Posterior Features Research Articles

Assessment of heterogeneity of residual variances using changepoint techniques

Several studies using test-day models show clear heterogeneity of residual variance along lactation. A changepoint technique to account for this heterogeneity is proposed. The data set included 100 744 test-day records of 10 869 Holstein-Friesian cows from northern Spain. A three-stage hierarchical model using the Wood lactation function was employed. Two unknown changepoints at times T1 and T2, (0 <T1 <T2 <tmax), with continuity of residual variance at these points, were assumed. Also, a nonlinear relationship between residual variance and the number of days of milking t was postulated. The residual variance at a time t( ) in the lactation phase i was modeled as: for (i = 1, 2, 3), where λ ι is a phase-specific parameter. A Bayesian analysis using Gibbs sampling and the Metropolis-Hastings algorithm for marginalization was implemented. After a burn-in of 20 000 iterations, 40 000 samples were drawn to estimate posterior features. The posterior modes of T1, T2, λ1, λ2, λ3, , , were 53.2 and 248.2 days; 0.575, -0.406, 0.797 and 0.702, 34.63 and 0.0455 kg2, respectively. The residual variance predicted using these point estimates were 2.64, 6.88, 3.59 and 4.35 kg2 at days of milking 10, 53, 248 and 305, respectively. This technique requires less restrictive assumptions and the model has fewer parameters than other methods proposed to account for the heterogeneity of residual variance during lactation.

Assessment of heterogeneity of residual variances using changepoint techniques.

Several studies using test-day models show clear heterogeneity of residual variance along lactation. A changepoint technique to account for this heterogeneity is proposed. The data set included 100 744 test-day records of 10 869 Holstein-Friesian cows from northern Spain. A three-stage hierarchical model using the Wood lactation function was employed. Two unknown changepoints at times T1 and T2, (0 <T1 <T2 <tmax), with continuity of residual variance at these points, were assumed. Also, a nonlinear relationship between residual variance and the number of days of milking t was postulated. The residual variance at a time t() in the lactation phase i was modeled as: for (i = 1, 2, 3), where λι is a phase-specific parameter. A Bayesian analysis using Gibbs sampling and the Metropolis-Hastings algorithm for marginalization was implemented. After a burn-in of 20 000 iterations, 40 000 samples were drawn to estimate posterior features. The posterior modes of T1, T2, λ1, λ2, λ3, , , were 53.2 and 248.2 days; 0.575, -0.406, 0.797 and 0.702, 34.63 and 0.0455 kg2, respectively. The residual variance predicted using these point estimates were 2.64, 6.88, 3.59 and 4.35 kg2 at days of milking 10, 53, 248 and 305, respectively. This technique requires less restrictive assumptions and the model has fewer parameters than other methods proposed to account for the heterogeneity of residual variance during lactation.

Analyzing Ultimatum Bargaining: A Bayesian Approach to the Comparison of Two Potency Curves Under Shape Constraints

An experiment designed to test whether experimenter observation influences play of the ultimatum game led to a comparison of proportions of perfect equilibria obtained under different conditions. Our analysis features a Bayesian approach to this comparison. Our method extends recent work in the nonparametric Bayesian analysis of bioassay problems when the prior constrains the form of the potency curve. Sampling-based approaches to calculating posterior features of interest are used and discussed. We conclude that experimenter observation has a small influence but not enough to account for most of the deviation from perfect-equilibrium play.

Nonparametric Bayesian bioassay with prior constraints on the shape of the potency curve

SUMMARY We consider the problem of implementing nonparametric Bayesian analysis of bioassay problems when the prior constrains the form of the potency curve (for example, to be convex, concave or ogive). Sampling based approaches to calculating posterior features of interest are detailed and illustrated. Extensions to prior constraints on hazard rates are outlined.

Two applications of developmental genetics to paleontology: segmentation genes in molluscs and preoral appendages in taxa of uncertain affinity

