Science As Successful Prediction
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Generalized Linear Models (Glms)
San Jos´eState University Math 261A: Regression Theory & Methods Generalized Linear Models (GLMs) Dr. Guangliang Chen This lecture is based on the following textbook sections: • Chapter 13: 13.1 – 13.3 Outline of this presentation: • What is a GLM? • Logistic regression • Poisson regression Generalized Linear Models (GLMs) What is a GLM? In ordinary linear regression, we assume that the response is a linear function of the regressors plus Gaussian noise: 0 2 y = β0 + β1x1 + ··· + βkxk + ∼ N(x β, σ ) | {z } |{z} linear form x0β N(0,σ2) noise The model can be reformulate in terms of • distribution of the response: y | x ∼ N(µ, σ2), and • dependence of the mean on the predictors: µ = E(y | x) = x0β Dr. Guangliang Chen | Mathematics & Statistics, San Jos´e State University3/24 Generalized Linear Models (GLMs) beta=(1,2) 5 4 3 β0 + β1x b y 2 y 1 0 −1 0.0 0.2 0.4 0.6 0.8 1.0 x x Dr. Guangliang Chen | Mathematics & Statistics, San Jos´e State University4/24 Generalized Linear Models (GLMs) Generalized linear models (GLM) extend linear regression by allowing the response variable to have • a general distribution (with mean µ = E(y | x)) and • a mean that depends on the predictors through a link function g: That is, g(µ) = β0x or equivalently, µ = g−1(β0x) Dr. Guangliang Chen | Mathematics & Statistics, San Jos´e State University5/24 Generalized Linear Models (GLMs) In GLM, the response is typically assumed to have a distribution in the exponential family, which is a large class of probability distributions that have pdfs of the form f(x | θ) = a(x)b(θ) exp(c(θ) · T (x)), including • Normal - ordinary linear regression • Bernoulli - Logistic regression, modeling binary data • Binomial - Multinomial logistic regression, modeling general cate- gorical data • Poisson - Poisson regression, modeling count data • Exponential, Gamma - survival analysis Dr. -
How Prediction Statistics Can Help Us Cope When We Are Shaken, Scared and Irrational
EGU21-15219 https://doi.org/10.5194/egusphere-egu21-15219 EGU General Assembly 2021 © Author(s) 2021. This work is distributed under the Creative Commons Attribution 4.0 License. How prediction statistics can help us cope when we are shaken, scared and irrational Yavor Kamer1, Shyam Nandan2, Stefan Hiemer1, Guy Ouillon3, and Didier Sornette4,5 1RichterX.com, Zürich, Switzerland 2Windeggstrasse 5, 8953 Dietikon, Zurich, Switzerland 3Lithophyse, Nice, France 4Department of Management,Technology and Economics, ETH Zürich, Zürich, Switzerland 5Institute of Risk Analysis, Prediction and Management (Risks-X), SUSTech, Shenzhen, China Nature is scary. You can be sitting at your home and next thing you know you are trapped under the ruble of your own house or sucked into a sinkhole. For millions of years we have been the figurines of this precarious scene and we have found our own ways of dealing with the anxiety. It is natural that we create and consume prophecies, conspiracies and false predictions. Information technologies amplify not only our rational but also irrational deeds. Social media algorithms, tuned to maximize attention, make sure that misinformation spreads much faster than its counterpart. What can we do to minimize the adverse effects of misinformation, especially in the case of earthquakes? One option could be to designate one authoritative institute, set up a big surveillance network and cancel or ban every source of misinformation before it spreads. This might have worked a few centuries ago but not in this day and age. Instead we propose a more inclusive option: embrace all voices and channel them into an actual, prospective earthquake prediction platform (Kamer et al. -
Reliability Engineering: Trends, Strategies and Best Practices
Reliability Engineering: Trends, Strategies and Best Practices WHITE PAPER September 2007 Predictive HCL’s Predictive Engineering encompasses the complete product life-cycle process, from concept to design to prototyping/testing, all the way to manufacturing. This helps in making decisions early Engineering in the design process, perfecting the product – thereby cutting down cycle time and costs, and Think. Design. Perfect! meeting set reliability and quality standards. Reliability Engineering: Trends, Strategies and Best Practices | September 2007 TABLE OF CONTENTS Abstract 3 Importance of reliability engineering in product industry 3 Current trends in reliability engineering 4 Reliability planning – an important task 5 Strength of reliability analysis 6 Is your reliability test plan optimized? 