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Stan: a Probabilistic Programming Language
JSS Journal of Statistical Software January 2017, Volume 76, Issue 1. doi: 10.18637/jss.v076.i01 Stan: A Probabilistic Programming Language Bob Carpenter Andrew Gelman Matthew D. Hoffman Columbia University Columbia University Adobe Creative Technologies Lab Daniel Lee Ben Goodrich Michael Betancourt Columbia University Columbia University Columbia University Marcus A. Brubaker Jiqiang Guo Peter Li York University NPD Group Columbia University Allen Riddell Indiana University Abstract Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectation propa- gation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces sup- port sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting. -
Stan: a Probabilistic Programming Language
JSS Journal of Statistical Software MMMMMM YYYY, Volume VV, Issue II. http://www.jstatsoft.org/ Stan: A Probabilistic Programming Language Bob Carpenter Andrew Gelman Matt Hoffman Columbia University Columbia University Adobe Research Daniel Lee Ben Goodrich Michael Betancourt Columbia University Columbia University University of Warwick Marcus A. Brubaker Jiqiang Guo Peter Li University of Toronto, NPD Group Columbia University Scarborough Allen Riddell Dartmouth College Abstract Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.2.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectation propa- gation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can be called from the command line, through R using the RStan package, or through Python using the PyStan package. All three interfaces support sampling and optimization-based inference. RStan and PyStan also provide access to log probabilities, gradients, Hessians, and data I/O. Keywords: probabilistic program, Bayesian inference, algorithmic differentiation, Stan. -
Introduction to Ggplot2
Introduction to ggplot2 Dawn Koffman Office of Population Research Princeton University January 2014 1 Part 1: Concepts and Terminology 2 R Package: ggplot2 Used to produce statistical graphics, author = Hadley Wickham "attempt to take the good things about base and lattice graphics and improve on them with a strong, underlying model " based on The Grammar of Graphics by Leland Wilkinson, 2005 "... describes the meaning of what we do when we construct statistical graphics ... More than a taxonomy ... Computational system based on the underlying mathematics of representing statistical functions of data." - does not limit developer to a set of pre-specified graphics adds some concepts to grammar which allow it to work well with R 3 qplot() ggplot2 provides two ways to produce plot objects: qplot() # quick plot – not covered in this workshop uses some concepts of The Grammar of Graphics, but doesn’t provide full capability and designed to be very similar to plot() and simple to use may make it easy to produce basic graphs but may delay understanding philosophy of ggplot2 ggplot() # grammar of graphics plot – focus of this workshop provides fuller implementation of The Grammar of Graphics may have steeper learning curve but allows much more flexibility when building graphs 4 Grammar Defines Components of Graphics data: in ggplot2, data must be stored as an R data frame coordinate system: describes 2-D space that data is projected onto - for example, Cartesian coordinates, polar coordinates, map projections, ... geoms: describe type of geometric objects that represent data - for example, points, lines, polygons, ... aesthetics: describe visual characteristics that represent data - for example, position, size, color, shape, transparency, fill scales: for each aesthetic, describe how visual characteristic is converted to display values - for example, log scales, color scales, size scales, shape scales, .. -
Advancedhmc.Jl: a Robust, Modular and Efficient Implementation of Advanced HMC Algorithms
2nd Symposium on Advances in Approximate Bayesian Inference, 20191{10 AdvancedHMC.jl: A robust, modular and efficient implementation of advanced HMC algorithms Kai Xu [email protected] University of Edinburgh Hong Ge [email protected] University of Cambridge Will Tebbutt [email protected] University of Cambridge Mohamed Tarek [email protected] UNSW Canberra Martin Trapp [email protected] Graz University of Technology Zoubin Ghahramani [email protected] University of Cambridge & Uber AI Labs Abstract Stan's Hamilton Monte Carlo (HMC) has demonstrated remarkable sampling robustness and efficiency in a wide range of Bayesian inference problems through carefully crafted adaption schemes to the celebrated No-U-Turn sampler (NUTS) algorithm. It is challeng- ing to implement these adaption schemes robustly in practice, hindering wider adoption amongst practitioners who are not directly working with the Stan modelling language. AdvancedHMC.jl (AHMC) contributes a modular, well-tested, standalone implementation of NUTS that recovers and extends Stan's NUTS algorithm. AHMC is written in Julia, a modern high-level language for scientific computing, benefiting from optional hardware acceleration and interoperability with a wealth of existing software written in both Julia and other languages, such as Python. Efficacy is demonstrated empirically by comparison with Stan through a third-party Markov chain Monte Carlo benchmarking suite. 