Statistics for Spatial Data.

Foundations Of Statistics

Prospection (Gilbert & Wilson, 2007), the representation of possible futures, is a ubiquitous feature of the human mind. Much psychological theory and practice, in contrast, has understood human action as determined by the past and viewed any such teleology (selection of action in light of goals) as a violation of natural law because the future cannot act on the present. Prospection involves no backward causation; rather, it is guidance not by the future itself but by present, evaluative representations of possible future states. These representations can be understood minimally as “If X, then Y” conditionals, and the process of prospection can be understood as the generation and evaluation of these conditionals. We review the history of the attempt to cast teleology out of science, culminating in the failures of behaviorism and psychoanalysis to account adequately for action without teleology. A wide range of evidence suggests that prospection is a central organizing feature of perception, cognition, affect, memory, motivation, and action. The authors speculate that prospection casts new light on why subjectivity is part of consciousness, what is “free” and “willing” in “free will,” and on mental disorders and their treatment. Viewing behavior as driven by the past was a powerful framework that helped create scientific psychology, but accumulating evidence in a wide range of areas of research suggests a shift in framework, in which navigation into the future is seen as a core organizing principle of animal and human behavior.

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Navigating Into the Future or Driven by the Past

A sizeable literature exists on the use of frequentist power analysis in the null-hypothesis significance testing (NHST) paradigm to facilitate the design of informative experiments. In contrast, there is almost no literature that discusses the design of experiments when Bayes factors (BFs) are used as a measure of evidence. Here we explore Bayes Factor Design Analysis (BFDA) as a useful tool to design studies for maximum efficiency and informativeness. We elaborate on three possible BF designs, (a) a fixed-n design, (b) an open-ended Sequential Bayes Factor (SBF) design, where researchers can test after each participant and can stop data collection whenever there is strong evidence for either [Formula: see text] or [Formula: see text], and (c) a modified SBF design that defines a maximal sample size where data collection is stopped regardless of the current state of evidence. We demonstrate how the properties of each design (i.e., expected strength of evidence, expected sample size, expected probability of misleading evidence, expected probability of weak evidence) can be evaluated using Monte Carlo simulations and equip researchers with the necessary information to compute their own Bayesian design analyses.

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Bayes factor design analysis: Planning for compelling evidence

Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is independent of the causal relation that holds between the conditioned variable and the conditioning variable, in the conventional quantum formalism, there is a significant difference between how one treats experiments involving two systems at a single time and those involving a single system at two times. In this article, we develop the formalism of quantum conditional states, which provides a unified description of these two sorts of experiment. In addition, concepts that are distinct in the conventional formalism become unified: Channels, sets of states, and positive operator valued measures are all seen to be instances of conditional states; the action of a channel on a state, ensemble averaging, the Born rule, the composition of channels, and nonselective state-update rules are all seen to be instances of belief propagation. Using a quantum generalization of Bayes' theorem and the associated notion of Bayesian conditioning, we also show that the remote steering of quantum states can be described within our formalism as a mere updating of beliefs about one system given new information about another, and retrodictive inferences can be expressed using the same belief propagation rule as is used for predictive inferences. Finally, we show that previous arguments for interpreting the projection postulate as a quantum generalization of Bayesian conditioning are based on a misleading analogy and that it is best understood as a combination of belief propagation (corresponding to the nonselective state-update map) and conditioning on the measurement outcome.

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Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference

The logic of decision

Foreword. Preface. I The Foundations of Inference and Decision in Forensic Science. 1 Introduction. 1.1 The Inevitability of Uncertainty. 1.2 Desiderata in Evidential Assessment. 1.3 The Importance of the Propositional Framework and the Nature of Evidential Assessment. 1.4 From Desiderata to Applications. 1.5 The Bayesian Core of Forensic Science. 1.6 Structure of the Book. 2 Scientific Reasoning and Decision Making. 2.1 Coherent Reasoning Under Uncertainty. 2.2 Coherent Decision Making Under Uncertainty of Reasoning. 2.3 Scientific Reasoning as Coherent Decision Making. 2.4 Forensic Reasoning as Coherent Decision Making. 3 Concepts of Statistical Science and Decision Theory. 3.1 Random Variables and Distribution Functions. 3.2 Statistical Inference and Decision Theory. 3.3 The Bayesian Paradigm. 3.4 Bayesian Decision Theory. 3.5 R Code. II Forensic Data Analysis. 4 Point Estimation. 4.1 Introduction. 4.2 Bayesian Decision for a Proportion. 4.3 Bayesian Decision for a Poisson Mean. 4.4 Bayesian Decision for Normal Mean. 4.5 R Code. 5 Credible Intervals. 5.1 Introduction. 5.2 Credible Intervals. 5.3 Decision-Theoretic Evaluation of Credible Intervals. 5.4 R Code. 6 Hypothesis Testing. 6.1 Introduction. 6.2 Bayesian Hypothesis Testing. 6.3 One-sided testing. 6.4 Two-Sided Testing. 6.5 R Code. 7 Sampling. 7.1 Introduction. 7.2 Sampling Inspection. 7.3 Graphical Models for Sampling Inspection. 7.4 Sampling Inspection under a Decision-Theoretic Approach. 7.5 R Code. 8 Classification of Observations. 8.1 Introduction. 8.2 Standards of Coherent Classification. 8.3 Comparing Models using Discrete Data. 8.4 Comparison of Models using Continuous Data. 8.5 Non-Normal Distributions and Cocaine on Bank Notes. 8.6 A note on Multivariate Continuous Data. 8.7 R Code. 9 Bayesian Forensic Data Analysis: Conclusions and Implications. 9.1 Introduction. 9.2 What is the Past and Current Position of Statistics in Forensic Science? 9.3 Why Should Forensic Scientists Conform to a Bayesian Framework for Inference and Decision Making? 9.4 Why Regard Probability as a Personal Degree of Belief? 9.5 Why Should Scientists be Aware of Decision Analysis? 9.6 How to Implement Bayesian Inference and Decision Analysis? A Discrete Distributions. B Continuous Distributions. Bibliography. Author Index. Subject Index.

Data Analysis in Forensic Science: A Bayesian Decision Perspective

Decision theoretic properties of forensic identification: underlying logic and argumentative implications.

Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science: Taroni/Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science

The use of the Bayes factor (BF) or likelihood ratio as a metric to assess the probative value of forensic traces is largely supported by operational standards and recommendations in different forensic disciplines. However, the progress towards more widespread consensus about foundational principles is still fragile as it raises new problems about which views differ. It is not uncommon e.g. to encounter scientists who feel the need to compute the probability distribution of a given expression of evidential value (i.e. a BF), or to place intervals or significance probabilities on such a quantity. The article here presents arguments to show that such views involve a misconception of principles and abuse of language. The conclusion of the discussion is that, in a given case at hand, forensic scientists ought to offer to a court of justice a given single value for the BF, rather than an expression based on a distribution over a range of values.

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Silvia Bozza

Papers

The logic of decision

Data Analysis in Forensic Science: A Bayesian Decision Perspective

Decision theoretic properties of forensic identification: underlying logic and argumentative implications.

Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science: Taroni/Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science

Dismissal of the illusion of uncertainty in the assessment of a likelihood ratio