Priors for the Bayesian star paradox

We show that the Bayesian star paradox, first proved mathematically by Steel and Matsen for a specific class of prior distributions, occurs in a wider context including less regular, possibly discontinuous, prior distributions.     

Bayesian Inference from Count Data Using Discrete Uniform Priors

We consider a set of sample counts obtained by sampling arbitrary fractions of a finite volume containing an homogeneously dispersed population of identical objects. We report a Bayesian derivation of the posterior probability distribution of the population size using a binomial likelihood and non-conjugate, discrete uniform priors under sampling with or without replacement. Our derivation yields a computationally feasible formula that can prove useful in a variety of statistical problems involving absolute quantification under uncertainty. We implemented our algorithm in the R package dupiR and compared it with a previously proposed Bayesian method based on a Gamma prior. As a showcase, we demonstrate that our inference framework can be used to estimate bacterial survival curves from measurements characterized by extremely low or zero counts and rather high sampling fractions. All in all, we provide a versatile, general purpose algorithm to infer population sizes from count data, which can find application in a broad spectrum of biological and physical problems.     

Learning Universal Computations with Spikes

Providing the neurobiological basis of information processing in higher animals, spiking neural networks must be able to learn a variety of complicated computations, including the generation of appropriate, possibly delayed reactions to inputs and the self-sustained generation of complex activity patterns, e.g. for locomotion. Many such computations require previous building of intrinsic world models. Here we show how spiking neural networks may solve these different tasks. Firstly, we derive constraints under which classes of spiking neural networks lend themselves to substrates of powerful general purpose computing. The networks contain dendritic or synaptic nonlinearities and have a constrained connectivity. We then combine such networks with learning rules for outputs or recurrent connections. We show that this allows to learn even difficult benchmark tasks such as the self-sustained generation of desired low-dimensional chaotic dynamics or memory-dependent computations. Furthermore, we show how spiking networks can build models of external world systems and use the acquired knowledge to control them.     

Neural Computations Mediating One-Shot Learning in the Human Brain

Incremental learning, in which new knowledge is acquired gradually through trial and error, can be distinguished from one-shot learning, in which the brain learns rapidly from only a single pairing of a stimulus and a consequence. Very little is known about how the brain transitions between these two fundamentally different forms of learning. Here we test a computational hypothesis that uncertainty about the causal relationship between a stimulus and an outcome induces rapid changes in the rate of learning, which in turn mediates the transition between incremental and one-shot learning. By using a novel behavioral task in combination with functional magnetic resonance imaging (fMRI) data from human volunteers, we found evidence implicating the ventrolateral prefrontal cortex and hippocampus in this process. The hippocampus was selectively “switched” on when one-shot learning was predicted to occur, while the ventrolateral prefrontal cortex was found to encode uncertainty about the causal association, exhibiting increased coupling with the hippocampus for high-learning rates, suggesting this region may act as a “switch,” turning on and off one-shot learning as required.     

An Integrative Framework for Bayesian Variable Selection with Informative Priors for Identifying Genes and Pathways

The discovery of genetic or genomic markers plays a central role in the development of personalized medicine. A notable challenge exists when dealing with the high dimensionality of the data sets, as thousands of genes or millions of genetic variants are collected on a relatively small number of subjects. Traditional gene-wise selection methods using univariate analyses face difficulty to incorporate correlational, structural, or functional structures amongst the molecular measures. For microarray gene expression data, we first summarize solutions in dealing with ‘large p, small n’ problems, and then propose an integrative Bayesian variable selection (iBVS) framework for simultaneously identifying causal or marker genes and regulatory pathways. A novel partial least squares (PLS) g-prior for iBVS is developed to allow the incorporation of prior knowledge on gene-gene interactions or functional relationships. From the point view of systems biology, iBVS enables user to directly target the joint effects of multiple genes and pathways in a hierarchical modeling diagram to predict disease status or phenotype. The estimated posterior selection probabilities offer probabilitic and biological interpretations. Both simulated data and a set of microarray data in predicting stroke status are used in validating the performance of iBVS in a Probit model with binary outcomes. iBVS offers a general framework for effective discovery of various molecular biomarkers by combining data-based statistics and knowledge-based priors. Guidelines on making posterior inferences, determining Bayesian significance levels, and improving computational efficiencies are also discussed.     