1. Introduction Hamiltonian Monte Carlo (HMC) is an efficient Markov chain Monte Carlo (MCMC) algo- rithm which avoids random walks by simulating Hamiltonian dynamics to make proposals (Duane et al., 1987; Neal et al., 2011). Due to the statistical efficiency of HMC, it has been widely applied to fields including physics (Duane et al., 1987), differential equations (Kramer et al., 2014), social science (Jackman, 2009) and Bayesian inference (e.g. -
Regression Models by Gretl and R Statistical Packages for Data Analysis in Marine Geology Polina Lemenkova
Regression Models by Gretl and R Statistical Packages for Data Analysis in Marine Geology Polina Lemenkova To cite this version: Polina Lemenkova. Regression Models by Gretl and R Statistical Packages for Data Analysis in Marine Geology. International Journal of Environmental Trends (IJENT), 2019, 3 (1), pp.39 - 59. hal-02163671 HAL Id: hal-02163671 https://hal.archives-ouvertes.fr/hal-02163671 Submitted on 3 Jul 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License International Journal of Environmental Trends (IJENT) 2019: 3 (1),39-59 ISSN: 2602-4160 Research Article REGRESSION MODELS BY GRETL AND R STATISTICAL PACKAGES FOR DATA ANALYSIS IN MARINE GEOLOGY Polina Lemenkova 1* 1 ORCID ID number: 0000-0002-5759-1089. Ocean University of China, College of Marine Geo-sciences. 238 Songling Rd., 266100, Qingdao, Shandong, P. R. C. Tel.: +86-1768-554-1605. Abstract Received 3 May 2018 Gretl and R statistical libraries enables to perform data analysis using various algorithms, modules and functions. The case study of this research consists in geospatial analysis of Accepted the Mariana Trench, a hadal trench located in the Pacific Ocean. -
Performance Assessment and Translation of Physiologically
TOXICOLOGICAL SCIENCES, 158(1), 2017, 23–35 doi: 10.1093/toxsci/kfx070 Advance Access Publication Date: April 8, 2017 Forum FORUM Performance Assessment and Translation of Physiologically Based Pharmacokinetic Models From acslX to Berkeley Madonna, MATLAB, and R Language: Oxytetracycline and Gold Nanoparticles As Case Examples Zhoumeng Lin,*,1 Majid Jaberi-Douraki,*,† Chunla He,‡ Shiqiang Jin,*,§ Raymond S. H. Yang,¶,k Jeffrey W. Fisher,kj and Jim E. Riviere* *Institute of Computational Comparative Medicine (ICCM), Department of Anatomy and Physiology, College of Veterinary Medicine, Kansas State University, Manhattan, Kansas 66506; †Department of Mathematics, College of Arts and Sciences, Kansas State University, Manhattan, Kansas 66506; ‡Department of Epidemiology and Biostatistics, College of Public Health, The University of Georgia, Athens, Georgia 30602; §Department of Statistics, College of Arts and Sciences, Kansas State University, Manhattan, Kansas 66506; ¶Department of Environmental and Radiological Health Sciences, College of Veterinary Medicine and Biomedical Sciences, Colorado State University, Fort Collins, Colorado 80523; kRay Yang Consulting LLC, Fort Collins, Colorado 80526; and kjDivision of Biochemical Toxicology, National Center for Toxicological Research, U.S. Food and Drug Administration, Jefferson, Arkansas 72079 1To whom correspondence should be addressed at Institute of Computational Comparative Medicine (ICCM), Department of Anatomy and Physiology, College of Veterinary Medicine, Kansas State University, 1800 Denison Avenue, P200 Mosier Hall, Manhattan, KS 66506. Fax: (785) 532-4953. E-mail: [email protected]. ABSTRACT Many physiologically based pharmacokinetic (PBPK) models for environmental chemicals, drugs, and nanomaterials have been developed to aid risk and safety assessments using acslX. However, acslX has been rendered sunset since November 2015. Alternative modeling tools and tutorials are needed for future PBPK applications. -
Maple Advanced Programming Guide
