Strategies for Fitting Nonlinear Ecological Models in R, AD Model
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Chapter 7 Assessing and Improving Convergence of the Markov Chain
Chapter 7 Assessing and improving convergence of the Markov chain Questions: . Are we getting the right answer? . Can we get the answer quicker? Bayesian Biostatistics - Piracicaba 2014 376 7.1 Introduction • MCMC sampling is powerful, but comes with a cost: dependent sampling + checking convergence is not easy: ◦ Convergence theorems do not tell us when convergence will occur ◦ In this chapter: graphical + formal diagnostics to assess convergence • Acceleration techniques to speed up MCMC sampling procedure • Data augmentation as Bayesian generalization of EM algorithm Bayesian Biostatistics - Piracicaba 2014 377 7.2 Assessing convergence of a Markov chain Bayesian Biostatistics - Piracicaba 2014 378 7.2.1 Definition of convergence for a Markov chain Loose definition: With increasing number of iterations (k −! 1), the distribution of k θ , pk(θ), converges to the target distribution p(θ j y). In practice, convergence means: • Histogram of θk remains the same along the chain • Summary statistics of θk remain the same along the chain Bayesian Biostatistics - Piracicaba 2014 379 Approaches • Theoretical research ◦ Establish conditions that ensure convergence, but in general these theoretical results cannot be used in practice • Two types of practical procedures to check convergence: ◦ Checking stationarity: from which iteration (k0) is the chain sampling from the posterior distribution (assessing burn-in part of the Markov chain). ◦ Checking accuracy: verify that the posterior summary measures are computed with the desired accuracy • Most -
Getting Started in Openbugs / Winbugs
Practical 1: Getting started in OpenBUGS Slide 1 An Introduction to Using WinBUGS for Cost-Effectiveness Analyses in Health Economics Dr. Christian Asseburg Centre for Health Economics University of York, UK [email protected] Practical 1 Getting started in OpenBUGS / WinB UGS 2007-03-12, Linköping Dr Christian Asseburg University of York, UK [email protected] Practical 1: Getting started in OpenBUGS Slide 2 ● Brief comparison WinBUGS / OpenBUGS ● Practical – Opening OpenBUGS – Entering a model and data – Some error messages – Starting the sampler – Checking sampling performance – Retrieving the posterior summaries 2007-03-12, Linköping Dr Christian Asseburg University of York, UK [email protected] Practical 1: Getting started in OpenBUGS Slide 3 WinBUGS / OpenBUGS ● WinBUGS was developed at the MRC Biostatistics unit in Cambridge. Free download, but registration required for a licence. No fee and no warranty. ● OpenBUGS is the current development of WinBUGS after its source code was released to the public. Download is free, no registration, GNU GPL licence. 2007-03-12, Linköping Dr Christian Asseburg University of York, UK [email protected] Practical 1: Getting started in OpenBUGS Slide 4 WinBUGS / OpenBUGS ● There are no major differences between the latest WinBUGS (1.4.1) and OpenBUGS (2.2.0) releases. ● Minor differences include: – OpenBUGS is occasionally a bit slower – WinBUGS requires Microsoft Windows OS – OpenBUGS error messages are sometimes more informative ● The examples in these slides use OpenBUGS. 2007-03-12, Linköping Dr Christian Asseburg University of York, UK [email protected] Practical 1: Getting started in OpenBUGS Slide 5 Practical 1: Target ● Start OpenBUGS ● Code the example from health economics from the earlier presentation ● Run the sampler and obtain posterior summaries 2007-03-12, Linköping Dr Christian Asseburg University of York, UK [email protected] Practical 1: Getting started in OpenBUGS Slide 6 Starting OpenBUGS ● You can download OpenBUGS from http://mathstat.helsinki.fi/openbugs/ ● Start the program. -
BUGS Code for Item Response Theory
JSS Journal of Statistical Software August 2010, Volume 36, Code Snippet 1. http://www.jstatsoft.org/ BUGS Code for Item Response Theory S. McKay Curtis University of Washington Abstract I present BUGS code to fit common models from item response theory (IRT), such as the two parameter logistic model, three parameter logisitic model, graded response model, generalized partial credit model, testlet model, and generalized testlet models. I demonstrate how the code in this article can easily be extended to fit more complicated IRT models, when the data at hand require a more sophisticated approach. Specifically, I describe modifications to the BUGS code that accommodate longitudinal item response data. Keywords: education, psychometrics, latent variable