Moritz Schulz explores counterfactual thought and language: what would have happened if things had gone a different way. Counterfactual questions may concern large scale derivations (what would have happened if Nixon had launched a nuclear attack) or small scale evaluations of minor derivations (what would have happened if I had decided to join a different profession). A common impression, which receives a thorough defence in the book, is that oftentimes we find it impossible to know what would have happened. However, this does not mean that we are completely at a loss: we are typically capable of evaluating counterfactual questions probabilistically: we can say what would have been likely or unlikely to happen. Schulz describes these probabilistic ways of evaluating counterfactual questions and turns the data into a novel account of the workings of counterfactual thought.

Moritz Schulz explores counterfactual thought and language: what would have happened if things had gone a different way. Counterfactual questions may concern large scale derivations (what would have happened if Nixon had launched a nuclear attack) or small scale evaluations of minor derivations (what would have happened if I had decided to join a different profession). A common impression, which receives a thorough defence in the book, is that oftentimes we find it impossible to know what would have happened. However, this does not mean that we are completely at a loss: we are typically capable of evaluating counterfactual questions probabilistically: we can say what would have been likely or unlikely to happen. Schulz describes these probabilistic ways of evaluating counterfactual questions and turns the data into a novel account of the workings of counterfactual thought.

This book is about making machine learning models and their decisions interpretable. After exploring the concepts of interpretability, you will learn about simple, interpretable models such as decision trees, decision rules and linear regression. Later chapters focus on general model-agnostic methods for interpreting black box models like feature importance and accumulated local effects and explaining individual predictions with Shapley values and LIME. All interpretation methods are explained in depth and discussed critically. How do they work under the hood? What are their strengths and weaknesses? How can their outputs be interpreted? This book will enable you to select and correctly apply the interpretation method that is most suitable for your machine learning project.

CAUSAL INFERENCE IN STATISTICS A Primer Causality is central to the understanding and use of data. Without an understanding of cause–effect relationships, we cannot use data to answer questions as basic as "Does this treatment harm or help patients?" But though hundreds of introductory texts are available on statistical methods of data analysis, until now, no beginner-level book has been written about the exploding arsenal of methods that can tease causal information from data. Causal Inference in Statistics fills that gap. Using simple examples and plain language, the book lays out how to define causal parameters; the assumptions necessary to estimate causal parameters in a variety of situations; how to express those assumptions mathematically; whether those assumptions have testable implications; how to predict the effects of interventions; and how to reason counterfactually. These are the foundational tools that any student of statistics needs to acquire in order to use statistical methods to answer causal questions of interest. This book is accessible to anyone with an interest in interpreting data, from undergraduates, professors, researchers, or to the interested layperson. Examples are drawn from a wide variety of fields, including medicine, public policy, and law; a brief introduction to probability and statistics is provided for the uninitiated; and each chapter comes with study questions to reinforce the readers understanding.

Counterfactual representations refer to people's imaginations about the alternative possibilities to the actual world (i.e., what might have been). The present thesis embraces the notion that the psychological impacts of those representations are dictated by the degree of certainty or uncertainty people assign to them, namely, their counterfactual probability judgments (i.e., 'How likely could things have been different?'). The thesis reports six experiments investigating the determinants as well as the emotional consequences of counterfactual probability judgments. Experiments 1, 2 and 3 found that both people's conditional and unconditional counterfactual probability judgments were heightened when a past outcome was physically or numerically proximate to its alternative. Experiments 4 and 5 found that people's counterfactual probability judgments were not only affected by the static proximity cue but also by its dynamic variations. When outcome proximity was equal, the shrinking physical distance towards a counterfactual outcome heightened one's subjective likelihood of that outcome, compared to if the distance stayed constant. Experiment 6 found that the effect of 'shrinking distance' could manifest itself as an antecedent temporal order effect on people's counterfactual probability judgments. That is, a counterfactual outcome was deemed more likely if the factual outcome was preceded by a decisive event that occurred latter in the causal sequence rather than earlier. These results are broadly consistent with the theory of the simulation heuristic which posits that subjective probabilities are estimated by assessing the ease with which a relevant scenario can be mentally constructed. The emotional consequences of counterfactual probability judgments were investigated within the theoretical framework of the Reflective and Evaluative Model of Comparative Thinking (REM). The evidence from Experiments 2, 3, 4 and 5 suggests that the effect of counterfactual probability judgments on emotions are contingent on people's temporal perspective - affective assimilation will be enhanced when future possibility is present (i.e., the outcome is indecisive or changeable) which encourages a reflective simulation while affective contrast will be enhanced when future possibility is absent (i.e., the outcome is decisive or unchangeable) which encourages an evaluative simulation. These findings suggest that the psychological impact of counterfactual thinking should be discussed in terms of a three-way interaction between its direction (upward or downward), probability (low or high), and simulation mode (reflection or evaluation).

Twelve essays explore what bearing empirical findings might have on philosophical concerns about counterfactuals and causation, and how, in turn, work in philosophy might help clarify issues in empirical work on the relationships between causal and counterfactual thought.

Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds.

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence ...