratios, therefore both the emulsion phase inversion and the phase inversion temperature were considered to fully explain their formation. Accordingly, it is hypothesized that the formation of these normal multiple emulsions is not a result of a temporary incompatibility (at the inversion point) during simple emulsion preparation, as previously reported. Rather, these normal W/O/W(m) emulsions are a result of the simultaneous occurrence of catastrophic and transitional phase inversion processes. The formation of the primary emulsions (W/O) is in accordance with the Ostwald theory and the formation of the multiple emulsions (W/O/W(m)) is in agreement with the Bancroft theory.

Dependence of transient dynamics in a class-C laser upon variation of inversion with time

The transient statistics of a gain-switched coherently pumped class-C laser displays a linear correlation between the first passage time and subsequent peak intensity. Measurements are reported showing a positive or negative sign of this linear correlation, controlled through the switching time and the laser detuning. Further measurements of the small-signal laser gain combined with calculations involving a three-level laser model indicate that this sign fundamentally depends upon the way the laser inversion varies during the gain switching, despite the added dynamics of the laser polarization in the class-C laser. [S1050-2947(97)07112-6].

Anomalous resonance fluorescence and dressed-state inversion by squeezed light in a Fabry-Perot microcavity

It has been suggested that phased atomic decay in a squeezed vacuum could be detected in the fluorescence spectrum emitted from a driven two-level atom in a cavity. Recently, the existence of other very distinctive features in the fluorescence spectra arising from the nonclassical features of the squeezed vacuum has been reported. In this paper, we investigate the possibility of experimental observation of these spectra. The main obstacle to the experimentalist is ensuring an effective squeezed-vacuum-atom coupling. To overcome this problem we propose the use of a Fabry-Perot microcavity. The analysis involves a consideration of the three-dimensional nature of the electromagnetic held, and the possibility of a mismatch between the squeezed and cavity modes. The problem of squeezing bandwidths is also addressed. We show that under experimentally realistic circumstances many of the spectral anomalies predicted in free space also occur in this environment. In addition, we report large population inversions in the dressed states of the two-level atom. [S1050-2947(98)02301-4].