We investigate the problem of truthfully eliciting an expert’s assessment of a property of a probability distribution, where a property is any real-valued function of the distribution such as mean or variance. We show that not all properties are elicitable; for example, the mean is elicitable and the variance is not. For those that are elicitable, we provide a representation theorem characterizing all payment (or “score”) functions that induce truthful revelation. We also consider the elicitation of sets of properties. We then observe that properties can always be inferred from sets of elicitable properties. This naturally suggests the concept of elicitation complexity; the elicitation complexity of property is the minimal size of such a set implying the property. Finally we discuss applications to prediction markets.

fire In the southwestern U.S., wildland fire frequency and area burned have steadily increased in recent decades, a pattern attributable to multiple ignition sources. To examine contributing landscape factors and patterns related to the occurrence of large (P20 ha in extent) fires in the forested region of northern Arizona, we assembled a database of lightning- and human-caused fires for the period 1 April to 30 September, 1986– 2000. At the landscape scale, we used a weights-of-evidence approach to model and map the probability of occurrence based on all fire types (n = 203), and lightning-caused fires alone (n = 136). In total, large fires burned 101,571 ha on our study area. Fires due to lightning were more frequent and extensive than those caused by humans, although human-caused fires burned large areas during the period of our analysis. For all fires, probability of occurrence was greatest in areas of high topographic roughness and lower road density. Ponderosa pine (Pinus ponderosa)-dominated forest vegetation and mean annual precipitation were less important predictors. Our modeling results indicate that seasonal large fire events are a consequence of non-random patterns of occurrence, and that patterns generated by these events may affect the regional fire regime more extensively than previously thought. Identifying the factors that influence large fires will improve our ability to target resource protection efforts and manage fire risk at the landscape scale.

Traditional statistical methods attempt to provide objective information about treatment effects through the use of easily computed P –values. However, much controversy surrounds the use of P –values, including statistical vs. clinical significance, artificiality of null hypotheses, 1–tailed vs. 2–tailed tests, difficulty in interpreting confidence intervals, falsely interpreting non– informative studies as ”negative”, arbitrariness in testing for equivalence, trading off type I and type II error, using P –values to quantify evidence, which statistical test should be used for 2 × 2 frequency tables, α–spending and adjusting for multiple comparisons, whether to adjust final P –values for the intention of terminating a trial early even though it completed as planned, complexity of group sequential monitoring procedures, and whether a promising but statistically insignificant trial can be extended. Bayesian methods allow calculation of probabilities that are usually of more interest to consumers, e.g. the probability that treatment A is similar to treatment B or the probability that treatment A is at least 5 % better than treatment B, and these methods are

University of Mannheim for valuable comments and insights. The Role of Non-financial Factors