Eliciting and estimating valid subjective probabilities: An experimental investigation of the Exchangeability Method.

Using a laboratory experiment, we investigate whether incentive compatibility affects subjective probabilities elicited via the exchangeability method (EM), an elicitation technique consisting of several chained questions. We hypothesize that subjects who are aware of the chaining strategically behave and provide invalid subjective probabilities, while subjects who are not aware of the chaining state their real beliefs and provide valid subjective probabilities. The validity of subjective probabilities is investigated using de Finetti's notion of coherence, under which probability estimates are valid if and only if they obey all axioms of probability theory.
Four experimental treatments are designed and implemented. Subjects are divided into two initial treatment groups: in the first, they are provided with real monetary incentives, and in the second, they are not. Each group is further sub-divided into two treatment groups, in the first, the chained structure of the experimental design is made clear to the subjects, while, in the second, the chained structure is hidden by randomizing the elicitation questions.
Our results suggest that subjects provided with monetary incentives and randomized questions provide valid subjective probabilities because they are not aware of the chaining which undermines the incentive compatibility of the exchangeability method.

Inference in Polytrees with Sets of Probabilities

Inferences in directed acyclic graphs associated with probability intervals and sets of probabilities are NP-hard, even for polytrees. We propose: 1) an improvement on Tessem’s A/R algorithm for inferences on polytrees associated with probability intervals; 2) a new algorithm for approximate inferences based on local search; 3) branch-and-bound algorithms that combine the previous techniques. The first two algorithms produce complementary approximate solutions, while branch-and-bound procedures can generate either exact or approximate solutions. We report improvements on existing techniques for inference with probability sets and intervals, in some cases reducing computational effort by several orders of magnitude.

Multilinear and Integer Programming for Markov Decision Processes with Imprecise Probabilities

Markov Decision Processes (MDPs) are extensively used to encode sequences of decisions with probabilistic effects. Markov Decision Processes with Imprecise Probabilities (MDPIPs) encode sequences of decisions whose effects are modeled using sets of probability distributions. In this paper we examine the computation of Γ-maximin policies for MDPIPs using multilinear and integer programming. We discuss the application of our algorithms to “factored” models and to a recent proposal, Markov Decision Processes with Set-valued Transitions (MDPSTs), that unifies the fields of probabilistic and “nondeterministic” planning in artificial intelligence research. 

Partially Ordered Preferences in Decision Trees: Computing Strategies with Imprecision in Probabilities

Partially ordered preferences generally lead to choices that do not abide by standard expected utility guidelines; often such preferences are revealed by imprecision in probability values. We investigate five criteria for strategy selection in decision trees with imprecision in probabilities: “extensive” Γ-maximin and Γ-maximax, interval dominance, maximality and E-admissibility. We present algorithms that generate strategies for all these criteria; our main contribution is an algorithm for Eadmissibility that runs over admissible strategies rather than over sets of probability distributions.

Interannual and (multi-)decadal variability in the sedimentary BIT index of Lake Challa, East Africa, over the past 2200 years: assessment of the precipitation proxy

The branched vs. isoprenoid tetraether (BIT) index is based on the relative abundance of branched tetraether lipids (brGDGTs) and the isoprenoidal GDGT crenarchaeol. In Lake Challa sediments the BIT index has been applied as a proxy for local monsoon precipitation on the assumption that the primary source of brGDGTs is soil washed in from the lake's catchment. Since then, microbial production within the water column has been identified as the primary source of brGDGTs in Lake Challa sediments, meaning that either an alternative mechanism links BIT index variation with rainfall or that the proxy's application must be reconsidered. We investigated GDGT concentrations and BIT index variation in Lake Challa sediments at a decadal resolution over the past 2200 years, in combination with GDGT time-series data from 45 monthly sediment-trap samples and a chronosequence of profundal surface sediments.

Our 2200-year geochemical record reveals high-frequency variability in GDGT concentrations, and therefore in the BIT index, superimposed on distinct lower-frequency fluctuations at multi-decadal to century timescales. These changes in BIT index are correlated with changes in the concentration of crenarchaeol but not with those of the brGDGTs. A clue for understanding the indirect link between rainfall and crenarchaeol concentration (and thus thaumarchaeotal abundance) was provided by the observation that surface sediments collected in January 2010 show a distinct shift in GDGT composition relative to sediments collected in August 2007. This shift is associated with increased bulk flux of settling mineral particles with high Ti / Al ratios during March–April 2008, reflecting an event of unusually high detrital input to Lake Challa concurrent with intense precipitation at the onset of the principal rain season that year. Although brGDGT distributions in the settling material are initially unaffected, this soil-erosion event is succeeded by a massive dry-season diatom bloom in July–September 2008 and a concurrent increase in the flux of GDGT-0. Complete absence of crenarchaeol in settling particles during the austral summer following this bloom indicates that no Thaumarchaeota bloom developed at that time. We suggest that increased nutrient availability, derived from the eroded soil washed into the lake, caused the massive bloom of diatoms and that the higher concentrations of ammonium (formed from breakdown of this algal matter) resulted in a replacement of nitrifying Thaumarchaeota, which in typical years prosper during the austral summer, by nitrifying bacteria. The decomposing dead diatoms passing through the suboxic zone of the water column probably also formed a substrate for GDGT-0-producing archaea. Hence, through a cascade of events, intensive rainfall affects thaumarchaeotal abundance, resulting in high BIT index values.

Decade-scale BIT index fluctuations in Lake Challa sediments exactly match the timing of three known episodes of prolonged regional drought within the past 250 years. Additionally, the principal trends of inferred rainfall variability over the past two millennia are consistent with the hydroclimatic history of equatorial East Africa, as has been documented from other (but less well dated) regional lake records. We therefore propose that variation in GDGT production originating from the episodic recurrence of strong soil-erosion events, when integrated over (multi-)decadal and longer timescales, generates a stable positive relationship between the sedimentary BIT index and monsoon rainfall at Lake Challa. Application of this paleoprecipitation proxy at other sites requires ascertaining the local processes which affect the productivity of crenarchaeol by Thaumarchaeota and brGDGTs.

Comments on “High-temperature creep resistance and effects on the austenite reversion and precipitation of 18 Ni (300) maraging steel” by dos Reis et al. [Materials Characterization 107 (2015) 350- 357]

This letter attempts to comment on an article by dos Reis et al., in the aspects of creep considerationand chemical analysis in maraging steels.