Epistemic processes : a basis for statistics and quantum theory

Preface to the Second Edition
Preface to the First Edition
Acknowledgments
Contents
1 The Epistemic View upon Science
	1.1 Introduction
	1.2 Different Views on the Foundation of Quantum Mechanics
	1.3 Theory of Decisions, Focusing, and Context
	1.4 The PBR Theorem: A Toy Model
	1.5 Epistemic Processes
		1.5.1 E-variables in Simple Epistemic Questions
		1.5.2 E-variables in Statistics
		1.5.3 E-variables in Causal Inference
		1.5.4 E-variables in Quantum Mechanics
		1.5.5 Real and Perfect Measurements in Quantum Mechanics
		1.5.6 Quantum States, Their Interpretations, and a Link to the Ensemble Interpretation
		1.5.7 Quantum States for Spin 1/2 Particles
		1.5.8 Inaccessible Conceptual Variables and Complementarity
	1.6 Quantum Theory, the Mind, and the Mathematics
	1.7 Convivial Solipsism
	References
2 Statistical Inference
	2.1 Basic Statistics
		2.1.1 Probability
		2.1.2 Statistical Models
		2.1.3 Inference for Continuous Parameters
		2.1.4 Inference for Discrete E-variables
	2.2 Group Actions and Model Reduction
	2.3 Interlude
	References
3 Inference in an Epistemic Process
	3.1 Conceptual Variables and Contexts
	3.2 Data; Generalized Sufficiency and Ancillarity
		3.2.1 Sufficiency
		3.2.2 Ancillarity and Conditioning
		3.2.3 Conditioning and the Conditionality Principle
		3.2.4 The Sufficiency and Likelihood Principles
	3.3 Prediction and Simple E-variables
	3.4 Epistemic Processes, Decisions, and Actions
	References
4 Towards Quantum Theory
	4.1 Inaccessible Conceptual Variables and Quantum Theory
	4.2 The Toy Model of Spekkens
	4.3 A Basic Development of the Main Ideas
		4.3.1 The Spin 1/2 Case
		4.3.2 Measurements and the Statistical Paradigm
		4.3.3 Entangled States
		4.3.4 Relative States and Many Worlds
		4.3.5 Convivial Solipsism
		4.3.6 The EPR Experiment
	4.4 A New Foundation for the Quantum Formalism
		4.4.1 Introduction
		4.4.2  A Summary of the Mathematical Results Obtained Below
		4.4.3 Basic Setting
		4.4.4 Operators and their Properties
			A Brief Discussion of Group Representation Theory
			A Resolution of the Identity
			Focusing and a New Resolution of the Identity
			Quantum Operators
			Several Accessible Variables
			A Projective Representation
			Conclusions, Several Accessible Variables
			The Spectral Theorem and Operators for Functions of θ
			Some Further Theorems
		4.4.5 The Non-Permissible Case
		4.4.6 Coupling Different E-variables Together
			The Maximal Case
			The General Case
		4.4.7 Three Examples
			Spin/Angular Momentum
			Position and Momentum
			Spekkens\' Toy Model
		4.4.8 Concluding Remarks for Sect.4.4
	4.5 Quantum States and Their Interpretation
		4.5.1 Introduction
		4.5.2 Quantum States and Question-and-Answer Pairs
			State Vectors Corresponding to Maximally Accessible E-Variables
			Question-and-Answers Correspond to States
		4.5.3 Spin and Angular Momentum
			Proofs and Details in the Spin/Angular Momentum Case
		4.5.4 Some Remarks
		4.5.5 The Epistemic Interpretation
		4.5.6 Concluding Remarks for Sect.4.5
	4.6 Conceptual Variables, Decisions, and Communication between Observers
	References
5 Aspects of Quantum Theory
	5.1 Basic Quantum Theory
	5.2 More on the Qubit Case: The Case of Dimension 2
	5.3 Continuous E-variables: Phase Space
	5.4 A Link to Statistical Inference
	5.5 Rationality and Experimental Evidence
	5.6 The Born Formula
		5.6.1 The Basic Formula
		5.6.2 Consequences
		5.6.3 Perfect Measurements
		5.6.4 A Macroscopic Example
		5.6.5 Superselection Rules
	5.7 Measurements and Quantum Statistical Inference
		5.7.1 Collapse of the Wave Packet
		5.7.2 Perfect Observations as Seen by a Single Observer
		5.7.3 Simple Real Measurements
		5.7.4 Quantum Statistical Inference
	5.8 Entanglement, EPR, and the Bell Theorem
	5.9 The Free will Theorem
	5.10 The Schrödinger Equation
		5.10.1 The General Argument: Unitary Transformations and Entanglement
		5.10.2 Position As An Inaccessible Stochastic Process
		5.10.3 Nelson\'s Stochastic Mechanics
	5.11 More on Quantum Measurements
	5.12 More on QBism
	5.13 Discussion
	5.14 A General e-variable Based Approach to Quantum Theory
	References
6 Connections to Statistical Inference and Epistemic Probabilities
	6.1 A Generalization of Statistical Theory
		6.1.1 A General E-variable Based Approach to Quantum Theory
		6.1.2 Projection Valued and Positive Operator Valued Measures
		6.1.3 A Link to Experimental Design
		6.1.4 Generalized Inference
	6.2 On Epistemic Probabilities
		6.2.1 Quantum Probabilities in Psychology
		6.2.2 Introduction to Epistemic Probabilities
		6.2.3 On Some Conceptual Variables
		6.2.4 Epistemic Probabilities from Confidence Distributions
	6.3 Fiducial Theory
		6.3.1 The Group Theory Approach
		6.3.2 Fisher\'s Original Argument and Confidence Distributions
		6.3.3 Subparameters and Fiducial Models
	6.4 Discussion
		6.4.1 Connection between Approaches to Statistical Inference
		6.4.2 More on Epistemic Probabilities
		6.4.3 Stone\'s Theorem and the Foundation of Statistical Inference
	6.5 The Partial Least Squares Regression History
	6.6 Quantum Measurements
	References
7 Macroscopic Consequences
	7.1 General Philosophical Considerations
	7.2 A Little More on Convivial Solipsism
	7.3 Quantum Mechanics, Decisions, and Complementarity
	References
A  Proof That the Generalized Likelihood Principle Follows from the GWCP and the GWSP (Birnbaum\'s Theorem): The Discrete Case
B  Some Group Theory, Operator Theory, and Group Representation Theory
C  Proof of Four Results Related to Quantum Mechanics
D  Proof of Busch\'s Theorem for the Finite-Dimensional Case
E  Propositional Logic, Probabilities, and Knowledge
F  Group Theory in Statistical Inference
	F.1 Basic Premises and Definitions
	F.2 Subparameters and Permissibility
	References
Bibliography
Index