Ambiguous correlation

Many decisions are made in environments where outcomes are determined by the realization of multiple random events. A decision maker may be uncertain how these events are related. We identify and experimentally substantiate behavior that intuitively reflects a lack of confidence in their joint distribution. Our findings suggest a dimension of ambiguity which is different from that in the classical distinction between risk and "Knightian uncertainty"

- A BAYESIAN APPROACH TO UNCERTAINTY AVERSION

The Ellsberg paradox demonstrates that peoples belief over uncertainevents might not be representable by subjective probability. We relate this paradox to other commonly observed anomalies, suchas a rejection of the backward induction prediction in the one-shot Ultimatum Game. We argue that the pattern common to theseobservations is that the behavior is governed by rational rules. These rules have evolved and are optimal within the repeated andconcurrent environments that people usually encounter. When an individual relies on these rules to analyzeone-shot or single circumstances, paradoxes emerge. We show that when a risk averse individualhas a Bayesian prior and uses a rule which is optimal for simultaneous and positively correlatedambiguous risks to evaluate a single vague circumstance, his behavior will exhibit uncertaintyaversion. Thus, the behavior predicted by Ellsberg may be explained within the Bayesian expectedutility paradigm.Ellsberg paradox, rule rationality, ambiguity aversion, risk aversion,

Other Regarding Preferences: Outcomes, Intentions, or Interdependence

The Ultimatum Game seems to be the ideal experiment to test for the structure of preferences or the sequential rationality assumptions underlying subgame perfection. We study the theoretical implications of introducing the possibility of misconceptions - that actions may potentially affect continuation payoffs - and show that the set of Perfect Bayesian Nash Equilibria does not converge to the subgame perfect equilibrium when the possibility of misconception approaches zero. The perfect equilibria studied corresponds qualitatively to the experimental findings of offers made and unfair offers rejected.ulitmatum game, asymmetric information, interdependent preferences

Uncertainty and Compound Lotteries: Calibration

The Ellsberg experiments provide an intuitive illustration that the Savage approach, which reduces subjective uncertainty to risk, is not rich enough to capture many decision makers' preferences. Recent experimental evidence suggests that decision makers reduce uncertainty to compound risk. This work presents a theoretical model of decision making in which preferences are defined on both Savage subjective acts and compound objective lotteries. Preferences are two-stage probabilistically sophisticated when the ranking of acts corresponds to a ranking of the respective compound lotteries induced by the acts through the decision maker's subjective belief. This family of preferences includes various theoretical models that have been proposed in the literature to accommodate non-neutral attitude towards ambiguity. The principle of calibration, which was used by Ramsey and de Finetti, allows an outside observer to relate preferences over acts and compound objective lotteries. If preferences abide by the calibration axioms, the evaluation of the compound lottery induced by an act through the subjective belief coincides with the evaluation of the corresponding compound objective lottery. Calibration provides the foundation that allows one to formalize and understand the tight empirical association between probabilistic sophistication and reduction of compound lotteries, for all two-stage probabilistically sophisticated preferences.

Sulfate Burial Constraints on the Phanerozoic Sulfur Cycle

The sulfur cycle influences the respiration of sedimentary organic matter, the oxidation state of the atmosphere and oceans, and the composition of seawater. However, the factors governing the major sulfur fluxes between seawater and sedimentary reservoirs remain incompletely understood. Using macrostratigraphic data, we quantified sulfate evaporite burial fluxes through Phanerozoic time. Approximately half of the modern riverine sulfate flux comes from weathering of recently deposited evaporites. Rates of sulfate burial are unsteady and linked to changes in the area of marine environments suitable for evaporite formation and preservation. By contrast, rates of pyrite burial and weathering are higher, less variable, and largely balanced, highlighting a greater role of the sulfur cycle in regulating atmospheric oxygen

PQL: A Declarative Query Language over Dynamic Biological Schemata

We introduce the PQL query language (PQL) used in the GeneSeek genetic data integration project. PQL incorporates many features of query languages for semi-structured data. To this we add the ability to express metadata constraints like intended semantics and database curation approach. These constraints guide the dynamic generation of potential query plans. This allows a single query to remain relevant even in the presence of source and mediated schemas that are continually evolving, as is often the case in data integration

Extensions of Laplacian Eigenmaps for Manifold Learning

This thesis deals with the theory and practice of manifold learning, especially as they relate to the problem of classification. We begin with a well known algorithm, Laplacian Eigenmaps, and then proceed to extend it in two independent directions. First, we generalize this algorithm to allow for the use of partially labeled data, and establish the theoretical foundation of the resulting semi-supervised learning method. Second, we consider two ways of accelerating the most computationally intensive step of Laplacian Eigenmaps, the construction of an adjacency graph. Both of them produce high quality approximations, and we conclude by showing that they work well together to achieve a dramatic reduction in computational time

Projection of two biphoton qutrits onto a maximally entangled state

Bell state measurements, in which two quantum bits are projected onto a maximally entangled state, are an essential component of quantum information science. We propose and experimentally demonstrate the projection of two quantum systems with three states (qutrits) onto a generalized maximally entangled state. Each qutrit is represented by the polarization of a pair of indistinguishable photons - a biphoton. The projection is a joint measurement on both biphotons using standard linear optics elements. This demonstration enables the realization of quantum information protocols with qutrits, such as teleportation and entanglement swapping.Comment: 4 pages, 3 figures, published versio