A quantum theoretical explanation for probability judgment errors

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning

Cost-effectiveness acceptability curves - facts, fallacies and frequently asked questions

Cost-effectiveness acceptability curves (CEACs) have been widely adopted as a method to quantify and graphically represent uncertainty in economic evaluation studies of health-care technologies. However, there remain some common fallacies regarding the nature and shape of CEACs that largely result from the textbook illustration of the CEAC. This textbook CEAC shows a smooth curve starting at probability 0, with an asymptote to 1 for higher money values of the health outcome (). But this familiar ogive shape which makes the textbook CEAC look like a cumulative distribution function is just one special case of the CEAC. The reality is that the CEAC can take many shapes and turns because it is a graphic transformation from the cost-effectiveness plane, where the joint density of incremental costs and effects may straddle quadrants with attendant discontinuities and asymptotes. In fact CEACs: (i) do not have to cut the y-axis at 0; (ii) do not have to asymptote to 1; (iii) are not always monotonically increasing in ; and (iv) do not represent cumulative distribution functions (cdfs). Within this paper we present a gallery of CEACs in order to identify the fallacies and illustrate the facts surrounding the CEAC. The aim of the paper is to serve as a reference tool to accompany the increased use of CEACs within major medical journals

Developing Critical Thinking Military Officers

Critical thinking is frequently identified as an important trait for military officers. This paper examines critical thinking from a historical, pedagogical, and warfighting perspective. The author uses his experience teaching mathematical reasoning at the Naval Postgraduate School to provide helpful advice for educators charged with teaching deductive and inductive reasoning. The paper argues that critical thinking should be taught early in an officer\u27s career. It emphasizes a systematic and Socratic instructional approach along with the importance of equipping students with the necessary tools to evaluate problem-solving techniques and critique their associated solutions. Finally, the paper discusses Augmented Intelligence and the growing need to adopt a more holistic view of the combined Human and Machine-Learning decision making system

Don’t blame the norms! On the challenges of ecological rationality

Enlightenment thinkers viewed logic and mathematical probability as the hallmarks of rationality. In psychological research on human (ir)rationality, human subjects are typically held accountable to this arcane ideal of Reason. If people fall short of these traditional standards, as indeed they often do, they are biased or irrational. Recent work in the program of ecological rationality, however, aims to rehabilitate human reason, and to upturn our traditional conception of rationality in the process. Put bluntly, these researchers are turning the tables on the traditionalist, showing that human reasoning often outperforms complex algorithms based on the traditional canons of rationality. If human reason still appears paltry from the vantage point of capital-R Rationality, then so much the worse for Rationality. Maybe the norms themselves are in need of revision. Perhaps human reasoning is better than rational. Though we welcome the naturalization of human reason, we argue that this backlash against the classical norms of rationality is uncalled for. Ecological rationality presents two apparent challenges to the traditional canons of rationality. In both cases, we contend, the norms emerge unscathed. In the first category, norms of rationality that appear violated by individual reasoners, re-emerge at the level of evolutionary adaptation. In the second category, the norms under challenge simply turn out to be not applicable to the case at hand. Moreover, we should keep in mind that, when they are assessing the efficiency of human reasoning, advocates of ecological rationality still use the traditional norms of rationality as a benchmark. We conclude that, even if we accept all the fascinating findings garnered by the advocates of ecological rationality (and there is ample reason to do so), we need not be taken in by the rhetoric against classical rationality, or the false opposition between logical and ecological rationality. When the dust has settled, the norms are still standing

Quantum-like models cannot account for the conjunction fallacy

Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities—this is the conjunction fallacy. One of the most discussed accounts of this fallacy is currently the quantum-like explanation, which relies on models exploiting the mathematics of quantum mechanics. The aim of this paper is to investigate the empirical adequacy of major quantum-like models which represent beliefs with quantum states. We first argue that they can be tested in three different ways, in a question order effect configuration which is different from the traditional conjunction fallacy experiment. We then carry out our proposed experiment, with varied methodologies from experimental economics. The experimental results we get are at odds with the predictions of the quantum-like models. This strongly suggests that this quantum-like account of the conjunction fallacy fails. Future possible research paths are discussed

Efficient inference about the tail weight in multivariate Student tt distributions

We propose a new testing procedure about the tail weight parameter of multivariate Student $t$ distributions by having recourse to the Le Cam methodology. Our test is asymptotically as efficient as the classical likelihood ratio test, but outperforms the latter by its flexibility and simplicity: indeed, our approach allows to estimate the location and scatter nuisance parameters by any root-$n$ consistent estimators, hereby avoiding numerically complex maximum likelihood estimation. The finite-sample properties of our test are analyzed in a Monte Carlo simulation study, and we apply our method on a financial data set. We conclude the paper by indicating how to use this framework for efficient point estimation.Comment: 23 page

A Critical Review of "Automatic Patch Generation Learned from Human-Written Patches": Essay on the Problem Statement and the Evaluation of Automatic Software Repair

At ICSE'2013, there was the first session ever dedicated to automatic program repair. In this session, Kim et al. presented PAR, a novel template-based approach for fixing Java bugs. We strongly disagree with key points of this paper. Our critical review has two goals. First, we aim at explaining why we disagree with Kim and colleagues and why the reasons behind this disagreement are important for research on automatic software repair in general. Second, we aim at contributing to the field with a clarification of the essential ideas behind automatic software repair. In particular we discuss the main evaluation criteria of automatic software repair: understandability, correctness and completeness. We show that depending on how one sets up the repair scenario, the evaluation goals may be contradictory. Eventually, we discuss the nature of fix acceptability and its relation to the notion of software correctness.Comment: ICSE 2014, India (2014

A Project Based Approach to Statistics and Data Science

In an increasingly data-driven world, facility with statistics is more important than ever for our students. At institutions without a statistician, it often falls to the mathematics faculty to teach statistics courses. This paper presents a model that a mathematician asked to teach statistics can follow. This model entails connecting with faculty from numerous departments on campus to develop a list of topics, building a repository of real-world datasets from these faculty, and creating projects where students interface with these datasets to write lab reports aimed at consumers of statistics in other disciplines. The end result is students who are well prepared for interdisciplinary research, who are accustomed to coping with the idiosyncrasies of real data, and who have sharpened their technical writing and speaking skills