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.

Genetic maternity and paternity in a local population of armadillos assessed by microsatellite DNA markers and field data.

Genetic data from polymorphic microsatellite loci were employed to estimate paternity and maternity in a local population of nine-banded armadillos (Dasypus novemcinctus) in northern Florida. The parentage assessments took advantage of maximum likelihood procedures developed expressly for situations when individuals of neither gender can be excluded a priori as candidate parents. The molecular data for 290 individuals, interpreted alone and in conjunction with detailed biological and spatial information for the population, demonstrate high exclusion probabilities and reasonably strong likelihoods of genetic parentage assignment in many cases; low mean probabilities of successful reproductive contribution to the local population by individual armadillo adults in a given year; and statistically significant microspatial associations of parents and their offspring. Results suggest that molecular assays of highly polymorphic genetic systems can add considerable power to assessments of biological parentage in natural populations even when neither parent is otherwise known.

Holocene climate change and past Irish societal response

The extent to which North Atlantic Holocene climatic perturbations influenced past human societies is an area of considerable uncertainty and fierce debate. Ireland is ideally placed to help resolve this issue, being occupied for over 9000 yr and located on the eastern Atlantic seaboard, a region dominated by westerly airflow. Irish bog and lake tree populations provide unambiguous evidence of major shifts in surface moisture through the Holocene similar to cycles recorded in the marine realm of the North Atlantic, indicating significant changes in the latitude and intensity of zonal atmospheric circulation across the region. To test for human response to these cycles we summed the probabilities of 465 radiocarbon ages obtained from Irish archaeological contexts and observe enhanced archaeological visibility during periods of sustained wet conditions. These results suggest either increasing density of human populations in key, often defensive locations, and/or the development of subsistence strategies to overcome changing conditions, the latter recently proposed as a significant factor in avoiding societal collapse. Regardless, we demonstrate environmental change is a significantly more important factor in influencing human activity in the landscape than has hitherto been acknowledged.

Oscillator strengths for transitions in C-like ions between K XIV and Mn XX

Energy levels and oscillator strengths (transition probabilities) have been calculated for transitions among 46 fine-structure levels of the (1s(2)) 2s(2) 2p(2), 2s2p(3),2p(4), 2s(2)2p3s, 2s(2) 2p3p and 2s(2)2p3d configurations of C-like K XIV, Sc XVI, Ti XVII, V XVIII, Cr XIX and Mn XX using the GRASP code. Configuration interaction and relativistic effects have been included while generating the wavefunctions. Calculated values of energy levels agree within 3% with the experimentally compiled results, and the length and velocity forms of oscillator strengths agree within 20% for a majority of allowed transitions.

Oscillator strengths for transitions in C-like ions between FIV and Ar XIII

Energy levels and oscillator strengths (transition probabilities) have been calculated for the fine-structure transitions among the levels of the (1s(2)) 2s(2)2p(2), 2s2p(3), 2p(4), 2s(2)2p3s, 2s(2)2p3p, and 2s(2)2p3d configurations of C-like F IV, Na VI, Al VIII, P X, Cl XII, and Ar XIII using the CIV3 program. The extensive configuration interaction and relativistic effects have been included while generating the wavefunctions. Calculated values of energy levels generally agree within 5% with the experimentally compiled results, and the length and velocity forms of oscillator strengths agree within 20% for a majority of allowed transitions.

Opacity in the upper atmosphere of AU Mic

In this paper we investigate the validity of the optically thin assumption in the transition region of the late-type star AU Mic. We use Far-Ultraviolet Spectroscopic Explorer (FUSE) observations of the C III multiplet and O VI resonance lines, hence yielding information at two different levels within the atmosphere. Significant deviations from the optically thin fluxes are found for C III in both quiescent and flare spectra, where only 60% of the flux is actually observed. This could explain the apparent deviation of C III observed in emission measure distributions. We utilize escape probabilities for both homogeneous and inhomogeneous geometries and calculate optical depths as high as 10 for the C III 1175.71 Angstrom component of the multiplet. Using a lower limit to the electron density (10(11) cm(-3))we derive an effective thickness of

