Price adjustment to news with uncertain precision

Bayesian learning provides the core concept of processing noisy information. In standard Bayesian frameworks, assessing the price impact of information requires perfect knowledge of news’ precision. In practice, however, precision is rarely dis- closed. Therefore, we extend standard Bayesian learning, suggesting traders infer news’ precision from magnitudes of surprises and from external sources. We show that interactions of the different precision signals may result in highly nonlinear price responses. Empirical tests based on intra-day T-bond futures price reactions to employment releases confirm the model’s predictions and show that the effects are statistically and economically significant

Updating beliefs with incomplete observations

Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete. This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently, Grunwald and Halpern have shown that commonly used updating strategies fail in this case, except under very special assumptions. In this paper we propose a new method for updating probabilities with incomplete observations. Our approach is deliberately conservative: we make no assumptions about the so-called incompleteness mechanism that associates complete with incomplete observations. We model our ignorance about this mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities, and we use only coherence arguments to turn prior into posterior probabilities. In general, this new approach to updating produces lower and upper posterior probabilities and expectations, as well as partially determinate decisions. This is a logical consequence of the existing ignorance about the incompleteness mechanism. We apply the new approach to the problem of classification of new evidence in probabilistic expert systems, where it leads to a new, so-called conservative updating rule. In the special case of Bayesian networks constructed using expert knowledge, we provide an exact algorithm for classification based on our updating rule, which has linear-time complexity for a class of networks wider than polytrees. This result is then extended to the more general framework of credal networks, where computations are often much harder than with Bayesian nets. Using an example, we show that our rule appears to provide a solid basis for reliable updating with incomplete observations, when no strong assumptions about the incompleteness mechanism are justified.Comment: Replaced with extended versio

Verification of Uncertain POMDPs Using Barrier Certificates

We consider a class of partially observable Markov decision processes (POMDPs) with uncertain transition and/or observation probabilities. The uncertainty takes the form of probability intervals. Such uncertain POMDPs can be used, for example, to model autonomous agents with sensors with limited accuracy, or agents undergoing a sudden component failure, or structural damage [1]. Given an uncertain POMDP representation of the autonomous agent, our goal is to propose a method for checking whether the system will satisfy an optimal performance, while not violating a safety requirement (e.g. fuel level, velocity, and etc.). To this end, we cast the POMDP problem into a switched system scenario. We then take advantage of this switched system characterization and propose a method based on barrier certificates for optimality and/or safety verification. We then show that the verification task can be carried out computationally by sum-of-squares programming. We illustrate the efficacy of our method by applying it to a Mars rover exploration example.Comment: 8 pages, 4 figure

Radial Velocity Studies of Close Binary Stars.XIII

Radial-velocity measurements and sine-curve fits to the orbital radial velocity variations are presented for ten close binary systems: EG Cep,V1191 Cyg, V1003 Her, BD+7_3142, V357 Peg, V407 Peg, V1123 Tau, V1128 Tau, HH UMa, and PY Vir. While most of the studied eclipsing systems are contact binaries, EG Cep is a detached or a semi-detached double-lined binary and V1003 Her is a close binary of an uncertain type seen at a very low inclination angle. We discovered two previously unknown triple systems, BD+7_3142 and PY Vir, both with late spectral-type (K2V) binaries. Of interest is the low-mass ratio (q = 0.106) close binary V1191 Cyg showing an extremely fast period increase; the system has a very short period for its spectral type and shows a W-type light curve, a feature rather unexpected for such a low mass-ratio system.Comment: Accepted by AJ. 19 pages including 5 figure

Bayesian Learning for a Class of Priors with Prescribed Marginals

We present Bayesian updating of an imprecise probability measure, represented by a class of precise multidimensional probability measures. Choice and analysis of our class are motivated by expert interviews that we conducted with modelers in the context of climatic change. From the interviews we deduce that generically, experts hold a much more informed opinion on the marginals of uncertain parameters rather than on their correlations. Accordingly, we specify the class by prescribing precise measures for the marginals while letting the correlation structure subject to complete ignorance. For sake of transparency, our discussion focuses on the tutorial example of a linear two-dimensional Gaussian model. We operationalize Bayesian learning for that class by various updating rules, starting with (a modified version of) the generalized Bayes' rule and the maximum likelihood update rule (after Gilboa and Schmeidler). Over a large range of potential observations, the generalized Bayes' rule would provide non-informative results. We restrict this counter-intuitive and unnecessary growth of uncertainty by two means, the discussion of which refers to any kind of imprecise model, not only to our class. First, we find our class of priors too inclusive and, hence, require certain additional properties of prior measures in terms of smoothness of probability density functions. Second, we argue that both updating rules are dissatisfying, the generalized Bayes' rule being too conservative, i.e., too inclusive, the maximum likelihood rule being too exclusive. Instead, we introduce two new ways of Bayesian updating of imprecise probabilities: a ``weighted maximum likelihood method'' and a ``semi-classical method.'' The former bases Bayesian updating on the whole set of priors, however, with weighted influence of its members. By referring to the whole set, the weighted maximum likelihood method allows for more robust inferences than the standard maximum likelihood method and, hence, is better to justify than the latter.Furthermore, the semi-classical method is more objective than the weighted maximum likelihood method as it does not require the subjective definition of a weighting function. Both new methods reveal much more informative results than the generalized Bayes' rule, what we demonstrate for the example of a stylized insurance model

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Price Adjustment to News with Uncertain Precision

Bayesian learning provides the core concept of processing noisy information. In standard Bayesian frameworks, assessing the price impact of information requires perfect knowledge of news’ precision. In practice, however, precision is rarely dis- closed. Therefore, we extend standard Bayesian learning, suggesting traders infer news’ precision from magnitudes of surprises and from external sources. We show that interactions of the different precision signals may result in highly nonlinear price responses. Empirical tests based on intra-day T-bond futures price reactions to employment releases confirm the model’s predictions and show that the effects are statistically and economically significant.Bayesian Learning, Macroeconomic Announcements, Information Quality, Precision Signals

Multi-Objective Approaches to Markov Decision Processes with Uncertain Transition Parameters

Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not known precisely. Different types of MDPs with uncertain, imprecise or bounded transition rates or probabilities and rewards exist in the literature. Commonly, analysis of models with uncertainties amounts to searching for the most robust policy which means that the goal is to generate a policy with the greatest lower bound on performance (or, symmetrically, the lowest upper bound on costs). However, hedging against an unlikely worst case may lead to losses in other situations. In general, one is interested in policies that behave well in all situations which results in a multi-objective view on decision making. In this paper, we consider policies for the expected discounted reward measure of MDPs with uncertain parameters. In particular, the approach is defined for bounded-parameter MDPs (BMDPs) [8]. In this setting the worst, best and average case performances of a policy are analyzed simultaneously, which yields a multi-scenario multi-objective optimization problem. The paper presents and evaluates approaches to compute the pure Pareto optimal policies in the value vector space.Comment: 9 pages, 5 figures, preprint for VALUETOOLS 201