Effects of Causes and Causes of Effects

We describe and contrast two distinct problem areas for statistical causality: studying the likely effects of an intervention (effects of causes) and studying whether there is a causal link between the observed exposure and outcome in an individual case (causes of effects). For each of these, we introduce and compare various formal frameworks that have been proposed for that purpose, including the decision-theoretic approach, structural equations, structural and stochastic causal models, and potential outcomes. We argue that counterfactual concepts are unnecessary for studying effects of causes but are needed for analyzing causes of effects. They are, however, subject to a degree of arbitrariness, which can be reduced, though not in general eliminated, by taking account of additional structure in the problem. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Value of Information Analysis in Models to Inform Health Policy

Value of information (VoI) is a decision-theoretic approach to estimating the expected benefits from collecting further information of different kinds, in scientific problems based on combining one or more sources of data. VoI methods can assess the sensitivity of models to different sources of uncertainty and help to set priorities for further data collection. They have been widely applied in healthcare policy making, but the ideas are general to a range of evidence synthesis and decision problems. This article gives a broad overview of VoI methods, explaining the principles behind them, the range of problems that can be tackled with them, and how they can be implemented, and discusses the ongoing challenges in the area. Expected final online publication date for the Annual Review of Statistics, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Optimal Sample Size for the Birnbaum–Saunders Distribution under Decision Theory with Symmetric and Asymmetric Loss Functions

The fatigue-life or Birnbaum–Saunders distribution is an asymmetrical model that has been widely applied in several areas of science and mainly in reliability. Although diverse methodologies related to this distribution have been proposed, the problem of determining the optimal sample size when estimating its mean has not yet been studied. In this paper, we derive a methodology to determine the optimal sample size under a decision-theoretic approach. In this approach, we consider symmetric and asymmetric loss functions for point and interval inference. Computational tools in the R language were implemented to use this methodology in practice. An illustrative example with real data is also provided to show potential applications.

The Wisdom of the Coherent: Improving Correspondence with Coherence-Weighted Aggregation

Previous research shows that variation in coherence (i.e., degrees of respect for axioms of probability calculus), when used as a basis for performance-weighted aggregation, can improve the accuracy of probability judgments. However, many aspects of coherence-weighted aggregation remain a mystery, including both prescriptive issues (e.g. how best to use coherence measures) and theoretical issues (e.g. why coherence-weighted aggregation is effective). Using data from previous experiments employing either general-knowledge or statistical information-integration tasks, we addressed many of these issues. Of prescriptive relevance, we examined the effectiveness of coherence-weighted aggregation as a function of judgment elicitation method, group size, weighting function, and the aggressivity of the function’s tuning parameter. Of descriptive relevance, we propose that coherence-weighted aggregation can improve accuracy via two distinct, task-dependent routes: a deterministic route in which the bases for scoring accuracy depend on conformity to coherence principles (e.g., Bayesian information integration) and a diagnostic route in which coherence serves as a cue to correct knowledge. The findings provide support for the efficacy of both routes, but they also highlight why coherence weighting, especially the most aggressive forms, sometimes impose costs to accuracy. We conclude by sketching a decision-theoretic approach to how the wisdom of the coherent within the wisdom of the crowd can be sensibly leveraged.

Intelligent Data Fusion and Multi-Agent Coordination for Target Allocation

This paper addresses the fusion processing techniques for multi-sensor data perceived through the infrared sensors of military surveillance robots, and proposes their decision-theoretic coordination to effectively monitor multiple targets. To combine the multi-sensor data from the distributed battlefield robots, a set of fusion rules are used to formulate a combined prediction from the multi-source data. The possible type of a target is estimated through the fusion rules. For the identification of targets, agents need to keep track of targets for continuous situation awareness. The coordination of the agents with limited range of surveillance is indispensable for their successful monitoring of multiple targets. For dynamic and flexible coordination, our agents follow the decision-theoretic approach. We implement a military simulator to compare the capabilities of fusion processing and those of coordination, and conduct experiments with our framework in distributed and uncertain battlefield environments. The experimental results show that the fusion process of multi-sensor data from military robots can improve the performance of estimation of the type of a target, and our coordinated agents outperform agents using random strategy for their target selection in various military scenarios.

How to Do Things with Words: A Bayesian Approach

Communication changes the beliefs of the listener and of the speaker. The value of a communicative act stems from the valuable belief states which result from this act. To model this we build on the Interactive POMDP (IPOMDP) framework, which extends POMDPs to allow agents to model others in multi-agent settings, and we include communication that can take place between the agents to formulate Communicative IPOMDPs (CIPOMDPs). We treat communication as a type of action and therefore, decisions regarding communicative acts are based on decision-theoretic planning using the Bellman optimality principle and value iteration, just as they are for all other rational actions. As in any form of planning, the results of actions need to be precisely specified. We use the Bayes’ theorem to derive how agents update their beliefs in CIPOMDPs; updates are due to agents’ actions, observations, messages they send to other agents, and messages they receive from others. The Bayesian decision-theoretic approach frees us from the commonly made assumption of cooperative discourse – we consider agents which are free to be dishonest while communicating and are guided only by their selfish rationality. We use a simple Tiger game to illustrate the belief update, and to show that the ability to rationally communicate allows agents to improve efficiency of their interactions.