## 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

## How to Improve Bayesian Reasoning without Instruction

*Gerd Gigerenzer*

### in Adaptive Thinking: Rationality in the Real World

- Published in print:
- 2002
- Published Online:
- October 2011
- ISBN:
- 9780195153729
- eISBN:
- 9780199849222
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195153729.003.0006
- Subject:
- Philosophy, General

This chapter defines the concepts of natural sampling, natural frequencies, and reports experimental evidence for the impact of various external representations on statistical thinking. The mental ... More

## Innateness and (Bayesian) Visual Perception: Reconciling Nativism and Development

*Brian J. Scholl*

### in The Innate Mind: Structure and Contents

- Published in print:
- 2005
- Published Online:
- January 2007
- ISBN:
- 9780195179675
- eISBN:
- 9780199869794
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195179675.003.0003
- Subject:
- Philosophy, Metaphysics/Epistemology

This chapter explores a way in which visual processing may involve innate constraints and attempts to show how such processing overcomes one enduring challenge to nativism. In particular, many ... More

## Simple Bayesian Models

*N. Thompson Hobbs and Mevin B. Hooten*

### in Bayesian Models: A Statistical Primer for Ecologists

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691159287
- eISBN:
- 9781400866557
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159287.003.0005
- Subject:
- Biology, Ecology

This chapter lays out the basic principles of Bayesian inference, building on the concepts of probability developed in Chapter 3. It seeks to use the rules of probability to show how Bayes' theorem ... More

## Murder and (of?) the Likelihood Principle: A Trialogue

*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/9780195322989.003.0017
- Subject:
- Psychology, Cognitive Psychology

The Likelihood Principle of Bayesian inference asserts that only likelihoods matter to single-stage inference. A likelihood is the probability of evidence given a hypothesis multiplied by a positive ... More

## Rational Statistical Inference and Cognitive Development

*Fei Xu*

### in The Innate Mind, Volume 3: Foundations and the Future

- Published in print:
- 2008
- Published Online:
- January 2008
- ISBN:
- 9780195332834
- eISBN:
- 9780199868117
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195332834.003.0010
- Subject:
- Philosophy, Philosophy of Mind

This chapter advocates a view that is a substantive middle ground between the extreme versions of nativism and empiricism — a view dubbed ‘rational constructivism’. This is a view that commits us to ... More

## Decision Theory and Bayesian Inference

*Luc Bauwens, Michel Lubrano, and Jean-François Richard*

### in Bayesian Inference in Dynamic Econometric Models

- Published in print:
- 2000
- Published Online:
- September 2011
- ISBN:
- 9780198773122
- eISBN:
- 9780191695315
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198773122.003.0001
- Subject:
- Economics and Finance, Econometrics

This chapter discusses the relationship between mathematical statistics, decision theory, and the application of Bayesian inference to econometrics. It analyses the Bayesian approach to decision ... More

## Humans' Multisensory Perception, from Integration to Segregation, Follows Bayesian Inference

*Ladan Shams and Ulrik Beierholm*

### in Sensory Cue Integration

- Published in print:
- 2011
- Published Online:
- September 2012
- ISBN:
- 9780195387247
- eISBN:
- 9780199918379
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195387247.003.0013
- Subject:
- Psychology, Cognitive Neuroscience, Cognitive Psychology

This chapter first discusses experimental findings showing that multisensory perception encompasses a spectrum of phenomena ranging from full integration (or fusion), to partial integration, to ... More

## Bayesian Statistics and Linear Regression

*Luc Bauwens, Michel Lubrano, and Jean-François Richard*

### in Bayesian Inference in Dynamic Econometric Models

- Published in print:
- 2000
- Published Online:
- September 2011
- ISBN:
- 9780198773122
- eISBN:
- 9780191695315
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198773122.003.0002
- Subject:
- Economics and Finance, Econometrics

This chapter presents the basic concepts and tools that are useful for modelling and for Bayesian inference. It defines density kernels useful for simplifying notation and computations and explains ... More

## Intuitive Theories as Grammars for Causal Inference

*Joshua B. Tenenbaum, Thomas L. Griffiths, and Sourabh Niyogi*

### in Causal Learning: Psychology, Philosophy, and Computation

- Published in print:
- 2007
- Published Online:
- April 2010
- ISBN:
- 9780195176803
- eISBN:
- 9780199958511
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195176803.003.0020
- Subject:
- Psychology, Developmental Psychology

This chapter presents a framework for understanding the structure, function, and acquisition of causal theories from a rational computational perspective. Using a “reverse engineering” approach, it ... More

## Semiparametric Mixed Models for Longitudinal Data

*Ludwig Fahrmeir and Thomas Kneib*

### in Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199533022
- eISBN:
- 9780191728501
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199533022.003.0004
- Subject:
- Mathematics, Probability / Statistics, Biostatistics

