Teaching statistics in the physics curriculum: Unifying and clarifying role of subjective probability

Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief introduction to subjective probability and Bayesian inference is given, with comments on typical misconceptions which tend to discredit it and comparisons to other approaches.Comment: 15 pages, LateX, 1 eps figure, corrected some typos. Invited paper for the American Journal of Physics. This paper and related work are also available at http://www-zeus.roma1.infn.it/~agostini

Bayesian Inference in Processing Experimental Data: Principles and Basic Applications

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as: model comparison (including the automatic Ockham's Razor filter provided by the Bayesian approach); parametric inference; quantification of the uncertainty about the value of physical quantities, also taking into account systematic effects; role of marginalization; posterior characterization; predictive distributions; hierarchical modelling and hyperparameters; Gaussian approximation of the posterior and recovery of conventional methods, especially maximum likelihood and chi-square fits under well defined conditions; conjugate priors, transformation invariance and maximum entropy motivated priors; Monte Carlo estimates of expectation, including a short introduction to Markov Chain Monte Carlo methods.Comment: 40 pages, 2 figures, invited paper for Reports on Progress in Physic

Causal Induction from Continuous Event Streams: Evidence for Delay-Induced Attribution Shifts

Contemporary theories of Human Causal Induction assume that causal knowledge is inferred from observable contingencies. While this assumption is well supported by empirical results, it fails to consider an important problem-solving aspect of causal induction in real time: In the absence of well structured learning trials, it is not clear whether the effect of interest occurred because of the cause under investigation, or on its own accord. Attributing the effect to either the cause of interest or alternative background causes is an important precursor to induction. We present a new paradigm based on the presentation of continuous event streams, and use it to test the Attribution-Shift Hypothesis (Shanks & Dickinson, 1987), according to which temporal delays sever the attributional link between cause and effect. Delays generally impaired attribution to the candidate, and increased attribution to the constant background of alternative causes. In line with earlier research (Buehner & May, 2002, 2003, 2004) prior knowledge and experience mediated this effect. Pre-exposure to a causally ineffective background context was found to facilitate the discovery of delayed causal relationships by reducing the tendency for attributional shifts to occur. However, longer exposure to a delayed causal relationship did not improve discovery. This complex pattern of results is problematic for associative learning theories, but supports the Attribution-Shift Hypothesi

Technology assessment between risk, uncertainty and ignorance

The use of most if not all technologies is accompanied by negative side effects, While we may profit from today’s technologies, it is most often future generations who bear most risks. Risk analysis therefore becomes a delicate issue, because future risks often cannot be assigned a meaningful occurance probability. This paper argues that technology assessement most often deal with uncertainty and ignorance rather than risk when we include future generations into our ethical, political or juridal thinking. This has serious implications as probabilistic decision approaches are not applicable anymore. I contend that a virtue ethical approach in which dianoetic virtues play a central role may supplement a welfare based ethics in order to overcome the difficulties in dealing with uncertainty and ignorance in technology assessement

Studying clinical reasoning, part 2: Applying social judgement theory

Part 1 of this paper (Harries and Harries 2001) examined the reasoning studies of the 1980s and 1990s and critiqued the ethnographic and informationprocessing approaches, based on stated information use. The need for an approach that acknowledged the intuitive nature of experienced thinkers’ reasoning was identified. Part 2 describes such an approach ± social judgement theory ± and presents a pilot application in occupational therapy research. The method used is judgement analysis. The issue under study is that of prioritisation policies in community mental health work. The results present the prioritisation policies of four occupational therapists in relation to managing community mental health referrals

von Neumann-Morgenstern and Savage Theorems for Causal Decision Making

Causal thinking and decision making under uncertainty are fundamental aspects of intelligent reasoning. Decision making under uncertainty has been well studied when information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using purely associative information. Causal inference often yields uncertainty about the exact causal structure, so we consider what kinds of decisions are possible in those conditions. In this work, we consider decision problems in which available actions and consequences are causally connected. After recalling a previous causal decision making result, which relies on a known causal model, we consider the case in which the causal mechanism that controls some environment is unknown to a rational decision maker. In this setting we state and prove a causal version of Savage's Theorem, which we then use to develop a notion of causal games with its respective causal Nash equilibrium. These results highlight the importance of causal models in decision making and the variety of potential applications.Comment: Submitted to Journal of Causal Inferenc