6 Challenges to overcome 7 Outsourcing of a reliability task 7 About HCL 10 © 2007, HCL Technologies. Reproduction Prohibited. This document is protected under Copyright by the Author, all rights reserved. Reliability Engineering: Trends, Strategies and Best Practices | September 2007 Abstract In reliability engineering, product industries now follow a conscious and planned approach to effectively address multiple issues related to product certification, failure returns, customer satisfaction, market competition and product lifecycle cost. Today, reliability professionals face new challenges posed by advanced and complex technology. Expertise and experience are necessary to provide an optimized solution meeting time and cost constraints associated with analysis and testing. In the changed scenario, the reliability approach has also become more objective and result oriented. This is well supported by analysis software. This paper discusses all associated issues including outsourcing of reliability tasks to a professional service provider as an alternate cost-effective option. Importance of reliability engineering in product industry The degree of importance given to the reliability of products varies depending on their criticality. -
Imre Lakatos's Philosophy of Mathematics
Imre Lakatos’s Philosophy of Mathematics Gábor Kutrovátz Eötvös Loránd University, Budapest e-mail: [email protected] Introduction Imre Lakatos (1922-1974) is known world-wide by at least two different groups of philosophers. For the philosophers of science, he was a great defender of scientific rationality: he gave up the idea of ‘instant’ methodological rationality and substituted it with the historiographical methodology based on the notion of ‘rational reconstruction’. For the philosophers of mathematics, he was a great attacker at the formalist school, and instead of the formal-axiomatic features of mathematics he put the emphasis on heuristics, the historical processes of theory building and conceptualisation. These two ‘incarnations’ of Lakatos are rarely discussed within a unique philosophical framework, and not without reason: Lakatos himself never really tried to harmonise these two fields of interest. There are signs showing that he intended to build a common ground for them, but perhaps this project could not even take a very definite shape before his early death. In this paper I shall concentrate on only one of these topics: his philosophy of mathematics; and my primary aim is to give a brief and coherent summary of his ideas concerning this field. It should be noted, however, that his philosophy of mathematics and that of science obviously have some characteristics in common, since they were contrived by the same man, and not at a great temporal distance in his academic life, when he was under very similar intellectual influences. My secondary purpose therefore is to build this summary in a way that is in accordance with his general philosophical theory of science, that is, to give a mild ‘rational reconstruction’ of his ideas.1 The context of Lakatos’s philosophy of mathematics In the Acknowledgements of his doctoral thesis wrote on the philosophy of mathematics, Lakatos mentions three authors as the most influential sources for his philosophy. -
Prediction in Multilevel Generalized Linear Models
J. R. Statist. Soc. A (2009) 172, Part 3, pp. 659–687 Prediction in multilevel generalized linear models Anders Skrondal Norwegian Institute of Public Health, Oslo, Norway and Sophia Rabe-Hesketh University of California, Berkeley, USA, and Institute of Education, London, UK [Received February 2008. Final revision October 2008] Summary. We discuss prediction of random effects and of expected responses in multilevel generalized linear models. Prediction of random effects is useful for instance in small area estimation and disease mapping, effectiveness studies and model diagnostics. Prediction of expected responses is useful for planning, model interpretation and diagnostics. For prediction of random effects, we concentrate on empirical Bayes prediction and discuss three different kinds of standard errors; the posterior standard deviation and the marginal prediction error standard deviation (comparative standard errors) and the marginal sampling standard devi- ation (diagnostic standard error). Analytical expressions are available only for linear models and are provided in an appendix. For other multilevel generalized linear models we present approximations and suggest using parametric