This chapter considers Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. Section 4.1 assumes Gaussian smoothness priors, focusing on Bayesian P-splines in combination ... More

## Basic Concepts for Smoothing and Semiparametric Regression

*Ludwig Fahrmeir and Thomas Kneib*

### in Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199533022
- eISBN:
- 9780191728501
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199533022.003.0002
- Subject:
- Mathematics, Probability / Statistics, Biostatistics

This chapter reviews basic concepts for smoothing and semiparametric regression based on roughness penalties or — from a Bayesian perspective — corresponding smoothness priors. In particular, it ... More

## What's the H in H‐likelihood: A Holy Grail or an Achilles' Heel? *

*Xiao‐Li Meng*

### in Bayesian Statistics 9

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199694587
- eISBN:
- 9780191731921
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199694587.003.0016
- Subject:
- Mathematics, Probability / Statistics

H‐likelihood refers to a likelihood function of both fixed parameters and random “unobservables,” such as missing data and latent variables. The method then typically proceeds by maximizing over the ... More

## Population Variability and Bayesian Inference

*Terran Lane*

### in The Dynamic Brain: An Exploration of Neuronal Variability and Its Functional Significance

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780195393798
- eISBN:
- 9780199897049
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195393798.003.0015
- Subject:
- Neuroscience, Behavioral Neuroscience, Development

Neuroscience data, from single-neuron recordings to whole-brain functional neuroimaging, is swamped with variability. The system under examination changes from subject to subject, trial to trial, ... More

## Dynamic Regression Models

*Luc Bauwens, Michel Lubrano, and Jean-François Richard*

### in Bayesian Inference in Dynamic Econometric Models

- Published in print:
- 2000
- Published Online:
- September 2011
- ISBN:
- 9780198773122
- eISBN:
- 9780191695315
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198773122.003.0005
- Subject:
- Economics and Finance, Econometrics

This chapter examines the application of the dynamic regression models for inference and prediction with dynamic econometric models. It shows how to extend to the dynamic case the notion of Bayesian ... More

## Neurobiology of Decision Making: An Intentional Framework

*Michael N. Shadlen, Roozbeh Kiani, Timothy D. Hanks, and Anne K. Churchland*

### in Better Than Conscious?: Decision Making, the Human Mind, and Implications For Institutions

- Published in print:
- 2008
- Published Online:
- May 2016
- ISBN:
- 9780262195805
- eISBN:
- 9780262272353
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262195805.003.0004
- Subject:
- Psychology, Social Psychology

The aim of statistical decision theories is to understand how evidence, prior knowledge, and values lead an organism to commit to one of a number of alternatives. Two main statistical decision ... More

## Heteroscedasticity and ARCH

*Luc Bauwens, Michel Lubrano, and Jean-François Richard*

### in Bayesian Inference in Dynamic Econometric Models

- Published in print:
- 2000
- Published Online:
- September 2011
- ISBN:
- 9780198773122
- eISBN:
- 9780191695315
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198773122.003.0007
- Subject:
- Economics and Finance, Econometrics

This chapter examines the importance of heteroscedasticity and the autoregressive conditional heteroscedasticity (ARCH) model in econometric analysis, particularly in the Bayesian inference approach. ... More

## Two Proposals for Causal Grammars

*Thomas L. Griffiths and Joshua B. Tenenbaum*

### in Causal Learning: Psychology, Philosophy, and Computation

- Published in print:
- 2007
- Published Online:
- April 2010
- ISBN:
- 9780195176803
- eISBN:
- 9780199958511
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195176803.003.0021
- Subject:
- Psychology, Developmental Psychology

A causal theory can be thought of as a grammar that generates events, and that can be used to parse events to identify underlying causal structure. This chapter considers what the components of such ... More

## Ecological Intelligence

*Gerd Gigerenzer*

### in Adaptive Thinking: Rationality in the Real World

- Published in print:
- 2002
- Published Online:
- October 2011
- ISBN:
- 9780195153729
- eISBN:
- 9780199849222
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195153729.003.0004
- Subject:
- Philosophy, General

Human color vision is adapted to the spectral properties of natural sunlight. More generally, the perceptual system has been shaped by the environment in which human ancestors evolved, the ... More

## Unit Root Inference

*Luc Bauwens, Michel Lubrano, and Jean-François Richard*

### in Bayesian Inference in Dynamic Econometric Models

- Published in print:
- 2000
- Published Online:
- September 2011
- ISBN:
- 9780198773122
- eISBN:
- 9780191695315
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198773122.003.0006
- Subject:
- Economics and Finance, Econometrics

This chapter examines the application of the unit root hypothesis in econometric analysis, particularly in the Bayesian inference approach. It explains that testing for a unit root in a Bayesian ... More