Bayesian entropy estimators for spike trains

Il Memming Park and Jonathan Pillow are with the Institute for Neuroscience and Department of Psychology, The University of Texas at Austin, TX 78712, USA -- Evan Archer is with the Institute for Computational and Engineering Sciences, The University of Texas at Austin, TX 78712, USA -- Jonathan Pillow is with the Division of Statistics and Scientific Computation, The University of Texas at Austin, Austin, TX 78712, USAPoster presentation: Information theoretic quantities have played a central role in neuroscience for quantifying neural codes [1]. Entropy and mutual information can be used to measure the maximum encoding capacity of a neuron, quantify the amount of noise, spatial and temporal functional dependence, learning process, and provide a fundamental limit for neural coding. Unfortunately, estimating entropy or mutual information is notoriously difficult--especially when the number of observations N is less than the number of possible symbols K [2]. For the neural spike trains, this is often the case due to the combinatorial nature of the symbols: for n simultaneously recorded neurons on m time bins, the number of possible symbols is K = 2n+m. Therefore, the question is how to extrapolate when you may have a severely under-sampled distribution. Here we describe a couple of recent advances in Bayesian entropy estimation for spike trains. Our approach follows that of Nemenman et al. [2], who formulated a Bayesian entropy estimator using a mixture-of-Dirichlet prior over the space of discrete distributions on K bins. We extend this approach to formulate two Bayesian estimators with different strategies to deal with severe under-sampling. For the first estimator, we design a novel mixture prior over countable distributions using the Pitman-Yor (PY) process [3]. The PY process is useful when the number of parameters is unknown a priori, and as a result finds many applications in Bayesian nonparametrics. PY process can model the heavy, power-law distributed tails which often occur in neural data. To reduce the bias of the estimator we analytically derive a set of mixing weights so that the resulting improper prior over entropy is approximately flat. We consider the posterior over entropy given a dataset (which contains some observed number of words but an unknown number of unobserved words), and show that the posterior mean can be efficiently computed via a simple numerical integral. The second estimator incorporates the prior knowledge about the spike trains. We use a simple Bernoulli process as a parametric model of the spike trains, and use a Dirichlet process to allow arbitrary deviation from the Bernoulli process. Under this model, very sparse spike trains are a priori orders of magnitude more likely than those with many spikes. Both estimators are computationally efficient, and statistically consistent. We applied those estimators to spike trains from early visual system to quantify neural coding [email protected]

Bayesian Entropy Estimation for Countable Discrete Distributions

We consider the problem of estimating Shannon's entropy $H$ from discrete data, in cases where the number of possible symbols is unknown or even countably infinite. The Pitman-Yor process, a generalization of Dirichlet process, provides a tractable prior distribution over the space of countably infinite discrete distributions, and has found major applications in Bayesian non-parametric statistics and machine learning. Here we show that it also provides a natural family of priors for Bayesian entropy estimation, due to the fact that moments of the induced posterior distribution over $H$ can be computed analytically. We derive formulas for the posterior mean (Bayes' least squares estimate) and variance under Dirichlet and Pitman-Yor process priors. Moreover, we show that a fixed Dirichlet or Pitman-Yor process prior implies a narrow prior distribution over $H$, meaning the prior strongly determines the entropy estimate in the under-sampled regime. We derive a family of continuous mixing measures such that the resulting mixture of Pitman-Yor processes produces an approximately flat prior over $H$. We show that the resulting Pitman-Yor Mixture (PYM) entropy estimator is consistent for a large class of distributions. We explore the theoretical properties of the resulting estimator, and show that it performs well both in simulation and in application to real data.Comment: 38 pages LaTeX. Revised and resubmitted to JML

Mainstreaming domestic and gender-based violence into sociology and the criminology of violence

Sociological and criminological views of domestic and gender-based violencegenerally either dismiss it as not worthy of consideration, or focus on specificgroups of offenders and victims (male youth gangs, partner violence victims). Inthis paper, we take a holistic approach to violence, extending the definition fromthat commonly in use to encompass domestic violence and sexual violence. Weoperationalize that definition by using data from the latest sweep of the CrimeSurvey for England and Wales. By so doing, we identify that violence is currentlyunder-measured and ubiquitous; that it is gendered, and that other forms of violence (family violence, acquaintance violence against women) are equally ofconcern. We argue that violence studies are an important form of activity forsociologists

Sustainability of terrestrial carbon sequestration: A case study in Duke Forest with inversion approach