bootstrapping to obtain standard errors. We also discuss prediction of expectations of responses or probabilities for a new unit in a hypotheti- cal cluster, or in a new (randomly sampled) cluster or in an existing cluster. The methods are implemented in gllamm and illustrated by applying them to survey data on reading proficiency of children nested in schools. Simulations are used to assess the performance of various pre- dictions and associated standard errors for logistic random-intercept models under a range of conditions. Keywords: Adaptive quadrature; Best linear unbiased predictor (BLUP); Comparative standard error; Diagnostic standard error; Empirical Bayes; Generalized linear mixed model; gllamm; Mean-squared error of prediction; Multilevel model; Posterior; Prediction; Random effects; Scoring 1. -
A Philosophical Treatise of Universal Induction
Entropy 2011, 13, 1076-1136; doi:10.3390/e13061076 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article A Philosophical Treatise of Universal Induction Samuel Rathmanner and Marcus Hutter ? Research School of Computer Science, Australian National University, Corner of North and Daley Road, Canberra ACT 0200, Australia ? Author to whom correspondence should be addressed; E-Mail: [email protected]. Received: 20 April 2011; in revised form: 24 May 2011 / Accepted: 27 May 2011 / Published: 3 June 2011 Abstract: Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more recently computer scientists. In this article we argue the case for Solomonoff Induction, a formal inductive framework which combines algorithmic information theory with the Bayesian framework. Although it achieves excellent theoretical results and is based on solid philosophical foundations, the requisite technical knowledge necessary for understanding this framework has caused it to remain largely unknown and unappreciated in the wider scientific community. The main contribution of this article is to convey Solomonoff induction and its related concepts in a generally accessible form with the aim of bridging this current technical gap. In the process we examine the major historical contributions that have led to the formulation of Solomonoff Induction as well as criticisms of Solomonoff and induction in general. In particular we examine how Solomonoff induction addresses many issues that have plagued other inductive systems, such as the black ravens paradox and the confirmation problem, and compare this approach with other recent approaches. -
Kuhn Versus Lakatos, Or Paradigms Ver Su S Research Programmes in the History of Economics
[HOPE Vol. 7 (1975) No. 41 Kuhn versus Lakatos, or paradigms ver su s research programmes in the history of economics Mark Blaug In the 1950’s and 1960’s economists learned their methodology from Popper. Not that many of them read Popper. Instead, they read Friedman, and perhaps few of them realized that Friedman is simply Popper-with-a-twist applied to economics. To be sure, Friedman was criticized, but the “Essay on the Methodology of Positive Economics” nevertheless survived to become the one arti- cle on methodology that virtually every economist has read at some stage in his career. The idea that unrealistic “assumptions” are nothing to worry about, provided that the theory deduced from them culminates in falsifiable predictions, carried conviction to economists long inclined by habit and tradition to take a purely instrumentalist view of their subject. All that is almost ancient history, however. The new wave is not Popper’s “falsifiability” but Kuhn’s “paradigms.” Again, it is un- likely that many economists read The Structure oj Scientific Revolu- tions (1962). Nevertheless, appeal to paradigmatic reasoning quickly became a regular feature of controversies in economics and “paradigm” is now the byword of every historian of economic thought.’ Recently, however, some commentators have expressed misgivings about Kuhnian methodology applied to economics, throw- ing doubt in particular on the view that “scientific revolutions” characterize the history of economic thought.* With these doubts I heartily concur. I will argue that the term “paradigm” ought to be banished from economic literature, unless surrounded by inverted commas. Suitably qualified, however, the term retains a function in the historical exposition of economic doctrines as a reminder of the Copyright 1976 by Mark Blaug MARKBLAUG is Head of the Research Unit in the Economics of Education at the University of London. -
PHI230 Philosophy of Science
