Structuring Probability Assessments

A probability assessment framework is outlined that enables decision-makers to determine a probability distribution over possible events or scenarios they could face in the future.The methodology of the analytic hierarchy process can be utilized in the procedures.Bayesian revision accounting for new developments can be used to calculate posterior probabilities using the same procedures.

A New Approach to Probability Assessment

Using spreadsheets and ranges for pairwise judgments,candidate probability distributions are generated for the decision-maker to consider.This replaces event-by-event determination of probabilities.Basic statistics of the distributions are then used to determine a final distribution for decision purposes as in buy,sell,or hold.

Probability Assessment

The methodology presented below can be viewed as a means of quantifying intuitions,guesses,hunches etc.,about relative likelihoods for alternative events leading to a“ballpark”probability distribution.Different intuitions etc.,will lead to different“ballpark”distributions.A final distribution can then be formulated by the decision-maker using other information as in minimum or maximum collective probabilities for groups of events or similar assessments.Final judgments may be idiosyncratic to the decision-maker and not easily replicable in an algorithm.

Variations in Probability Assessment With Atypical Scenarios

Probability assessment in some scenarios may involve unusual aspects such as requiring certain values for some events and extremely high or low probabilities in other cases.

Assessing probabilities of unique events： Calibrating qualitative likelihood judgments into a probability distribution

Multifaceted events in an organizational environment usually need to be assigned probabilities as a prerequisite to analytical decision-making. If the decision situation is unique, a lack of relevant historical frequency data may preclude use of traditional probability models such as the normal, binomial etc. In this case, an individual decision maker （DM） or an informed group of persons can input into a procedure as outlined here to determine a probability distribution that leads to the expected values of alternative actions or fair values of securities. The individual or group member must decide qualitatively on the extent to which one event is ＂more likely＂ than another where both events are ranked adjacent （i.e., closest to each other） in terms of likelihood. Even though the individual or group members may lack experience in orthodox probability assessment, these pairwise ＂more likely＂ judgments on the relative likelihood of events are not overly demanding for persons familiar with the possible outcomes in the situation under analysis.

Ecological risk assessment of heavy metals in surface seawater and sediment near the outlet of a zinc factory in Huludao City, Liaoning Province, China

At present, the methods widely applied to assess ecological risk of heavy metals are essentially single-point estimates in which exposure and toxicity data cannot be fully used and probabilities of adverse biological effects cannot be achieved. In this study, based on investigation of concentrations of six heavy metals(As, Hg, Pb, Cd, Cu, and Zn) in the surface seawater and sediment near the outlet of a zinc factory, located in Huludao City, Liaoning Province, China, a tiered approach consisting of several probabilistic options was used to refi ne ecological risk assessment for the individuals. A mixture of various heavy metals was detected in the surface seawater, and potential ecological risk index(PERI) was adopted to assess the potential ecological risk of heavy metals in the surface sediment. The results from all levels of aquatic ecological risk assessment in the tiered framework, ranging from comparison of single effects and exposure values to the use of distribution-based Hazard Quotient obtained through Monte Carlo simulation, are consistent with each other. Briefl y, aquatic Zn and Cu posed a clear ecological risk, while Cd, Pb, Hg, and As in the water column posed potential risk. As expected, combined ecological risk of heavy metal mixture in the surface seawater was proved signifi cantly higher than the risk caused by any individual heavy metal, calculated using the concept of total equivalent concentration. According to PERI, the severity of pollution by the six heavy metals in the surface sediment decreased in the following sequence: Cd>Hg>As>Pb>Cu>Zn, and the total heavy metals in the sediment posed a very high risk to the marine environment. This study provides a useful mathematical framework for ecological risk assessment of heavy metals.

Thinking Probabilistically Revisited

Probability distributions are derived for real-world situations where the environment may be subject to high volatility involving radical revisions in probability judgments.A simple procedure is outlined deriving an initial probability distribution which may then be adjusted to reflect additional or new information.The trade-off between minimal computation and maximum information is examined.

Thinking Probabilistically

Probability distributions are derived for real-world situations involving hard-to-quantify outcomes unlike drug trials for example.Scenarios may involve levels of satisfaction,risk,inflation,etc.,that show extreme volatility over time requiring frequent updating.Pairwise judgments by the decision-maker form the basis for the simple calculations that could replace traditional revision of prior distributions.

Assessing Probabilities for Events Pertaining to Buy/Sell and Similar Decisions

Assessing probabilities for relevant and sometimes unique events in real-world decision situations can be problematic. This paper elucidates a 2-step process for assigning probabilities to relevant events enabling a rational decision process to supersede decision choices based only on a gut feeling. After assessing probabilities the decision maker can confirm or reverse a gut feeling choice using expected values for each available act and traditional decision theory methodology. A simple example involving a buy now or buy later situation with market uncertainty illustrates the process for typical yes or no decisions.

An experimental method to obtain the hard alpha anomaly distribution for titanium alloy aeroengine disks

A probability-based damage tolerance methodology has been proposed to improve the recognition of material anomalies, especially hard alpha(TiN) anomalies for aeroengine rotor disks. A key input to this method is hard alpha anomaly distribution, which reflects the occurrence rate and size of anomalies present in the finished part material of titanium rotors. Since anomalies rarely occur naturally, an experimental method is proposed to obtain the anomaly distribution for titanium alloy aeroengine disks to reflect and equivalently replace the manufacturing development in titanium industry. In general, the anomaly distribution information can be divided into two parts: the Probability of Detection(POD) curve and the detected anomaly distribution, which contains the size and frequency data of the detected anomalies. The distribution can be established based on several appropriate assumptions and derivation steps with different confidence levels of POD curves and detected anomaly distributions. In this case, the distribution can be obtained in a relatively short time as a key input to the probability-based damage tolerance methodology. Then the Probability of Failure(POF) can be calculated, and the value is found to vary with different confidence levels. On this basis, the conservative estimated POF can be obtained in conjunction with confidence levels.