How are emergent constraints quantifying uncertainty and what do they leave behind?

The use of emergent constraints to quantify uncertainty for key policy relevant quantities such as Equilibrium Climate Sensitivity (ECS) has become increasingly widespread in recent years. Many researchers, however, claim that emergent constraints are inappropriate or even under-report uncertainty. In this paper we contribute to this discussion by examining the emergent constraints methodology in terms of its underpinning statistical assumptions. We argue that the existing frameworks are based on indefensible assumptions, then show how weakening them leads to a more transparent Bayesian framework wherein hitherto ignored sources of uncertainty, such as how reality might differ from models, can be quantified. We present a guided framework for the quantification of additional uncertainties that is linked to the confidence we can have in the underpinning physical arguments for using linear constraints. We provide a software tool for implementing our general framework for emergent constraints and use it to illustrate the framework on a number of recent emergent constraints for ECS. We find that the robustness of any constraint to additional uncertainties depends strongly on the confidence we can have in the underpinning physics, allowing a future framing of the debate over the validity of a particular constraint around the underlying physical arguments, rather than statistical assumptions

Chance-Constrained Probabilistic Simple Temporal Problems

Scheduling under uncertainty is essential to many autonomous systems and logistics tasks. Probabilistic methods for solving temporal problems exist which quantify and attempt to minimize the probability of schedule failure. These methods are overly conservative, resulting in a loss in schedule utility. Chance constrained formalism address over-conservatism by imposing bounds on risk, while maximizing utility subject to these risk bounds. In this paper we present the probabilistic Simple Temporal Network (pSTN), a probabilistic formalism for representing temporal problems with bounded risk and a utility over event timing. We introduce a constrained optimisation algorithm for pSTNs that achieves compactness and efficiency through a problem encoding in terms of a parameterised STNU and its reformulation as a parameterised STN. We demonstrate through a car sharing application that our chance-constrained approach runs in the same time as the previous probabilistic approach, yields solutions with utility improvements of at least 5% over previous arts, while guaranteeing operation within the specified risk bound.National Science Foundation (U.S.) (Grant No. IIS-1017992

Comparing stochastic design decision belief models : pointwise versus interval probabilities.

Decision support systems can either directly support a product designer or support an agent operating within a multi-agent system (MAS). Stochastic based decision support systems require an underlying belief model that encodes domain knowledge. The underlying supporting belief model has traditionally been a probability distribution function (PDF) which uses pointwise probabilities for all possible outcomes. This can present a challenge during the knowledge elicitation process. To overcome this, it is proposed to test the performance of a credal set belief model. Credal sets (sometimes also referred to as p-boxes) use interval probabilities rather than pointwise probabilities and therefore are more easier to elicit from domain experts. The PDF and credal set belief models are compared using a design domain MAS which is able to learn, and thereby refine, the belief model based on its experience. The outcome of the experiment illustrates that there is no significant difference between the PDF based and credal set based belief models in the performance of the MAS