Efficient Decomposition of Bayesian Networks With Non-graded Variables

Elicitation, estimation and exact inference in Bayesian Networks (BNs) are often difficult because the dimension of each Conditional Probability Table (CPT) grows exponentially with the increase in the number of parent variables. The Noisy-MAX decomposition has been proposed to break down a large CPT into several smaller CPTs exploiting the assumption of causal independence, i.e., absence of causal interaction among parent variables. In this way, the number of conditional probabilities to be elicited or estimated and the computational burden of the joint tree algorithm for exact inference are reduced. Unfortunately, the Noisy-MAX decomposition is suited to graded variables only, i.e., ordinal variables with the lowest state as reference, but real-world applications of BNs may also involve a number of non-graded variables, like the ones with reference state in the middle of the sample space (double-graded variables) and with two or more unordered non-reference states (multi-valued nominal variables). In this paper, we propose the causal independence decomposition, which includes the Noisy-MAX and two generalizations suited to double-graded and multi-valued nominal variables. While the general definition of BN implicitly assumes the presence of all the possible causal interactions, our proposal is based on causal independence, and causal interaction is a feature that can be added upon need. The impact of our proposal is investigated on a published BN for the diagnosis of acute cardiopulmonary diseases.

Testing character-evolution models in phylogenetic paleobiology: a case study with Cambrian echinoderms

Macroevolutionary inference has historically been treated as a two-step process, involving the inference of a phylogenetic tree, and then inference of a macroevolutionary model using that tree. Newer models, such as the fossilized birth-death model, blend the two steps. These methods make more complete use of fossils than the previous generation of Bayesian phylogenetic models. They also involve many more parameters than prior models, including parameters about which empiricists may have little intuition. In this paper, we set forth a framework for fitting complex, hierarchical models.We ultimately fit and use a joint tree and diversification model to estimate a dated phylogeny of the Cincta (Echinodermata), a morphologically distinct group of Cambrian echinoderms that lack the five-fold radial symmetry characteristic of extant members of the phylum. Although the phylogeny of cinctans remains poorly supported in places, we show how models of character change and diversification contribute to understanding patterns of phylogenetic relatedness and testing macroevolutionary hypotheses. Finally our new analysis raises interesting questions about how incorporating age information is expected to affect a phylogeny, and provides a framework for future systematic and macroevolutionary studies of cinctan echinoderms.

Phylogeography by diffusion on a sphere: whole world phylogeography

BackgroundTechniques for reconstructing geographical history along a phylogeny can answer many questions of interest about the geographical origins of species. Bayesian models based on the assumption that taxa move through a diffusion process have found many applications. However, these methods rely on diffusion processes on a plane, and do not take the spherical nature of our planet in account. Performing an analysis that covers the whole world thus does not take in account the distortions caused by projections like the Mercator projection.ResultsIn this paper, we introduce a Bayesian phylogeographical method based on diffusion on a sphere. When the area where taxa are sampled from is small, a sphere can be approximated by a plane and the model results in the same inferences as with models using diffusion on a plane. For taxa sampled from the whole world, we obtain substantial differences. We present an efficient algorithm for performing inference in a Markov Chain Monte Carlo (MCMC) algorithm, and show applications to small and large samples areas. We compare results between planar and spherical diffusion in a simulation study and apply the method by inferring the origin of Hepatitis B based on sequences sampled from Eurasia and Africa.ConclusionsWe describe a framework for performing phylogeographical inference, which is suitable when the distortion introduced by map projections is large, but works well on a smaller scale as well. The framework allows sampling tips from regions, which is useful when the exact sample location is unknown, and placing prior information on locations of clades in the tree. The method is implemented in the GEO_SPHERE package in BEAST 2, which is open source licensed under LGPL and allows joint tree and geography inference under a wide range of models.

A. Hepatica in European ground squirrel (Citellus Citellus) compared to other experimental animals

European ground squirrel is the only representative of its genus in Serbia. It is used as experimental animal in microbioogy, parasitology, pharmacology and immunology. The objective of this work was to investigate a part of cardiovascular system of ground squirrel so in that way to contribute to a better knowledge of this animal body structure and accordingly to comparative anatomy in general. The investigation included 6 ground squirrels, of both gender, body weight 200-300 grams. For obtaining the liver arterial vascularization, after exsanguination of the animal, contrast mass of gelatin coloured with tempera was injected into abdominal aorta (Aorta abdominalis). After injecting, the blood vessels were prepared and photographed. In ground squirrel A. celiaca is odd, larger vessel that exits the abdominal aorta. It is divided into three branches: A. lienalis, A. gastrica sinistra and A. hepatica. A. hepatica is divided into A. hepatica propria and A. gastroduodenalis. A. hepatica propria further gives A. cystica, Rami cardiaci and small branches for Lnn. portales. A. gastroduodenalis is divided into A. pancreaticoduodenalis and A. gastroepiploica dextra. A. celiaca in nutria and rat is an odd artery, divided into A. lienalis, A. gastrica sinistra and A. hepatica. In rabbits, celiac artery (A. celiaca) is divided into A. lienalis and short trunk from which A. gastrica sinistra and A. Hepatica emerge. A. celiaca in golden hamster does not exist in the form of tripus coeliacus (A. lienalis, A. gastrica sinistra and A. hepatica), but from A. celiaca it is firstly separated A. hepatica, and then short trunk from which A. gastrica sinistra and A. Lienalis emerge. In guinea-pig, from abdominal aorta a joint tree branches off into A. celiaca and A. mesenterica cranialis (Truncus celiacomesentericus). Based on the above mentioned results, it can be concluded that A. celiaca in European ground squirrel, nutria and rat branches from abdominal aorta as a separate blood vessel. In these animals A. celiaca branches are: A. lienalis, A. gastrica sinistra and A. hepatica. <br><br><font color="red"><b> This article has been corrected. Link to the correction <u><a href="http://dx.doi.org/10.2298/VETGL1702141E">10.2298/VETGL1702141E</a><u></b></font>