Subjective confidence in forecasts: A response to fischhoff and MacGregor

Here we evaluate the generalizability of calibration studies which have used general knowledge questions, and argue that on conceptual, methodological and empirical grounds the results have limited applicability to judgemental forecasting. We also review evidence which suggests that judgemental forecast probabilities are influenced by variables such as the desirability, imminence, time period and perceived controllability of the event to be forecast. As these variables do not apply to judgement in the domain of general knowledge, a need for research recognizing and exploring the psychological processes underlying uncertainty about the future is apparent.     

Beyond heuristics and biases: A contingency model of judgemental forecasting

The conflicting viewpoints about the quality of judgemental forecasts are examined and a model is proposed that attempts to resolve the conflict. The model sees forecasts as contingent upon the repertory of forecasting strategies that the forecaster brings to the forecasting task, the strategy that he or she selects as a function of the characteristics of the task, and the rigour with which he or she applies the strategy as a function of the motivating characteristics of the environment in which the task is encountered. The implications of differences in subjects' and experimenters' assumptions about which strategies are appropriate in experimental studies are examined, as are the implications of the differences between the motivating aspects of experimental and applied settings on both performance and on the generatizability of the results of experiments to applied judgemental forecasting.     

Conditional distribution analyses of probabilistic forecasts

Probabilistic forecasts have good ‘external correspondence’ if events that are assigned probabilities close to 1 tend to occur frequently, whereas those assigned probabilities near 0 tend to occur rarely. This paper describes simple procedures for analysing external correspondence into meaningful components that might guide efforts to understand and improve forecasting performance. The procedures focus on differences between the judgements made by the forecaster when the target event occurs, as compared to when it does not. The illustrations involve a professional oddsmaker's predictions of baseball game outcomes, meteorologists' precipitation forecasts and physicians' diagnoses of pneumonia. The illustrations demonstrate the ability of the procedures to highlight important forecasting tendencies that are sometimes more difficult to discern by other means.     

The consistency,coherence and calibration of holistic,decomposed and recomposed judgemental probability forecasts

In this paper we make an empirical investigation of the relationship between the consistency, coherence and validity of probability judgements in a real-world forecasting context. Our results indicate that these measures of the adequacy of an individual's probability assessments are not closely related as we anticipated. Twenty-nine of our thirty-six subjects were better calibrated in point probabilities than in odds and our subjects were, in general more coherent using point probabilities than odds forecasts. Contrary to our expectations we found very little difference in forecasting response and performance between simple and compound holistic forecasts. This result is evidence against the ‘divide-and-conquer’ rationale underlying most applications of normative decision theory. In addition, our recompositions of marginal and conditional assessments into compound forecasts were no better calibrated or resolved than their holistic counterparts. These findings convey two implications for forecasting. First, untrained judgemental forecasters should use point probabilities in preference to odds. Second, judgemental forecasts of complex compound probabilities may be as well assessed holistically as they are using methods of decomposition and recomposition. In addition, our study provides a paradigm for further studies of the relationship between consistency, coherence and validity in judgemental probability forecasting.     

Relative accuracy of judgemental and extrapolative methods in forecasting annual earnings

This paper identifies and analyses previously published studies on annual earnings forecasts. Comparisons of forecasts produced by management, analysts, and extrapolative techniques indicated that: (1) management forecasts were superior to professional analyst forecasts (the mean absolute percentage errors were 15.9 and 17.7, respectively, based on five studies using data from 1967–1974) and (2) judgemental forecasts (both management and analysts) were superior to extrapolation forecasts on 14 of 17 comparisons from 13 studies using data from 1964–1979 (the mean absolute percentage errors were 21.0 and 28.4 for judgement and extrapolation, respectively). These conclusions, based on recent research, differ from those reported in previous reviews, which commented on less than half of the studies identified here.     

A model of calibration for subjective probability distributions and its application to aggregation of judgements

A simple model is proposed of the statistical structure underlying the calibration of auditors' subjective probability distributions for account balances, and potentially for other unknown quantities. The model relates calibration curve shape to two parameters which represent over- or underconfidence and over- or underestimation. It is fitted to data from expert auditors. Different types of account appear to have different calibration characteristics. The model helps predict approximately the effects on calibration of aggregating individual subject distributions. Aggregation improves accuracy, but produces a strong tendency towards underconfidence. One aggregation method, predicting the best judgement in the group and using it as the group judgement, is found to be quite effective, much better than averaging the fractiles of individual distributions.     

Some practical aspects of forecasting in organizations

This paper presents the writer's experience, over a period of 25 years, in analysing organizational systems and, in particular, concentrates on the overall forecasting activity. The paper first looks at the relationship between forecasting and decision taking–with emphasis on the fact that forecasting is a means to aid decision taking and not an end in itself. It states that there are many types of forecasting problems, each requiring different methods of treatment. The paper then discusses attitudes which are emerging about the relative advantages of different forecasting techniques. It suggests a model building process which requires‘experience’and‘craftsmanship’, extensive practical application, frequent interaction between theory and practice and a methodology that eventually leads to models that contain no detectable inadequacies. Furthermore, it argues that although models which forecast a time series from its past history have a very important role to play, for effective policy making it is necessary to augment the model by introducing policy variables, again in a systematic not an ‘ad hoc’ manner. Finally, the paper discusses how forecasting systems can be introduced into the management process in the first place and how they should be monitored and updated when found wanting.     

Evaluating probability forecasts in terms of refinement and strictly proper scoring rules

This note gives an easily verified necessary and sufficient condition for one probability forecaster to empirically outperform another one in terms of all strictly proper scoring rules. Copyright © 2006 John Wiley & Sons, Ltd.     