Department of Philosophy Level 2 Module PHI230 Philosophy of Science LECTURER: George Botterill Office Hours Wed 12-1, Fri 1-2; external tel: (0114)2220580; email: [email protected] Lectures: Monday 2-3 in Hicks Building LT6 Friday 11-12 in Hicks Building LT5 Seminars: See MOLE unit to join: Monday 4-5 Jessop Building 215, Friday 12-1 Jessop Building 215 GENERAL OUTLINE This course will deal with major issues in the philosophy of science, with particular emphasis on the rationality of theory-change, explanation, the status of scientific laws, observation, and the structure of scientific theories. Most of the course will be devoted to the methodology of natural science, though we may also discuss some issues in the philosophy of the social sciences. Most of the issues presented revolve around two major debates in the philosophy of science: (1) the dispute between Kuhn and Popper about theory change (2) disagreements between positivist (or instrumentalist) and realist conceptions of science. Modern philosophy of science has become closely linked with the history of science. The course will reflect this by considering how well major developments in the history of science fit proposed methodological rules about how science ought to proceed. The Copernican Revolution in astronomy will be used as a case-study. 1 AIMS AND OBJECTIVES The main aims of this module are: • to introduce students to the debate about theory-change in science, deriving from the work of Popper, Kuhn, Feyerabend and Lakatos • to help students acquire an understanding of some important problems in the philosophy of science (concerning the topics of: explanation, observation, scientific realism, and the nature of laws) • to encourage students to enter into serious engagement with some of the major problems in the philosophy of science. -
Some Statistical Models for Prediction Jonathan Auerbach Submitted In
Some Statistical Models for Prediction Jonathan Auerbach Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy under the Executive Committee of the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2020 © 2020 Jonathan Auerbach All Rights Reserved Abstract Some Statistical Models for Prediction Jonathan Auerbach This dissertation examines the use of statistical models for prediction. Examples are drawn from public policy and chosen because they represent pressing problems facing U.S. governments at the local, state, and federal level. The first five chapters provide examples where the perfunctory use of linear models, the prediction tool of choice in government, failed to produce reasonable predictions. Methodological flaws are identified, and more accurate models are proposed that draw on advances in statistics, data science, and machine learning. Chapter 1 examines skyscraper construction, where the normality assumption is violated and extreme value analysis is more appropriate. Chapters 2 and 3 examine presidential approval and voting (a leading measure of civic participation), where the non-collinearity assumption is violated and an index model is more appropriate. Chapter 4 examines changes in temperature sensitivity due to global warming, where the linearity assumption is violated and a first-hitting-time model is more appropriate. Chapter 5 examines the crime rate, where the independence assumption is violated and a block model is more appropriate. The last chapter provides an example where simple linear regression was overlooked as providing a sensible solution. Chapter 6 examines traffic fatalities, where the linear assumption provides a better predictor than the more popular non-linear probability model, logistic regression. -
The Case of Astrology –
The relation between paranormal beliefs and psychological traits: The case of Astrology – Brief report Antonis Koutsoumpis Department of Behavioral and Social Sciences, Vrije Universiteit Amsterdam Author Note Antonis Koutsoumpis ORCID: https://orcid.org/0000-0001-9242-4959 OSF data: https://osf.io/62yfj/?view_only=c6bf948a5f3e4f5a89ab9bdd8976a1e2 I have no conflicts of interest to disclose Correspondence concerning this article should be addressed to: De Boelelaan 1105, 1081HV Amsterdam, The Netherlands. Email: [email protected] The present manuscript briefly reports and makes public data collected in the spring of 2016 as part of my b-thesis at the University of Crete, Greece. The raw data, syntax, and the Greek translation of scales and tasks are publicly available at the OSF page of the project. An extended version of the manuscript (in Greek), is available upon request. To the best of my knowledge, this is the first public dataset on the astrological