model, measurement model, Bayesian inference, Markov chain Monte Carlo, longitudinal data. 1. Introduction In this paper, I present BUGS (Gilks, Thomas, and Spiegelhalter 1994) code to fit several models from item response theory (IRT). Several different software packages are available for fitting IRT models. These programs include packages from Scientific Software International (du Toit 2003), such as PARSCALE (Muraki and Bock 2005), BILOG-MG (Zimowski, Mu- raki, Mislevy, and Bock 2005), MULTILOG (Thissen, Chen, and Bock 2003), and TESTFACT (Wood, Wilson, Gibbons, Schilling, Muraki, and Bock 2003). The Comprehensive R Archive Network (CRAN) task view \Psychometric Models and Methods" (Mair and Hatzinger 2010) contains a description of many different R packages that can be used to fit IRT models in the R computing environment (R Development Core Team 2010). Among these R packages are ltm (Rizopoulos 2006) and gpcm (Johnson 2007), which contain several functions to fit IRT models using marginal maximum likelihood methods, and eRm (Mair and Hatzinger 2007), which contains functions to fit several variations of the Rasch model (Fischer and Molenaar 1995). -
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. -
Installing BUGS and the R to BUGS Interface 1. Brief Overview
File = E:\bugs\installing.bugs.jags.docm 1 John Miyamoto (email: [email protected]) Installing BUGS and the R to BUGS Interface Caveat: I am a Windows user so these notes are focused on Windows 7 installations. I will include what I know about the Mac and Linux versions of these programs but I cannot swear to the accuracy of my comments. Contents (Cntrl-left click on a link to jump to the corresponding section) Section Topic 1 Brief Overview 2 Installing OpenBUGS 3 Installing WinBUGs (Windows only) 4 OpenBUGS versus WinBUGS 5 Installing JAGS 6 Installing R packages that are used with OpenBUGS, WinBUGS, and JAGS 7 Running BRugs on a 32-bit or 64-bit Windows computer 8 Hints for Mac and Linux Users 9 References # End of Contents Table 1. Brief Overview TOC BUGS stands for Bayesian Inference Under Gibbs Sampling1. The BUGS program serves two critical functions in Bayesian statistics. First, given appropriate inputs, it computes the posterior distribution over model parameters - this is critical in any Bayesian statistical analysis. Second, it allows the user to compute a Bayesian analysis without requiring extensive knowledge of the mathematical analysis and computer programming required for the analysis. The user does need to understand the statistical model or models that are being analyzed, the assumptions that are made about model parameters including their prior distributions, and the structure of the data, but the BUGS program relieves the user of the necessity of creating an algorithm to sample from the posterior distribution and the necessity of writing the computer program that computes this algorithm. -
R G M B.Ec. M.Sc. Ph.D
Rolando Kristiansand, Norway www.bayesgroup.org Gonzales Martinez +47 41224721 [email protected] JOBS & AWARDS M.Sc. B.Ec. Applied Ph.D. Economics candidate Statistics Jobs Events Awards Del Valle University University of Alcalá Universitetet i Agder 2018 Bolivia, 2000-2004 Spain, 2009-2010 Norway, 2018- 1/2018 Ph.D scholarship 8/2017 International Consultant, OPHI OTHER EDUCATION First prize, International Young 12/2016 J-PAL Course on Evaluating Social Programs Macro-prudential Policies Statistician Prize, IAOS Massachusetts Institute of Technology - MIT International Monetary Fund (IMF) 5/2016 Deputy manager, BCP bank Systematic Literature Reviews and Meta-analysis Theorizing and Theory Building Campbell foundation - Vrije Universiteit Halmstad University (HH, Sweden) 1/2016 Consultant, UNFPA Bayesian Modeling, Inference and Prediction Multidimensional Poverty Analysis University of Reading OPHI, Oxford University Researcher, data analyst & SKILLS AND TECHNOLOGIES 1/2015 project coordinator, PEP Academic Research & publishing Financial & Risk analysis 12 years of experience making economic/nancial analysis 3/2014 Director, BayesGroup.org and building mathemati- Consulting cal/statistical/econometric models for the government, private organizations and non- prot NGOs Research & project Mathematical 1/2013 modeling coordinator, UNFPA LANGUAGES 04/2012 First award, BCG competition Spanish (native) Statistical analysis English (TOEFL: 106) 9/2011 Financial Economist, UDAPE MatLab Macro-economic R, RStudio 11/2010 Currently, I work mainly analyst, MEFP Stata, SPSS with MatLab and R . SQL, SAS When needed, I use 3/2010 First award, BCB competition Eviews Stata, SAS or Eviews. I started working in LaTex, WinBugs Python recently. 8/2009 M.Sc. scholarship Python, Spyder RECENT PUBLICATIONS Disjunction between universality and targeting of social policies: Demographic opportunities for depolarized de- velopment in Paraguay. -
