Harold Jeffreys's Theory of Probability Revisited

Published exactly seventy years ago, Jeffreys's Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes school. In particular, its advances on the derivation of noninformative priors as well as on the scaling of Bayes factors have had a lasting impact on the field. However, the book reflects the characteristics of the time, especially in terms of mathematical rigor. In this paper we point out the fundamental aspects of this reference work, especially the thorough coverage of testing problems and the construction of both estimation and testing noninformative priors based on functional divergences. Our major aim here is to help modern readers in navigating in this difficult text and in concentrating on passages that are still relevant today.Comment: This paper commented in: [arXiv:1001.2967], [arXiv:1001.2968], [arXiv:1001.2970], [arXiv:1001.2975], [arXiv:1001.2985], [arXiv:1001.3073]. Rejoinder in [arXiv:0909.1008]. Published in at http://dx.doi.org/10.1214/09-STS284 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Exploring manual asymmetries during grasping: a dynamic causal modeling approach

Recording of neural activity during grasping actions in macaques showed that grasp-related sensorimotor transformations are accomplished in a circuit constituted by the anterior part of the intraparietal sulcus (AIP), the ventral (F5) and the dorsal (F2) region of the premotor area. In humans, neuroimaging studies have revealed the existence of a similar circuit, involving the putative homolog of macaque areas AIP, F5 and F2. These studies have mainly considered grasping movements performed with the right dominant hand and only a few studies have measured brain activity associated with a movement performed with the left non-dominant hand. As a consequence of this gap, how the brain controls for grasping movement performed with the dominant and the non-dominant hand still represents an open question. A functional resonance imaging experiment (fMRI) has been conducted, and effective connectivity (Dynamic Causal Modelling, DCM) was used to assess how connectivity among grasping-related areas is modulated by hand (i.e., left and right) during the execution of grasping movements towards a small object requiring precision grasping. Results underlined boosted inter-hemispheric couplings between dorsal premotor cortices during the execution of movements performed with the left rather than the right dominant hand. More specifically, they suggest that the dorsal premotor cortices may play a fundamental role in monitoring the configuration of fingers when grasping movements are performed by either the right and the left hand. This role becomes particularly evident when the hand less-skilled (i.e., the left hand) to perform such action is utilized. The results are discussed in light of recent theories put forward to explain how parieto-frontal connectivity is modulated by the execution of prehensile movements

Learning the Structure for Structured Sparsity

Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity rely on prior knowledge on how to weight (or how to penalize) individual subsets of variables during the subset selection process, which is not available in general. Inferring group weights from data is a key open research problem in structured sparsity.In this paper, we propose a Bayesian approach to the problem of group weight learning. We model the group weights as hyperparameters of heavy-tailed priors on groups of variables and derive an approximate inference scheme to infer these hyperparameters. We empirically show that we are able to recover the model hyperparameters when the data are generated from the model, and we demonstrate the utility of learning weights in synthetic and real denoising problems

Assessing the reliability of adaptive power system protection schemes

Adaptive power system protection can be used to improve the performance of existing protection schemes under certain network conditions. However, their deployment in the field is impeded by their perceived inferior reliability compared to existing protection arrangements. Moreover, their validation can be problematic due to the perceived high likelihood of the occurrence of failure modes or incorrect setting selection with variable network conditions. Reliability (including risk assessment) is one of the decisive measures that can be used in the process of verifying adaptive protection scheme performance. This paper proposes a generic methodology for assessing the reliability of adaptive protection. The method involves the identification of initiating events and scenarios that lead to protection failures and quantification of the probability of the occurrence of each failure. A numerical example of the methodology for an adaptive distance protection scheme is provided

A tutorial on group effective connectivity analysis, part 2: second level analysis with PEB

This tutorial provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). This involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject's neuroimaging timeseries (e.g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i.e., posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors. We walk through this approach in detail, using data from a published fMRI experiment that characterised individual differences in hemispheric lateralization in a semantic processing task. The preliminary subject specific DCM analysis is covered in detail in a companion paper. This tutorial is accompanied by the example dataset and step-by-step instructions to reproduce the analyses

Structure Learning in Coupled Dynamical Systems and Dynamic Causal Modelling

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of (ie, hypotheses about) network architectures and implicit coupling functions in terms of their Bayesian model evidence. These methods are collectively referred to as dynamical casual modelling (DCM). We focus on a relatively new approach that is proving remarkably useful; namely, Bayesian model reduction (BMR), which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems