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Classical Statistical Inference

Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray

in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691151687
eISBN:
9781400848911
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151687.003.0004
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces the main concepts of statistical inference, or drawing conclusions from data. There are three main types of inference: point estimation, confidence estimation, and hypothesis ... More


Bayesian Statistical Inference

Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray

in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691151687
eISBN:
9781400848911
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151687.003.0005
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter introduces the most important aspects of Bayesian statistical inference and techniques for performing such calculations in practice. It first reviews the basic steps in Bayesian ... More


Tactical Note on the Relation Between Scientific and Statistical Hypotheses

Jie W Weiss and David J Weiss

in A Science of Decision Making: The Legacy of Ward Edwards

Published in print:
2008
Published Online:
January 2009
ISBN:
9780195322989
eISBN:
9780199869206
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195322989.003.0013
Subject:
Psychology, Cognitive Psychology

This chapter explores the relationship between scientific hypotheses and the customary procedures of classical statistical inference. It argues that classical significance tests are violently biased ... More


Probability

Jr. Henry E. Kyburg

in Science & Reason

Published in print:
1991
Published Online:
October 2011
ISBN:
9780195062533
eISBN:
9780199853038
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195062533.003.0003
Subject:
Philosophy, Philosophy of Science

There are two main classes of interpretations of probability. The first are those that rely on a measure of frequency. The other is those that take a logical or subjective view of a unique event, ... More


Everettian Statistical Inference

David Wallace

in The Emergent Multiverse: Quantum Theory according to the Everett Interpretation

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199546961
eISBN:
9780191741418
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199546961.003.0008
Subject:
Philosophy, Philosophy of Science, Metaphysics/Epistemology

This chapter extends chapter 5's formal proof into a general discussion of how we should assess evidence — and, in particular, how we should test scientific theories — given the possibility that ... More


Reasonable Doubt: Uncertainty in Education, Science and Law

TONY GARDNER-MEDWIN

in Evidence, Inference and Enquiry

Published in print:
2011
Published Online:
January 2013
ISBN:
9780197264843
eISBN:
9780191754050
Item type:
chapter
Publisher:
British Academy
DOI:
10.5871/bacad/9780197264843.003.0017
Subject:
Sociology, Methodology and Statistics

This chapter champions the elicitation and use of probabilistic measures of uncertainty. It compares two different views (roughly corresponding, respectively, to the Bayesian and frequentist ... More


Numerical Methods for Nonlinear Estimating Equations

Christopher G. Small and Jinfang Wang

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.001.0001
Subject:
Mathematics, Probability / Statistics

Nonlinearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive ... More


An Error-Statistical Philosophy of Evidence

Deborah G. Mayo

in The Nature of Scientific Evidence: Statistical, Philosophical, and Empirical Considerations

Published in print:
2004
Published Online:
February 2013
ISBN:
9780226789552
eISBN:
9780226789583
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226789583.003.0004
Subject:
Biology, Ecology

Error-statistical methods in science have been the subject of enormous criticism, giving rise to the popular statistical “reform” movement and bolstering subjective Bayesian philosophy of science. Is ... More


A Fair Deal for Everettians

David Papineau

in Many Worlds?: Everett, Quantum Theory, and Reality

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199560561
eISBN:
9780191721380
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199560561.003.0009
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

Those who criticize the Everett interpretation on the grounds that it makes no sense of probability apply a double-standard, for no other physical theory of probability does any better in explaining ... More


Induction

Jr. Henry E. Kyburg

in Science & Reason

Published in print:
1991
Published Online:
October 2011
ISBN:
9780195062533
eISBN:
9780199853038
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195062533.003.0004
Subject:
Philosophy, Philosophy of Science

Induction is the inference from a sample to a population, regardless of the possible existence of exceptions. Induction is used in the practice of science and engineering based on knowledge that can ... More


Reasoning Defeasibly about Probabilities

John L. Pollock

in Knowledge and Skepticism

Published in print:
2010
Published Online:
August 2013
ISBN:
9780262014083
eISBN:
9780262265782
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262014083.003.0011
Subject:
Philosophy, Metaphysics/Epistemology

This chapter discusses the often-acknowledged notion that, for practical decision-making, definite probabilities are required instead of indefinite ones. Theories that take indefinite probabilities ... More


Statistical Distances as Loss Functions in Assessing Model Adequacy

Bruce G. Lindsay

in The Nature of Scientific Evidence: Statistical, Philosophical, and Empirical Considerations