Inner-shell photoexcitation of Fe XV and Fe XVI

The configuration-interaction method as implemented in the computer code CIV3 is used to determine energy levels, electric dipole radiative transition wavelengths, oscillator strengths and transition probabilities for inner-shell excitation of transitions in Fe XV and Fe XVI. Specifically, transitions are considered of the type 1s(2) 2s(2) 2p(6) 3s(2) -1s(2) 2s(2) 2p(5) 3l3l' 3l" (l, l' and l" = s,p or d) in FeXV and 1s(2) 2s(2) 2p(6) 3s- 1s(2) 2s(2) 2p(5) 3l3l' (l and l' = s,p or d) in FeXVI, using the relativistic Breit-Pauli approach. An assessment of the accuracy of the derived atomic data is performed.

A discrete time-dependent method for metastable atoms and molecules in intense fields

The full-dimensional time-dependent Schrodinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange mesh methods. The method is applied to calculate the quasienergies and ionization probabilities of atomic and molecular systems in intense static and dynamic electric fields. The gauge invariance and accuracy of the method is established. Applications to multiphoton ionization of positronium, the hydrogen atom and the hydrogen molecular ion are presented. At very high laser intensity, above the saturation threshold, we extend the method using a scaling technique to estimate the quasienergies of metastable states of the hydrogen molecular ion. The results are in good agreement with recent experiments. (C) 2004 American Institute of Physics.

Nature of quantum measurement for quantities not represented by Hermitian operators

In the case of a simple quantum system, we investigate the possibility of defining meaningful probabilities for a quantity that cannot be represented by a Hermitian operator. We find that the consistent-histories approach, recently applied to the case of quantum traversal time [N. Yamada, Phys. Rev. Lett. 83, 3350 (1999)], does not provide a suitable criterion and we dispute Yamada's claim of finding a simple solution to the tunneling-time problem. Rather, we define the probabilities for certain types of generally nonorthogonal decomposition of the system's quantum state. These relate to the interaction between the system and its environment, can be observed in a generalized von Neumann measurement, and are consistent with a particular class of positive-operator-valued measures.

A comparison of conformal and intensity-modulated techniques for oesophageal radiotherapy.

Background and purpose: To investigate the potential of intensity-modulated radiotherapy (IMRT) to reduce lung irradiation in the treatment of oesophageal carcinoma with radical radiotherapy.Materials and methods: A treatment planning study was performed to compare two-phase conformal radiotherapy (CFRT) with IMRT in five patients. The CFRT plans consisted of anterior, posterior and bilateral posterior oblique fields, while the IMRT plans consisted of either nine equispaced fields (9F), or four fields (4F) with orientations equal to the CFRT plans. IMRT plans with seven, five or three equispaced fields were also investigated in one patient. Treatment plans were compared using dose-volume histograms and normal tissue complication probabilities.Results: The 9F IMRT plan was unable to improve on the homogeneity of dose to the planning target volume (PTV), compared with the CFRT plan (dose range, 16.9+/-4.5 (1 SD) vs. 12.4+/-3.9%; P=0.06). Similarly, the 9F IMRT plan was unable to reduce the mean lung dose (11.7+/-3.2 vs. 11.0+/-2.9 Gy; P=0.2). Similar results were obtained for seven, five and three equispaced fields in the single patient studied. The 4F IMRT plan provided comparable PTV dose homogeneity with the CFRT plan (11.8+/-3.3 vs. 12.4+/-3.9%; P=0.6), with reduced mean lung dose (9.5+/-2.3 vs 11.0+/-2.9 Gy; P=0.001).Conclusions: IMRT using nine equispaced fields provided no improvement over CFRT. This was because the larger number of fields in the IMRT plan distributed a low dose over the entire lung. In contrast, IMRT using four fields equal to the CFRT fields offered an improvement in lung sparing. Thus, IMRT with a few carefully chosen field directions may lead to a modest reduction in pneumonitis, or allow tumour dose escalation within the currently accepted lung toxicity.