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). -
Admb Package
Using AD Model Builder and R together: getting started with the R2admb package Ben Bolker March 9, 2020 1 Introduction AD Model Builder (ADMB: http://admb-project.org) is a standalone program, developed by Dave Fournier continuously since the 1980s and re- leased as an open source project in 2007, that takes as input an objective function (typically a negative log-likelihood function) and outputs the co- efficients that minimize the objective function, along with various auxiliary information. AD Model Builder uses automatic differentiation (that's what \AD" stands for), a powerful algorithm for computing the derivatives of a specified objective function efficiently and without the typical errors due to finite differencing. Because of this algorithm, and because the objective function is compiled into machine code before optimization, ADMB can solve large, difficult likelihood problems efficiently. ADMB also has the capability to fit random-effects models (typically via Laplace approximation). To the average R user, however, ADMB represents a challenge. The first (unavoidable) challenge is that the objective function needs to be written in a superset of C++; the second is learning the particular sequence of steps that need to be followed in order to output data in a suitable format for ADMB; compile and run the ADMB model; and read the data into R for analysis. The R2admb package aims to eliminate the second challenge by automating the R{ADMB interface as much as possible. 2 Installation The R2admb package can be installed in R in the standard way (with install.packages() or via a Packages menu, depending on your platform. -
Automated Likelihood Based Inference for Stochastic Volatility Models H
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Institutional Knowledge at Singapore Management University Singapore Management University Institutional Knowledge at Singapore Management University Research Collection School Of Economics School of Economics 11-2009 Automated Likelihood Based Inference for Stochastic Volatility Models H. Skaug Jun YU Singapore Management University, [email protected] Follow this and additional works at: https://ink.library.smu.edu.sg/soe_research Part of the Econometrics Commons Citation Skaug, H. and YU, Jun. Automated Likelihood Based Inference for Stochastic Volatility Models. (2009). 1-28. Research Collection School Of Economics. Available at: https://ink.library.smu.edu.sg/soe_research/1151 This Working Paper is brought to you for free and open access by the School of Economics at Institutional Knowledge at Singapore Management University. It has been accepted for inclusion in Research Collection School Of Economics by an authorized administrator of Institutional Knowledge at Singapore Management University. For more information, please email [email protected]. Automated Likelihood Based Inference for Stochastic Volatility Models Hans J. SKAUG , Jun YU November 2009 Paper No. 15-2009 ANY OPINIONS EXPRESSED ARE THOSE OF THE AUTHOR(S) AND NOT NECESSARILY THOSE OF THE SCHOOL OF ECONOMICS, SMU Automated Likelihood Based Inference for Stochastic Volatility Models¤ Hans J. Skaug,y Jun Yuz October 7, 2008 Abstract: In this paper the Laplace approximation is used to perform classical and Bayesian analyses of univariate and multivariate stochastic volatility (SV) models. We show that imple- mentation of the Laplace approximation is greatly simpli¯ed by the use of a numerical technique known as automatic di®erentiation (AD). -
Bayesian Data Analysis and Probabilistic Programming
Probabilistic programming and Stan mc-stan.org Outline What is probabilistic programming Stan now Stan in the future A bit about other software The next wave of probabilistic programming Stan even wider adoption including wider use in companies simulators (likelihood free) autonomus agents (reinforcmenet learning) deep learning Probabilistic programming Probabilistic programming framework BUGS started revolution in statistical analysis in early 1990’s allowed easier use of elaborate models by domain experts was widely adopted in many fields of science Probabilistic programming Probabilistic programming framework BUGS started revolution in statistical analysis in early 1990’s allowed easier use of elaborate models by domain experts was widely adopted in many fields of science