“不愤不启,不悱不发”之一种做法——研究式教学管见

〕本文探讨了研究式教学的问题。其基本的步骤是：摆出问题、分析问题、解决问题和总结规律。其意义在于能有效地提高教学质量     

启发式教学的进一步探讨和实践

启发式教学,可提高学习的积极性和主动性,注重能力的培养,是一种好的教学方式.但教学条件基本相同,不同的教师采用,其教学效果却有较大的差别.如何运用好启发式教学,提高教学质量,许多教育工作者正在深入地研究和探索.通过教学实践对启发式教学进行了进一步的探讨.     

Combining Experts’ Judgments: Comparison of Algorithmic Methods Using Synthetic Data

Expert judgment (or expert elicitation) is a formal process for eliciting judgments from subject‐matter experts about the value of a decision‐relevant quantity. Judgments in the form of subjective probability distributions are obtained from several experts, raising the question how best to combine information from multiple experts. A number of algorithmic approaches have been proposed, of which the most commonly employed is the equal‐weight combination (the average of the experts’ distributions). We evaluate the properties of five combination methods (equal‐weight, best‐expert, performance, frequentist, and copula) using simulated expert‐judgment data for which we know the process generating the experts’ distributions. We examine cases in which two well‐calibrated experts are of equal or unequal quality and their judgments are independent, positively or negatively dependent. In this setting, the copula, frequentist, and best‐expert approaches perform better and the equal‐weight combination method performs worse than the alternative approaches.     

Reducing Overconfidence in the Interval Judgments of Experts

Elicitation of expert opinion is important for risk analysis when only limited data are available. Expert opinion is often elicited in the form of subjective confidence intervals; however, these are prone to substantial overconfidence. We investigated the influence of elicitation question format, in particular the number of steps in the elicitation procedure. In a 3‐point elicitation procedure, an expert is asked for a lower limit, upper limit, and best guess, the two limits creating an interval of some assigned confidence level (e.g., 80%). In our 4‐step interval elicitation procedure, experts were also asked for a realistic lower limit, upper limit, and best guess, but no confidence level was assigned; the fourth step was to rate their anticipated confidence in the interval produced. In our three studies, experts made interval predictions of rates of infectious diseases (Study 1, n = 21 and Study 2, n = 24: epidemiologists and public health experts), or marine invertebrate populations (Study 3, n = 34: ecologists and biologists). We combined the results from our studies using meta‐analysis, which found average overconfidence of 11.9%, 95% CI [3.5, 20.3] (a hit rate of 68.1% for 80% intervals)—a substantial decrease in overconfidence compared with previous studies. Studies 2 and 3 suggest that the 4‐step procedure is more likely to reduce overconfidence than the 3‐point procedure (Cohen's d = 0.61, [0.04, 1.18]).     

Correlated Binary Variables and Multi-level Probability Assessments

Abstract.  We introduce a fully parametric approach for updating beliefs regarding correlated binary variables, after marginal probability assessments based on information of varying quality are provided by an expert. This approach allows for the calculation of a predictive joint density for future assessments. The proposed methodology offers new insight into the parameters that control the dependence of the binary variables, and the relation of these parameters to the joint density of the probability assessments. A comprehensible elicitation procedure for the model parameters is put forward. The approach taken is motivated and illustrated through a practical application.     

A Method for Eliciting Utilities and its Application to Collective Choice

Designing a mechanism that provides a direct incentive for an individual to report her utility function over several alternatives is a difficult task. A framework for such mechanism design is the following: an individual (a decision maker) is faced with an optimization problem (e.g., maximization of expected utility), and a mechanism designer observes the decision maker’s action. The mechanism does reveal the individual’s utility truthfully if the mechanism designer, having observed the decision maker’s action, infers the decision maker’s utilities over several alternatives. This paper studies an example of such a mechanism and discusses its application to the problem of optimal social choice. Under certain simplifying assumptions about individuals’ utility functions and about how voters choose their voting strategies, this mechanism selects the alternative that maximizes Harsanyi’s social utility function and is Pareto-efficient.     

Selection of suitable prior for the Bayesian mixture of a class of lifetime distributions under type-I censored datasets

This paper explores the study on mixture of a class of probability density functions under type-I censoring scheme. In this paper, we mold a heterogeneous population by means of a two-component mixture of the class of probability density functions. The parameters of the class of mixture density functions are estimated and compared using the Bayes estimates under the squared-error and precautionary loss functions. A censored mixture dataset is simulated by probabilistic mixing for the computational purpose considering particular case of the Maxwell distribution. Closed-form expressions for the Bayes estimators along with their posterior risks are derived for censored as well as complete samples. Some stimulating comparisons and properties of the estimates are presented here. A factual dataset has also been for illustration.     

Subjective elicitation of hyperparameters of a conjugate Dirichlet prior and the corresponding Bayes analysis

Abstract

The paper elicits subjectively the Dirichlet prior hyperparameters based on the realistic opinion collected from the experts. The procedure used for subjective elicitation considers several stages such as the choice of experts, formation of some relevant questions to be asked to the experts for getting their opinion, pooling of opinion, quantification of information and then the formation of exact prior distribution through quantile assessment based on an iterative procedure. The resulting prior distribution is used to provide the Bayes analysis assuming multinomial sampling plan. The results are illustrated by means of a data set involving two life style factors of gallbladder carcinoma patients. The results convey the message that matches closely with the opinion given by the medical experts.     

Prbposterior expected loss as a scoring rule for prior distributions

A scoring rule for evaluating the usefulness of an assessed prior distribution should reflect the purpose for which the distribution is to be used. In this paper we suppose that sample data is to become available and that the posterior distribution will be used to estimate some quantity under a quadratic loss function. The utility of a prior distribution is consequently determined by its preposterior expected quadratic loss. It is shown that this loss function has properties desirable in a scoring rule and formulae are derived for calculating the scores it gives in some common problems. Many scoring rules give a very poor score to any improper prior distribution but, in contrast, the scoring rule proposed here provides a meaningful measure for comparing the usefulness of assessed prior distributions and non-informative (improper) prior distributions. Results for making this comparison in various situations are also given.