How probable is probable? A numerical translation of verbal probability expressions

The reported experiment took place in a professional forecasting organization accustomed to giving verbal probability assessments (‘likely’, ‘probable’, etc.). It attempts to highlight the communication problems caused by verbal probability expressions and to offer possible solutions that are compatible with the forecasters overall perspective on their jobs Experts in the organization were first asked to give a numerical translation to 30 different verbal probability expressions most of which were taken from the organization's own published political forecasts. In a second part of the experiment the experts were given 15 paragraphs selected from the organization's political publications each of which contained at least one verbal expression of probability. Subjects were again asked to give a numerical translation to each verbal probability expression The results indicate that (a) there is a high variability in the interpretation of verbal probability expressions and (b) the variability is even higher in context. Possible reasons for the context effect are discussed and practical implications are suggested.     

A loose and separate certainty: Caves, Fuchs and Schack on quantum probability one

Carlton Caves, Fuchs, and Schack (2002) have recently appealed to an argument of mine (Stairs, 1983) to address a problem for their subjective Bayesian account of quantum probability. The difficulty is that on the face of it, quantum mechanical probabilities of one appear to be objective, but in that case, the Born Rule would yield a continuum of probabilities between zero and one. If so, we end up with objective probabilities strictly between zero and one. The authors claim that objective probabilities of one leads to a dilemma: give up locality or fall into contradiction. I argue that this conclusion depends on an overly strong interpretation of objectivism about quantum probabilities.     

The effectiveness of imprecise probability forecasts

In this paper we investigate the feasibility of algorithmically deriving precise probability forecasts from imprecise forecasts. We provide an empirical evaluation of precise probabilities that have been derived from two types of imprecise probability forecasts: probability intervals and probability intervals with second-order probability distributions. The minimum cross-entropy (MCE) principle is applied to the former to derive precise (i.e. additive) probabilities; expectation (EX) is used to derive precise probabilities in the latter case. Probability intervals that were constructed without second-order probabilities tended to be narrower than and contained in those that were amplified by second-order probabilities. Evidence that this narrowness is due to motivational bias is presented. Analysis of forecasters' mean Probability Scores for the derived precise probabilities indicates that it is possible to derive precise forecasts whose external correspondence is as good as directly assessed precise probability forecasts. The forecasts of the EX method, however, are more like the directly assessed precise forecasts than those of the MCE method.     

天宫一号基于控制力矩陀螺的智能多模自适应姿态控制系统设计与验证

天宫一号是目前我国在轨运行的体积最大、重量最重的载人航天器.它具有变构型、变参数的特性,采用控制力矩陀螺系统和喷气推进系统实现高精度、高稳定度姿态控制.本文通过对天宫一号控制对象参数缓变和跳变相结合特点的分析,规划了高可靠灵活的控制策略,设计了智能多模自适应姿态控制系统.利用智能控制中规则集设定多模自适应控制的指标切换函数分配,利用多模自适应控制算法建立多模型控制器实现不同控制对象,不同控制任务的姿态控制.天宫一号通过地面测试和物理仿真试验,最后发射在轨运行,与神舟八号、神舟九号、神舟十号载人飞船圆满完成交会对接任务,充分验证了姿态控制系统设计的正确性和有效性.该设计方法在解决大型航天器变构型、变参数组合体姿态控制方面有突出优点,在未来的载人航天领域空间站建设具有应用前景.     

Effects of volumetric allocation on heave response of semisubmersible in deep sea

The configuration of semisubmersibles consisting of pontoons and columns and their corresponding heave motion response in incident progressive waves are examined.The purpose of the present study is to provide a theoretical approach to estimating the effects of volumetric allocation on natural period and response amplitude operator (RAO) in heave motion.We conclude that the amplitude of heave motion response can be considerably suppressed by appropriately adjusting volumetric allocation so that the natural h...     

基于累积变形演化状态控制的高速铁路基床结构设计计算方法

实现长期循环荷载作用下基床结构累积变形有效控制是建造高速铁路的技术难点之一.基于高速铁路无砟与有砟轨道路基承受列车动荷载特征,提出和完善了用于基床结构设计的荷载作用模式;根据循环荷载作用下土工填料累积变形演化状态的分类及阈值判别准则,结合室内单元结构填土模型试验,获得了级配碎石基床填料变形状态演化的阈值参数.以设计荷载条件和填料设计参数为基础,针对无砟与有砟轨道对基床变形状态控制的不同要求,采用结构分析原理,构建了基于累积变形演化状态控制的高速铁路基床结构设计计算方法,确定了无砟与有砟轨道基床结构累积变形分别满足快速稳定和缓慢稳定的状态控制要求,以地基系数K30值表征的关键参数指标.研究成果为实现高速铁路基床结构由构造设计向状态控制定值分析转变奠定了基础.     

高速铁路路堤传递地基差异沉降特性及控制限值研究

为研究高速铁路地基差异沉降在路堤中的传递扩散特性,运用有限元方法,分析了路基在小变形条件下地基差异沉降与路基面不均匀变形的映射关系,并在得到土工离心模型试验校正的基础上,讨论了地基差异沉降模式、路堤高度等因素对路基面不均匀变形的影响规律.研究表明:地基差异沉降在路堤中的扩散程度随地基差异沉降渐变段长度与路堤高度比值的增大而减小,比值大于3~5以后,地基差异沉降与路基面不均匀变形具有良好的一致性;路基面不均匀变形与地基差异沉降呈正相关性,并随路堤高度、地基差异沉降渐变段长度的增加而减小;基于路基面不均匀变形限值提出了地基差异沉降控制标准,丰富了高速铁路路基沉降变形控制技术指标体系.