The next wave of probabilistic programming Stan even wider adoption including wider use in companies simulators (likelihood free) autonomus agents (reinforcmenet learning) deep learning Stan Tens of thousands of users, 100+ contributors, 50+ R packages building on Stan Commercial and scientific users in e.g. ecology, pharmacometrics, physics, political science, finance and econometrics, professional sports, real estate Used in scientific breakthroughs: LIGO gravitational wave discovery (2017 Nobel Prize in Physics) and counting black holes Used in hundreds of companies: Facebook, Amazon, Google, Novartis, Astra Zeneca, Zalando, Smartly.io, Reaktor, ... StanCon 2018 organized in Helsinki in 29-31 August http://mc-stan.org/events/stancon2018Helsinki/ Probabilistic program -
Multivariate Statistical Methods to Analyse Multidimensional Data in Applied Life Science
Multivariate statistical methods to analyse multidimensional data in applied life science Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften (Dr. rer. nat.) der Naturwissenschaftlichen Fakult¨atIII Agrar- und Ern¨ahrungswissenschaften, Geowissenschaften und Informatik der Martin-Luther-Universit¨atHalle-Wittenberg vorgelegt von Frau Trutschel (geb. Boronczyk), Diana Geb. am 18.02.1979 in Hohenm¨olsen Gutachter: 1. Prof. Dr. Ivo Grosse, MLU Halle/Saale 2. Dr. Steffen Neumann, IPB alle/Saale 3. Prof. Dr. Andr´eScherag, FSU Jena Datum der Verteidigung: 18.04.2019 I Eidesstattliche Erklärung / Declaration under Oath Ich erkläre an Eides statt, dass ich die Arbeit selbstständig und ohne fremde Hilfe verfasst, keine anderen als die von mir angegebenen Quellen und Hilfsmittel benutzt und die den benutzten Werken wörtlich oder inhaltlich entnommenen Stellen als solche kenntlich gemacht habe. I declare under penalty of perjury that this thesis is my own work entirely and has been written without any help from other people. I used only the sources mentioned and included all the citations correctly both in word or content. __________________________ ____________________________________________ Datum / Date Unterschrift des Antragstellers / Signature of the applicant III This thesis is a cumulative thesis, including five research articles that have previously been published in peer-reviewed international journals. In the following these publications are listed, whereby the first authors are underlined and my name (Trutschel) is marked in bold. 1. Trutschel, Diana and Schmidt, Stephan and Grosse, Ivo and Neumann, Steffen, "Ex- periment design beyond gut feeling: statistical tests and power to detect differential metabolites in mass spectrometry data", Metabolomics, 2015, available at: https:// link.springer.com/content/pdf/10.1007/s11306-014-0742-y.pdf 2. -
Software Packages – Overview There Are Many Software Packages Available for Performing Statistical Analyses. the Ones Highlig
APPENDIX C SOFTWARE OPTIONS Software Packages – Overview There are many software packages available for performing statistical analyses. The ones highlighted here are selected because they provide comprehensive statistical design and analysis tools and a user friendly interface. SAS SAS is arguably one of the most comprehensive packages in terms of statistical analyses. However, the individual license cost is expensive. Primarily, SAS is a macro based scripting language, making it challenging for new users. However, it provides a comprehensive analysis ranging from the simple t-test to Generalized Linear mixed models. SAS also provides limited Design of Experiments capability. SAS supports factorial designs and optimal designs. However, it does not handle design constraints well. SAS also has a GUI available: SAS Enterprise, however, it has limited capability. SAS is a good program to purchase if your organization conducts advanced statistical analyses or works with very large datasets. R R, similar to SAS, provides a comprehensive analysis toolbox. R is an open source software package that has been approved for use on some DoD computer (contact AFFTC for details). Because R is open source its price is very attractive (free). However, the help guides are not user friendly. R is primarily a scripting software with notation similar to MatLab. R’s GUI: R Commander provides limited DOE capabilities. R is a good language to download if you can get it approved for use and you have analysts with a strong programming background. MatLab w/ Statistical Toolbox MatLab has a statistical toolbox that provides a wide variety of statistical analyses. The analyses range from simple hypotheses test to complex models and the ability to use likelihood maximization.