Resolution of deep evolutionary problems, including the origin of the metazoa and the morphologic evolution of higher taxa within the metazoa, have long been sought in the developmental sequence. Haeckel's gastraea theory is perhaps the best example of this endeavor. Since Haeckel's time it has become apparent that the early evolution of animal life cannot be read directly from the developmental sequence. Ontogeny itself evolves making it difficult to even identify homologies in the early development between many phyla and classes. However, all may not be lost; during metazoan development gene expression must be localized in order to differentiate cell types in the body during development. It is this regionalized transcription and translation to protein product that differentiates cell types, organ systems, and the morphologic features that we can identify in the fossil record. The functional importance of the genes in question, and the fact that portions of the protein products of these genes must bind to DNA in order to perform their switching function, leads to extreme sequence conservation. This permits the identification and comparison of homologous genes important in the development of divergent taxa even after the passage of the entire Phanerozoic. If these genes retain a pattern of expression in development as well as conservation of the DNA sequence, then we can identify a homologous process derived from the development of the shared ancestor of the two taxa.This approach can be used to address the homology of metameric units. Preliminary results indicate that the segmentation gene engrailed is expressed in chiton trochophores in associated with each of the developing plate fields. The engrailed gene is known to control segmentation processes in arthropods and annelids. Evidently the plates in chitons evolved from serial features in a shared ancestor of annelids, arthropods and molluscs. This indicates that the serial features found in molluscs are ancestral (plesiomorphic), and that the evolution of the mollusca has involved the loss or reduction of serial features rather than their de novo evolution in chitons and monoplacophorans as has been suggested by a number of neontologists. The fossil record suggests successive reduction of serial features in molluscs. This paleontological interpretation now finds support in developmental genetics.Developmental genetics also provides a basis for evolution of body plans. Unusual preoral appendages have evolved in chelicerates, Burgess Shale arthropods such as Yohoia and Leanchoilia, and non arthropod forms such as Opabinia and Tullimonstrum. The differentiation of the vertebral column of vertebrates and the segments of arthropods are controlled by homologous genes that are expressed in a anterior to posterior sequence. Out of place (ectopic) expression of posterior genes in the anterior region produces posterior features in the antennal field of arthropods and in the most anterior vertebrae of the vertebrates. This potential for conversion of anterior features was present in the shared ancestor of vertebrates and arthropods. Thus evolution of novel anterior features resulting from ectopic expression could occur in both deuterostomes and protostomes and may account for a range of novel fossil forms. This suggests that parallel evolution of unusual anterior features could occur, and the presence of these features may not be the best character to use in a phylogenetic analyses.

The centriole cycle in the amoebae of the myxomycetePhysarum polycephalum

In the amoebae of the myxomycetePhysarum polycephalum, procentrioles are formed on the anterior and posterior centrioles in early prophase. Although the relative position of the parental and procentrioles is fixed, all relative positions of the daughter and parental centrioles were observed. During the different stages of mitosis daughter centrioles elongate and acquire anterior satellites, one of the characteristic features of the anterior centrioles. All other anterior morphological characteristics appear only in telophase and early reconstruction stages. In contrast to the parental posterior centrioles, which do not change morphologically during the successive mitotic stages, the parental anterior centrioles lose their morphological characteristics in late prophase and early prometaphase and then acquire the morphological features characteristic of the posterior centrioles. Thus, the following maturation scheme is suggested: a procentriole becomes an anterior centriole during the first mitosis and a posterior centriole during the second mitosis. Since posterior features are maintained during mitosis, the posterior centriole corresponds to the final state of centriole maturation.

Homoeosis in Drosophila: Roles and spatial patterns of expression of the Antennapedia and Sex combs reduced loci in embryogenesis

In order to gain insight into the roles and spatial patterns of the embryonic developmental significance of the Antennapedia ( Antp +) and Sex combs reduced ( Scr +) loci, we have studied the cuticular morphology of lethal embryos defective for these genes and either normal or deficient for the bithorax gene complex (BX-C). We have also analyzed the additional effects of the lack of Polycomb + ( Pc +) activity. Since the 9th and 10th abdominal segments of BX-C − embryos display homoeotic thoracic features, we have examined these caudal segments in our studies of other mutant phenotypes. Phenotypic comparisons indicate that in BX-C − embryos, the Scr + gene has a marked effect on the prothorax, a more limited effect on the region from the mesothorax through the anterior 8th abdominal segment, and no discernible effect on more posterior features. However, in embryos that are both BX-C − and Pc −, there is a marked effect of Scr + activity from the prothorax through the 9th abdominal segment, which develops prothoracic features. (The latter observation confirms previous suggestions of homoeotic changes posterior to the 8th abdominal segment in Pc − embryos, and shows that Scr + activity is necessary for this effect.) In BX-C − embryos, Antp + gene function appears limited in the anterior prothorax but has a marked effect on the region from the posterior prothorax through the 7th abdominal segment; this gene has a limited effect on the phenotype of the anterior 8th abdominal segment and no detectable effect posterior to that region. Embryos that are Pc − BX-C − as well are similar to Pc + BX-C − embryos with respect to the expression of the Antp + gene, except that the effect of the lack of Antp + function on the anterior 8th abdominal segment is more pronounced. We also suggest that Scr + function is necessary for normal development of prothoracic cuticle and some head structures, and that Antp + is involved in establishing the normal developmental pathway of a unit consisting of posterior prothorax and anterior mesothorax, with these regions forming head structures and anterior prothorax, respectively, in the absence of Antp + activity.