Apoptosis in the Nervous System

Apoptosis (from the Greek apoptosis, i.e., falling of leaves) is the phenomenon of programmed cell death, which plays an important role in the normal embryonic development and maintenance of the homeostasis of the differentiated tissues of adult organisms. Completion of the apoptosis process is accompanied by specific morphological and biochemical changes in the involved cells. Various disturbances in the control of apoptosis underlie various neurodegenerative diseases, the formation of malignant tumors, autoimmune disturbances, and developmental abnormalities. A deficit of neurotrophic factors leads to apoptosis of neurons. The survival of specific cell populations of neurons is controlled by neurotrophic factors and their combinations. Oncogene bcl-2, a repressor of cell death, belongs to the better-studied factors controlling apoptosis. The terminal stages of cell death, including the death of neurons, depend on the activation of caspases, specifically caspase-1 (interleukin-1-converting enzyme). Ca²⁺and reactive forms of oxygen play an important role in the initiation of apoptosis by changing the mitochondrial permeability. Neuregulin, a factor of neuronal origin, is the main controlling factor in apoptosis of Schwann cells, and this process determines the size of their definitive population. Fibroblast growth factor b diminishes the apoptosis of Schwann cells in regenerating nerve fibers.     

Octopamine in the Lobster Nervous System

A search for catecholamines which might serve as transmitters in the lobster nervous system demonstrated only small amounts of dopamine (about 0.2 µg/g tissue) and failed to detect noradrenaline or adrenaline (limit of sensitivity, 0.1 µg g^?1) (unpublished results of D. L. B., using standard procedures for isolation of catecholamines on alumina¹ and fluorescence assays^1,2). Octopamine (the phenol analogue of noradrenalin, Fig. 1) occurs in large amounts in the posterior salivary glands of Octopus vulgaris³ and recently has been identified as a normal minor constituent of sympathetically innervated tissues of rat⁴. The possible occurrence of octopamine or other phenolamines in the lobster was therefore investigated. Here we report the presence of octopamine in the lobster nervous system, its endogenous distribution and its biosynthesis from tyrosine.     

Lysophospholipid Receptors in the Nervous System

The lysophospholipid mediators, lysophosphatidic acid (LPA) and sphingosine-1-phosphate (S1P), are responsible for cell signaling in diverse pathways including survival, proliferation, motility, and differentiation. Most of this signaling occurs through an eight-member family of G-protein coupled receptors once known as the endothelial differentiation gene (EDG) family. More recently, the EDG receptors have been divided into two subfamilies: the lysophosphatidic acid subfamily, which includes LPA₁, (EDG-2/VZG-1), LPA₂ (EDG-4), and LPA₃ (EDG-7), and the sphingosine-1-phosphate receptor subfamily, which includes S1P₁ (EDG-1), S1P₂ (EDG-5/H218/AGR16), S1P₃ (EDG-3), S1P₄ (EDG-6), and S1P₅ (EDG-8/NRG-1). The ubiquitous expression of these receptors across species, coupled with their diverse cellular functions, has made lysophospholipid receptors an important focus of signal transduction research. Neuroscientists have recently begun to explore the role of lysophospholipid receptors in a number of cell types; this research has implicated these receptors in the survival, migration, and differentiation of cells in the mammalian nervous system.     

Structure Learning in Bayesian Sensorimotor Integration

Previous studies have shown that sensorimotor processing can often be described by Bayesian learning, in particular the integration of prior and feedback information depending on its degree of reliability. Here we test the hypothesis that the integration process itself can be tuned to the statistical structure of the environment. We exposed human participants to a reaching task in a three-dimensional virtual reality environment where we could displace the visual feedback of their hand position in a two dimensional plane. When introducing statistical structure between the two dimensions of the displacement, we found that over the course of several days participants adapted their feedback integration process in order to exploit this structure for performance improvement. In control experiments we found that this adaptation process critically depended on performance feedback and could not be induced by verbal instructions. Our results suggest that structural learning is an important meta-learning component of Bayesian sensorimotor integration.