## 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

## 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

## 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

## 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