Bayesian Decision-theoretic Model Research Articles

Policy Implications of Statistical Estimates: A General Bayesian Decision-Theoretic Model for Binary Outcomes

How should we evaluate the effect of a policy on the likelihood of an undesirable event, such as conflict? The significance test has three limitations. First, relying on statistical significance misses the fact that uncertainty is a continuous scale. Second, focusing on a standard point estimate overlooks the variation in plausible effect sizes. Third, the criterion of substantive significance is rarely explained or justified. A new Bayesian decision-theoretic model, “causal binary loss function model,” overcomes these issues. It compares the expected loss under a policy intervention with the one under no intervention. These losses are computed based on a particular range of the effect sizes of a policy, the probability mass of this effect size range, the cost of the policy, and the cost of the undesirable event the policy intends to address. The model is more applicable than common statistical decision-theoretic models using the standard loss functions or capturing costs in terms of false positives and false negatives. I exemplify the model’s use through three applications and provide an R package. Supplementary materials for this article are available online.

Cost-effective clinical trial design: Application of a Bayesian sequential model to the ProFHER pragmatic trial.

Background/Aims:There is growing interest in the use of adaptive designs to improve the efficiency of clinical trials. We apply a Bayesian decision-theoretic model of a sequential experiment using cost and outcome data from the ProFHER pragmatic trial. We assess the model’s potential for delivering value-based research.Methods:Using parameter values estimated from the ProFHER pragmatic trial, including the costs of carrying out the trial, we establish when the trial could have stopped, had the model’s value-based stopping rule been used. We use a bootstrap analysis and simulation study to assess a range of operating characteristics, which we compare with a fixed sample size design which does not allow for early stopping.Results:We estimate that application of the model could have stopped the ProFHER trial early, reducing the sample size by about 14%, saving about 5% of the research budget and resulting in a technology recommendation which was the same as that of the trial. The bootstrap analysis suggests that the expected sample size would have been 38% lower, saving around 13% of the research budget, with a probability of 0.92 of making the same technology recommendation decision. It also shows a large degree of variability in the trial’s sample size.Conclusions:Benefits to trial cost stewardship may be achieved by monitoring trial data as they accumulate and using a stopping rule which balances the benefit of obtaining more information through continued recruitment with the cost of obtaining that information. We present recommendations for further research investigating the application of value-based sequential designs.

Decision Analysis via Granulation Based on General Binary Relation

Decision theory considers how best to make decisions in the light of uncertainty about data. There are several methodologies that may be used to determine the best decision. In rough set theory, the classification of objects according to approximation operators can be fitted into the Bayesian decision-theoretic model, with respect to three regions (positive, negative, and boundary region). Granulation using equivalence classes is a restriction that limits the decision makers. In this paper, we introduce a generalization and modification of decision-theoretic rough set model by using granular computing on general binary relations. We obtain two new types of approximation that enable us to classify the objects into five regions instead of three regions. The classification of decision region into five areas will enlarge the range of choice for decision makers.

A Bayesian multiple comparison procedure for ranking the means of normally distributed data

We present a Bayesian decision-theoretic model for producing, via all pair-wise comparisons, a set of possible rankings for a given number of normal means. A simulation is performed to compare this constant loss model to popular frequentist methods used to rank normal means, including Tukeys method and the Benjamini–Hochberg procedure. The model will also be compared to a Bayesian model using a linear loss function. Properties to be compared include the probability of containing the true ranking and the expected number of possible rankings produced.

A Bayesian Approach to Managing Learning-Curve Uncertainty

This paper introduces a Bayesian decision theoretic model of optimal production in the presence of learning-curve uncertainty. The well-known learning-curve model is extended to allow for random va...

R&D managers' choices of development policies in simulated R&D environments

This paper describes the results of some experiments, based on a research and development (R&D) game that examined R&D managers' proclivities for various options that hedge against uncertainty and the overall quality of their choices with respect to the Bayesian decision-theoretic model. Thirty R&D managers participated in the experiments, which were conducted at an industrial R&D facility. R&D managers exhibited a higher proclivity for parallel approaches in information acquisition but a lower propensity for parallel approaches in terminal actions, with respect to the Bayesian norm.