Maple 9 Advanced Programming Guide M. B. Monagan K. O. Geddes K. M. Heal G. Labahn S. M. Vorkoetter J. McCarron P. DeMarco c Maplesoft, a division of Waterloo Maple Inc. 2003. ii ¯ Maple, Maplesoft, Maplet, and OpenMaple are trademarks of Water- loo Maple Inc. c Maplesoft, a division of Waterloo Maple Inc. 2003. All rights re- served. The electronic version (PDF) of this book may be downloaded and printed for personal use or stored as a copy on a personal machine. The electronic version (PDF) of this book may not be distributed. Information in this document is subject to change without notice and does not rep- resent a commitment on the part of the vendor. The software described in this document is furnished under a license agreement and may be used or copied only in accordance with the agreement. It is against the law to copy the software on any medium as specifically allowed in the agreement. Windows is a registered trademark of Microsoft Corporation. Java and all Java based marks are trademarks or registered trade- marks of Sun Microsystems, Inc. in the United States and other countries. Maplesoft is independent of Sun Microsystems, Inc. All other trademarks are the property of their respective owners. This document was produced using a special version of Maple that reads and updates LATEX files. Printed in Canada ISBN 1-894511-44-1 Contents Preface 1 Audience . 1 Worksheet Graphical Interface . 2 Manual Set . 2 Conventions . 3 Customer Feedback . 3 1 Procedures, Variables, and Extending Maple 5 Prerequisite Knowledge . 5 In This Chapter . -
End-User Probabilistic Programming
End-User Probabilistic Programming Judith Borghouts, Andrew D. Gordon, Advait Sarkar, and Neil Toronto Microsoft Research Abstract. Probabilistic programming aims to help users make deci- sions under uncertainty. The user writes code representing a probabilistic model, and receives outcomes as distributions or summary statistics. We consider probabilistic programming for end-users, in particular spread- sheet users, estimated to number in tens to hundreds of millions. We examine the sources of uncertainty actually encountered by spreadsheet users, and their coping mechanisms, via an interview study. We examine spreadsheet-based interfaces and technology to help reason under uncer- tainty, via probabilistic and other means. We show how uncertain values can propagate uncertainty through spreadsheets, and how sheet-defined functions can be applied to handle uncertainty. Hence, we draw conclu- sions about the promise and limitations of probabilistic programming for end-users. 1 Introduction In this paper, we discuss the potential of bringing together two rather distinct approaches to decision making under uncertainty: spreadsheets and probabilistic programming. We start by introducing these two approaches. 1.1 Background: Spreadsheets and End-User Programming The spreadsheet is the first \killer app" of the personal computer era, starting in 1979 with Dan Bricklin and Bob Frankston's VisiCalc for the Apple II [15]. The primary interface of a spreadsheet|then and now, four decades later|is the grid, a two-dimensional array of cells. Each cell may hold a literal data value, or a formula that computes a data value (and may depend on the data in other cells, which may themselves be computed by formulas). -
Julia: a Fresh Approach to Numerical Computing∗
SIAM REVIEW c 2017 Society for Industrial and Applied Mathematics Vol. 59, No. 1, pp. 65–98 Julia: A Fresh Approach to Numerical Computing∗ Jeff Bezansony Alan Edelmanz Stefan Karpinskix Viral B. Shahy Abstract. Bridging cultures that have often been distant, Julia combines expertise from the diverse fields of computer science and computational science to create a new approach to numerical computing. Julia is designed to be easy and fast and questions notions generally held to be \laws of nature" by practitioners of numerical computing: 1. High-level dynamic programs have to be slow. 2. One must prototype in one language and then rewrite in another language for speed or deployment. 3. There are parts of a system appropriate for the programmer, and other parts that are best left untouched as they have been built by the experts. We introduce the Julia programming language and its design|a dance between special- ization and abstraction. Specialization allows for custom treatment. Multiple dispatch, a technique from computer science, picks the right algorithm for the right circumstance. Abstraction, which is what good computation is really about, recognizes what remains the same after differences are stripped away. Abstractions in mathematics are captured as code through another technique from computer science, generic programming. Julia shows that one can achieve machine performance without sacrificing human con- venience. Key words. Julia, numerical, scientific computing, parallel AMS subject classifications. 68N15, 65Y05, 97P40 DOI. 10.1137/141000671 Contents 1 Scientific Computing Languages: The Julia Innovation 66 1.1 Julia Architecture and Language Design Philosophy . 67 ∗Received by the editors December 18, 2014; accepted for publication (in revised form) December 16, 2015; published electronically February 7, 2017. -
Revolution R Enterprise™ 7.1 Getting Started Guide