Published in print:
2004
Published Online:
February 2013
ISBN:
9780226789552
eISBN:
9780226789583
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226789583.003.0014
Subject:
Biology, Ecology

This chapter takes on the problem of model adequacy and makes an argument for reformulating the way model-based statistical inference is carried out. In the new formulation, it does not treat the ... More


Statistics and the Scientific Method in Ecology

Brian Dennis

in The Nature of Scientific Evidence: Statistical, Philosophical, and Empirical Considerations

Published in print:
2004
Published Online:
February 2013
ISBN:
9780226789552
eISBN:
9780226789583
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226789583.003.0011
Subject:
Biology, Ecology

The questioning of science and the scientific method continues within the science of ecology. The use of Bayesian statistical analysis has recently been advocated in ecology, supposedly to aid ... More


Searching for Structure in Point Data

Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, Alexander Gray, Željko Ivezi, Andrew J. Connolly, Jacob T. VanderPlas, and Alexander Gray

in Statistics, Data Mining, and Machine Learning in Astronomy: A Practical Python Guide for the Analysis of Survey Data

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691151687
eISBN:
9781400848911
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691151687.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

Inferring the probability density function (pdf) from a sample of data is known as density estimation. The same methodology is often called data smoothing. Density estimation in the one-dimensional ... More


Taking the Prior Seriously: Bayesian Analysis without Subjective Probability

Daniel Goodman

in The Nature of Scientific Evidence: Statistical, Philosophical, and Empirical Considerations

Published in print:
2004
Published Online:
February 2013
ISBN:
9780226789552
eISBN:
9780226789583
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226789583.003.0012
Subject:
Biology, Ecology

Decision theory requires the assignment of probabilities for the different possible states of nature. Bayesian inference provides such probabilities, but at the cost of requiring prior probabilities ... More


Statistical Models and Approaches to Inference

Kerrie Mengersen, Christopher H. Schmid, Michael D. Jennions, and Jessica Gurevitch

in Handbook of Meta-analysis in Ecology and Evolution

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691137285
eISBN:
9781400846184
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691137285.003.0008
Subject:
Biology, Ecology

This chapter provides an introduction and overview of the three statistical components of the meta-analysis: (1) the statistical model that describes how the study-specific estimates of interest will ... More


Introduction

Peter J. Diggle and Amanda G. Chetwynd

in Statistics and Scientific Method: An Introduction for Students and Researchers

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199543182
eISBN:
9780191774867
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199543182.003.0001
Subject:
Mathematics, Probability / Statistics, Biostatistics

This introductory chapter first outlines the book's main objectives. These are to provide students with a basic understanding of the role that statistics can play in scientific research; to introduce ... More


One-Sample and Difference-of-Means Tests

Quan Li

in Using R for Data Analysis in Social Sciences: A Research Project-Oriented Approach

Published in print:
2018
Published Online:
March 2019
ISBN:
9780190656218
eISBN:
9780190656256
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190656218.003.0003
Subject:
Political Science, Political Theory

This chapter demonstrates the types of questions one could ask about a continuous random variable of interest and answer using statistical inference. It provides conceptual preparation for ... More


A Monte Carlo Comparison of OLS Estimation Errors and Design Efficiencies in a Two‐Stage Stratified Random Sampling Procedure for a Contingent Valuation Study

Kyeongae Choe, William R. Parke, and Dale Whittington

in Valuing Environmental Preferences: Theory and Practice of the Contingent Valuation Method in the US, EU , and developing Countries

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199248919
eISBN:
9780191595950
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199248915.003.0010
Subject:
Economics and Finance, Development, Growth, and Environmental

In many settings, a random sample may not be cost‐inefficient, so that a two‐stage stratified random sample is adopted in contingent valuation (CV) studies. The first stage comprises identifying a ... More


Elicit Data, Not Prior: On Using Expert Opinion in Ecological Studies

Subhash R. Lele

in The Nature of Scientific Evidence: Statistical, Philosophical, and Empirical Considerations

Published in print:
2004
Published Online:
February 2013
ISBN:
9780226789552
eISBN:
9780226789583
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226789583.003.0013
Subject:
Biology, Ecology

Ecological studies are often hampered by insufficient data on the quantity of interest. Limited data usually lead to a relatively flat likelihood surface that is not very informative. One solution is ... More


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