and paranormal beliefs in Greek population. Introduction The main goal of this work was to test the relation between Astrological Belief (AB) to a plethora of psychological constructs. To avoid a very long task, the study was divided into three separate studies independently (but simultaneously) released. Study 1 explored the relation between AB, Locus of Control, Optimism, and Openness to Experience. Study 2 tested two astrological hypotheses (the sun-sign and water-sign effects), and explored the relation between personality, AB, and zodiac signs. Study 3 explored the relation between AB and paranormal beliefs. Recruitment followed both a snowball procedure and it was also posted in social media groups of various Greek university departments. -
Prediction in General Relativity
Synthese (2017) 194:491–509 DOI 10.1007/s11229-015-0954-3 ORIGINAL RESEARCH Prediction in general relativity C. D. McCoy1 Received: 2 July 2015 / Accepted: 17 October 2015 / Published online: 27 October 2015 © Springer Science+Business Media Dordrecht 2015 Abstract Several authors have claimed that prediction is essentially impossible in the general theory of relativity, the case being particularly strong, it is said, when one fully considers the epistemic predicament of the observer. Each of these claims rests on the support of an underdetermination argument and a particular interpretation of the concept of prediction. I argue that these underdetermination arguments fail and depend on an implausible explication of prediction in the theory. The technical results adduced in these arguments can be related to certain epistemic issues, but can only be misleadingly or mistakenly characterized as related to prediction. Keywords Prediction · General theory of relativity · Theory interpretation · Global spacetime structure 1 Introduction Several authors have investigated the subject of prediction in the general theory of relativity (GTR), arguing on the strength of various technical results that making predictions is essentially impossible for observers in the spacetimes permitted by the theory (Geroch 1977; Hogarth 1993, 1997; Earman 1995; Manchak 2008). On the face of it, such claims seem to be in significant tension with the important successful predictions made on the theoretical basis of GTR. The famous experimental predictions of the precession of the perihelion of Mercury and of gravitational lensing, for example, are widely understood as playing a significant role in the confirmation of the theory (Brush 1999). Well-known relativist Clifford Will observes furthermore that “today, B C. -
Introduction
M889 - FULLER TEXT.qxd 4/4/07 11:21 am Page 1 Phil's G4 Phil's G4:Users:phil:Public: PHIL'S JO Introduction Science and Technology Studies (STS) is an interdisciplinary field usually defined as the confluence of three fields with distinct intellec- tual lineages and orientations: history of science, philosophy of science, and sociology of science. All three have been marginal to their named disciplines, because surprisingly few of the original practitioners of history, philosophy, or sociology of science were primarily trained in history, philosophy, or sociology. Rather, they were natural or exact scientists who came to be disenchanted with the social entanglements of their chosen fields of study. In effect, they fell victim to an intellec- tual bait-and-switch, whereby the reasons they entered science failed to explain science’s continued support in the wider society. This point often makes STS appear more critical than many of its practitioners intend it to be. STS researchers are virtually in agreement that people tend to like science for the wrong reasons (i.e. they are too easily taken in by its hype), but relatively few STS researchers would thereby con- clude that there are no good reasons to like science. There have been three generations of STS research, and each tells a different story of disenchantment with science. First, the logical pos- itivists, including Karl Popper, were keen to protect the theoretical base of science from the technological devastation that was wrought in its name during World War I. Next, Thomas Kuhn and his con- temporaries on both sides of the Atlantic – including Paul Feyerabend, Imre Lakatos, Stephen Toulmin, Derek de Solla Price – tried to do the same vis-à-vis World War II, though, more than the previous genera- tion, they relied on science’s past for normative guidance, largely out of a realization of technology’s contemporary role in scaling up the sci- entific enterprise and giving it forward momentum.