Revolution R Enterprise™ 7.1 Getting Started Guide The correct bibliographic citation for this manual is as follows: Revolution Analytics, Inc. 2014. Revolution R Enterprise 7.1 Getting Started Guide. Revolution Analytics, Inc., Mountain View, CA. Revolution R Enterprise 7.1 Getting Started Guide Copyright © 2014 Revolution Analytics, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of Revolution Analytics. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the Government is subject to restrictions as set forth in subdivision (c) (1) (ii) of The Rights in Technical Data and Computer Software clause at 52.227-7013. Revolution R, Revolution R Enterprise, RPE, RevoScaleR, RevoDeployR, RevoTreeView, and Revolution Analytics are trademarks of Revolution Analytics. Other product names mentioned herein are used for identification purposes only and may be trademarks of their respective owners. Revolution Analytics. 2570 W. El Camino Real Suite 222 Mountain View, CA 94040 USA. Revised on March 3, 2014 We want our documentation to be useful, and we want it to address your needs. If you have comments on this or any Revolution document, send e-mail to [email protected]. We’d love to hear from you. Contents Chapter 1. What Is Revolution R Enterprise? .................................................................... -
A High-Performance Serial/Parallel Monte Carlo Simulation Library for C, C++, Fortran
ParaMonte: A high-performance serial/parallel Monte Carlo simulation library for C, C++, Fortran Amir Shahmoradi1, 2 and Fatemeh Bagheri1 DOI: 1 Department of Physics, The University of Texas, Arlington, TX 2 Data Science Program, The University of Texas, Arlington, TX Software • Review Summary • Repository • Archive ParaMonte (standing for Parallel Monte Carlo) is a serial and MPI/Coarray-parallelized library of Monte Carlo routines for sampling mathematical objective functions of arbitrary-dimensions, in Editor: particular, the posterior distributions of Bayesian models in data science, Machine Learning, and scientific inference. The ParaMonte library has been developed with the design goal of unifying Submitted: 29 September 2020 the automation, accessibility, high-performance, scalability, and reproducibility of Monte Published: Carlo simulations. The current implementation of the library includes ParaDRAM, a Parallel License Delyaed-Rejection Adaptive Metropolis Markov Chain Monte Carlo sampler, accessible from a Authors of papers retain wide range of programming languages including C, C++, Fortran, with a unified Application copyright and release the work Programming Interface and simulation environment across all supported programming languages. under a Creative Commons The ParaMonte library is MIT-licensed and is permanently located and maintained at https: Attribution 4.0 International //github.com/cdslaborg/paramonte. License (CC BY 4.0). Statement of need Monte Carlo simulation techniques, in particular, the Markov Chain Monte Carlo (MCMC) are among the most popular methods of quantifying uncertainty in scientific inference problems. Extensive work has been done over the past decades to develop Monte Carlo simulation programming environments that aim to partially or fully automate the problem of uncertainty quantification via Markov Chain Monte Carlo simulations. -
Julia: a Modern Language for Modern ML
Julia: A modern language for modern ML Dr. Viral Shah and Dr. Simon Byrne www.juliacomputing.com What we do: Modernize Technical Computing Today’s technical computing landscape: • Develop new learning algorithms • Run them in parallel on large datasets • Leverage accelerators like GPUs, Xeon Phis • Embed into intelligent products “Business as usual” will simply not do! General Micro-benchmarks: Julia performs almost as fast as C • 10X faster than Python • 100X faster than R & MATLAB Performance benchmark relative to C. A value of 1 means as fast as C. Lower values are better. A real application: Gillespie simulations in systems biology 745x faster than R • Gillespie simulations are used in the field of drug discovery. • Also used for simulations of epidemiological models to study disease propagation • Julia package (Gillespie.jl) is the state of the art in Gillespie simulations • https://github.com/openjournals/joss- papers/blob/master/joss.00042/10.21105.joss.00042.pdf Implementation Time per simulation (ms) R (GillespieSSA) 894.25 R (handcoded) 1087.94 Rcpp (handcoded) 1.31 Julia (Gillespie.jl) 3.99 Julia (Gillespie.jl, passing object) 1.78 Julia (handcoded) 1.2 Those who convert ideas to products fastest will win Computer Quants develop Scientists prepare algorithms The last 25 years for production (Python, R, SAS, DEPLOY (C++, C#, Java) Matlab) Quants and Computer Compress the Scientists DEPLOY innovation cycle collaborate on one platform - JULIA with Julia Julia offers competitive advantages to its users Julia is poised to become one of the Thank you for Julia. Yo u ' v e k i n d l ed leading tools deployed by developers serious excitement.