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.

Does climate change information affect stated risks of pine beetle impacts on forests? An application of the exchangeability method

Risks are an essential feature of future climate change impacts. We explore whether knowledge that climate change might be the source of increasing pine beetle impacts on public or private forests affects stated risk estimates of damage, elicited using the exchangeability method. We find that across subjects the difference between public and private forest status does not influence stated risks, but the group told that global warming is the cause of pine beetle damage has significantly higher risk perceptions than the group not given this information.

Exchangeability of mammalian DNA ligases between base excision repair pathways

In mammalian cells, DNA ligase IIIalpha and DNA ligase I participate in the short- and long-patch base excision repair pathways, respectively. Using an in vitro repair assay employing DNA ligase-depleted cell extracts and DNA substrates containing a single lesion repaired either through short-patch (regular abasic site) or long-patch (reduced abasic site) base excision repair pathways, we addressed the question whether DNA ligases are specific to each pathway or if they are exchangeable. We find that immunodepletion of DNA ligase I did not affect the short-patch repair pathway but blocked long-patch repair, suggesting that DNA ligase IIIa is not able to substitute DNA ligase I during long-patch repair. In contrast, immunodepletion of DNA ligase IIIa did not significantly affect either pathway. Moreover, repair of normal abasic sites in wild-type and X-ray cross-complementing gene 1 (XRCC1)-DNA ligase IIIalpha-immunodepleted cell extracts involved similar proportions of short- and long-patch repair events. This suggests that DNA ligase I was able to efficiently substitute the XRCC1-DNA ligase IIIa complex during short-patch repair.

The concept of exchangeability in ensemble forecasting

A set of random variables is exchangeable if its joint distribution function is invariant under permutation of the arguments. The concept of exchangeability is discussed, with a view towards potential application in evaluating ensemble forecasts. It is argued that the paradigm of ensembles being an independent draw from an underlying distribution function is probably too narrow; allowing ensemble members to be merely exchangeable might be a more versatile model. The question is discussed whether established methods of ensemble evaluation need alteration under this model, with reliability being given particular attention. It turns out that the standard methodology of rank histograms can still be applied. As a first application of the exchangeability concept, it is shown that the method of minimum spanning trees to evaluate the reliability of high dimensional ensembles is mathematically sound.

On probability-based inference under data missing by design

Whether a statistician wants to complement a probability model for observed data with a prior distribution and carry out fully probabilistic inference, or base the inference only on the likelihood function, may be a fundamental question in theory, but in practice it may well be of less importance if the likelihood contains much more information than the prior. Maximum likelihood inference can be justified as a Gaussian approximation at the posterior mode, using flat priors. However, in situations where parametric assumptions in standard statistical models would be too rigid, more flexible model formulation, combined with fully probabilistic inference, can be achieved using hierarchical Bayesian parametrization. This work includes five articles, all of which apply probability modeling under various problems involving incomplete observation. Three of the papers apply maximum likelihood estimation and two of them hierarchical Bayesian modeling. Because maximum likelihood may be presented as a special case of Bayesian inference, but not the other way round, in the introductory part of this work we present a framework for probability-based inference using only Bayesian concepts. We also re-derive some results presented in the original articles using the toolbox equipped herein, to show that they are also justifiable under this more general framework. Here the assumption of exchangeability and de Finetti's representation theorem are applied repeatedly for justifying the use of standard parametric probability models with conditionally independent likelihood contributions. It is argued that this same reasoning can be applied also under sampling from a finite population. The main emphasis here is in probability-based inference under incomplete observation due to study design. This is illustrated using a generic two-phase cohort sampling design as an example. The alternative approaches presented for analysis of such a design are full likelihood, which utilizes all observed information, and conditional likelihood, which is restricted to a completely observed set, conditioning on the rule that generated that set. Conditional likelihood inference is also applied for a joint analysis of prevalence and incidence data, a situation subject to both left censoring and left truncation. Other topics covered are model uncertainty and causal inference using posterior predictive distributions. We formulate a non-parametric monotonic regression model for one or more covariates and a Bayesian estimation procedure, and apply the model in the context of optimal sequential treatment regimes, demonstrating that inference based on posterior predictive distributions is feasible also in this case.

Genetic evaluation of a proposed introduction: the case of the greater prairie chicken and the extinct heath hen.

Population introduction is an important tool for ecosystem restoration. However, before introductions should be conducted, it is important to evaluate the genetic, phenotypic and ecological suitability of possible replacement populations. Careful genetic analysis is particularly important if it is suspected that the extirpated population was unique or genetically divergent. On the island of Martha's Vineyard, Massachusetts, the introduction of greater prairie chickens (Tympanuchus cupido pinnatus) to replace the extinct heath hen (T. cupido cupido) is being considered as part of an ecosystem restoration project. Martha's Vineyard was home to the last remaining heath hen population until its extinction in 1932. We conducted this study to aid in determining the suitability of greater prairie chickens as a possible replacement for the heath hen. We examined mitochondrial control region sequences from extant populations of all prairie grouse species (Tympanuchus) and from museum skin heath hen specimens. Our data suggest that the Martha's Vineyard heath hen population represents a divergent mitochondrial lineage. This result is attributable either to a long period of geographical isolation from other prairie grouse populations or to a population bottleneck resulting from human disturbance. The mtDNA diagnosability of the heath hen contrasts with the network of mtDNA haplotypes of other prairie grouse (T. cupido attwateri, T. pallidicinctus and T. phasianellus), which do not form distinguishable mtDNA groupings. Our findings suggest that the Martha's Vineyard heath hen was more genetically isolated than are current populations of prairie grouse and place the emphasis for future research on examining prairie grouse adaptations to different habitat types to assess ecological exchangeability between heath hens and greater prairie chickens.

How many bad apples are in a bunch? An experimental investigation of perceived pesticide residue risks

Subjective risks of having contaminated apples elicited via the Exchangeability Method (EM) are examined in this study. In particular, as the experimental design allows us to investigate the validity of elicited risk measures, we examine the magnitude of differences between valid and invalid observations. In addition, using an econometric model, we also explore the effect of consumers’ socioeconomic status and attitudes toward food safety on subjects’ perceptions of pesticide residues in apples. Results suggest first, that consumers do not expect an increase in the number of apples containing only one pesticide residue, but, rather, in the number of those apples with traces of multiple residues. Second, we find that valid subjective risk measures do not significantly diverge from invalid ones, indicative of little effect of internal validity on the actual magnitude of subjective risks. Finally, we show that subjective risks depend on age, education, a subject’s ties to the apple industry, and consumer association membership.

New methods for meta-analysis under a fixed effects framework, with frequentist and Bayesian estimation.

Thesis (Ph.D.)--University of Washington, 2015

Random sums of exchangeable variables and actuarial applications

In this paper we study the accumulated claim in some fixed time period, skipping the classical assumption of mutual independence between the variables involved. Two basic models are considered: Model I assumes that any pair of claims are equally correlated which means that the corresponding square-integrable sequence is exchangeable one. Model 2 states that the correlations between the adjacent claims are the same. Recurrence and explicit expressions for the joint probability generating function are derived and the impact of the dependence parameter (correlation coefficient) in both models is examined. The Markov binomial distribution is obtained as a particular case under assumptions of Model 2. (C) 2007 Elsevier B.V. All rights reserved.