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95430/1/gbc891.pd

Agribusiness Sheep Updates - 2004 part 2

Precision Pastures Using Species Diversity to Improve Pasture Performance Anyou Liu and Clinton Revell, Department of Agriculture, Western Australia New Annual Pasture Legumes for Sheep Graziers Phil Nichols, Angelo Loi, Brad Nutt and Darryl McClements Department of Agriculture Western Australia Pastures from Space – Can Satellite Estimates of Pasture Growth Rate be used to Increase Farm Profit? Lucy Anderton, Stephen Gherardi and Chris Oldham Department of Agriculture Western Australia Summer-active Perennial Grasses for Profitable Sheep Production Paul Sanford and John Gladman, Department of Agriculture, Western Australia Pastures From Space – Validation Of Predictions Of Pasture Growth Rates DONALD, G.E.A, EDIRISINGHE, A.A, HENRY, D.A.A, MATA, G.A, GHERARDI, S.G.B, OLDHAM, C.M.B, GITTINS, S.P.B AND SMITH, R. C. G.C ACSIRO, Livestock Industries, PMB 5, Wembley, WA, 6913. BDepartment of Agriculture Western Australia, Bentley, WA, 6983. C Department of Land Information Western Australia, Floreat, WA, 6214. Production and Management of Biserrula Pasture - Managing the Risk of Photosensitivity Dr Clinton Revell and Roy Butler, Department of Agriculture Western Australia Meat Quality of Sheep Grazed on a Saltbush-based Pasture Kelly Pearce1,2, David Masters1, David Pethick2, 1 CSIRO LIVESTOCK INDUSTRIES, WEMBLEY, WA 2 SCHOOL OF VETERINARY AND BIOMEDICAL SCIENCE, MURDOCH UNIVERSITY, MURDOCH, WA Precision Sheep Lifetime Wool – Carryover Effects on Subsequent Reproduction of the Ewe Flock Chris Oldham, Department of Agriculture Western Australia Andrew Thompson, Primary Industries Research Victoria (PIRVic), Dept of Primary Industries, Hamilton, Vic Ewe Productivity Trials - a Linked Analysis Ken Hart, Johan Greeff, Department of Agriculture Western Australia, Beth Paganoni, School of Animal Biology, Faculty of Natural and Agricultural Sciences, University of Western Australia. Grain Finishing Systems For Prime Lambs Rachel Kirby, Matt Ryan, Kira Buttler, Department of Agriculture, Western Australia The Effects of Nutrition and Genotype on the Growth and Development, Muscle Biochemistry and Consumer Response to Lamb Meat David Pethick, Department of Veterinary Science, Murdoch University, WA, Roger Heggarty and David Hopkins, New South Wales Agriculture ‘Lifetime Wool’ - Effects of Nutrition During Pregnancy and Lactation on Mortality of Progeny to Hogget Shearing Samantha Giles, Beth Paganoni and Tom Plaisted, Department of Agriculture Western Australia, Mark Ferguson and Darren Gordon, Primary Industries Research Victoria (PIRVic), Dept of Primary Industries, Hamilton, Vic Lifetime Wool - Target Liveweights for the Ewe Flock J. Young, Farming Systems Analysis Service, Kojonup, C. Oldham, Department of Agriculture Western Australia, A. Thompson, Primary Industries Research Victoria (PIRVic), Hamilton, VIC Lifetime Wool - Effects of Nutrition During Pregnancy and Lactation on the Growth and Wool Production of their Progeny at Hogget Shearing B. Paganoni, University of Western Australia, Nedlands WA, C. Oldham, Department of Agriculture Western Australia, M. Ferguson, A. Thompson, Primary Industries Research Victoria (PIRVic), Hamilton, VIC RFID Technology – Esperance Experiences Sandra Brown, Department of Agriculture Western Australia The Role of Radio Frequency Identification (RFID) Technology in Prime Lamb Production - a Case Study. Ian McFarland, Department of Agriculture, Western Australia. John Archer, Producer, Narrogin, Western Australia Win with Twins from Merinos John Milton, Rob Davidson, Graeme Martin and David Lindsay The University of Western Australia Precision Sheep Need Precision Wool Harvesters Jonathan England, Castle Carrock Merinos, Kingston SE, South Australia Business EBVs and Indexes – Genetic Tools for your Toolbox Sandra Brown, Department of Agriculture Western Australia Green Feed Budget Paddock Calculator Mandy Curnow, Department of Agriculture Western Australia Minimising the Impact of Drought - Evaluating Flock Recovery Options using the ImPack Model Karina P. Wood, Ashley K. White, B. Lloyd Davies, Paul M. Carberry, NSW Department of Primary Industries (NSW DPI), Lifetime Wool - Modifying GrazFeed® for WA Mike Hyder, Department of Agriculture Western Australia , Mike Freer, CSIRO Plant Industry, Canberra, A.C.T. , Andrew van Burgel, and Kazue Tanaka, Department of Agriculture Western Australia Profile Calculator – A Way to Manage Fibre Diameter Throughout the Year to Maximise Returns Andrew Peterson, Department of Agriculture, Western Australia Pasture Watch - a Farmer Friendly Tool for Downloading and Analysing Pastures from Space Data Roger Wiese,Fairport Technologies International, South Perth, WA, Stephen Gherardi, BDepartment of Agriculture Western Australia, Gonzalo Mata, CCSIRO, Livestock Industries, Wembley, Western Australia, and Chris Oldham, Department of Agriculture Western Australia Sy Sheep Cropping Systems An Analysis of a Cropping System Containing Sheep in a Low Rainfall Livestock System. Evan Burt, Amanda Miller, Anne Bennett, Department of Agriculture, Western Australia Lucerne-based Pasture for the Central Wheatbelt – is it Good Economics? Felicity FluggeA, Amir AbadiA,B and Perry DollingA,B,A CRC for Plant-based Management of Dryland Salinity: BDept. of Agriculture, WA Sheep and Biserrula can Control Annual Ryegrass Dean Thomas, John Milton, Mike Ewing and David Lindsay, The University of WA, Clinton Revell, Department of Agriculture, Western Australia Sustainable Management Pasture Utilisation, Fleece Weight and Weaning Rate are Integral to the Profitability of Dohnes and SAMMs. Emma Kopke,Department of Agriculture Western Australia, John Young, Farming Systems Analysis Service Environmental Impact of Sheep Confinement Feeding Systems E A Dowling and E K Crossley, Department of Agriculture, Western Australia Smart Grazing Management for Production and Environmental Outcomes Dr Brien E (Ben) Norton, Centre for the Management of Arid Environments, Curtin University of Technology, WA Common Causes of Plant Poisoning in the Eastern Wheatbelt of Western Australia. Roy Butler, Department of Agriculture, Western Australia Selecting Sheep for Resistance to Worms and Production Trait Responses John Karlsson, Johan Greeff, Department of Agriculture, Western Australia, Geoff Pollott, Imperial College, London UK Production and Water Use of Lucerne and French Serradella in Four Soil Types, Diana Fedorenko1,4, Darryl McClements2,4 and Robert Beard3,4, 12Department of Agriculture, Western Australia; 3Farmer, Meckering; 4CRC for Plant-based Management of Dryland Salinity. Worm Burdens in Sheep at Slaughter Brown Besier, Department of Agriculture Western Australia, Una Ryan, Caroline Bath, Murdoch Universit

Minimal information for studies of extracellular vesicles 2018 (MISEV2018):a position statement of the International Society for Extracellular Vesicles and update of the MISEV2014 guidelines

The last decade has seen a sharp increase in the number of scientific publications describing physiological and pathological functions of extracellular vesicles (EVs), a collective term covering various subtypes of cell-released, membranous structures, called exosomes, microvesicles, microparticles, ectosomes, oncosomes, apoptotic bodies, and many other names. However, specific issues arise when working with these entities, whose size and amount often make them difficult to obtain as relatively pure preparations, and to characterize properly. The International Society for Extracellular Vesicles (ISEV) proposed Minimal Information for Studies of Extracellular Vesicles (“MISEV”) guidelines for the field in 2014. We now update these “MISEV2014” guidelines based on evolution of the collective knowledge in the last four years. An important point to consider is that ascribing a specific function to EVs in general, or to subtypes of EVs, requires reporting of specific information beyond mere description of function in a crude, potentially contaminated, and heterogeneous preparation. For example, claims that exosomes are endowed with exquisite and specific activities remain difficult to support experimentally, given our still limited knowledge of their specific molecular machineries of biogenesis and release, as compared with other biophysically similar EVs. The MISEV2018 guidelines include tables and outlines of suggested protocols and steps to follow to document specific EV-associated functional activities. Finally, a checklist is provided with summaries of key points