27,020 research outputs found
Practical Theory Extension in Event-B
Abstract. The Rodin tool for Event-B supports formal modelling and proof using a mathematical language that is based on predicate logic and set theory. Although Rodin has in-built support for a rich set of operators and proof rules, for some application areas there may be a need to extend the set of operators and proof rules supported by the tool. This paper outlines a new feature of the Rodin tool, the theory component, that allows users to extend the mathematical language supported by the tool. Using theories, Rodin users may define new data types and polymorphic operators in a systematic and practical way. Theories also allow users to extend the proof capabilities of Rodin by defining new proof rules that get incorporated into the proof mechanisms. Soundness of new definitions and rules is provided through validity proof obligations.
Philosophy and the practice of Bayesian statistics
A substantial school in the philosophy of science identifies Bayesian
inference with inductive inference and even rationality as such, and seems to
be strengthened by the rise and practical success of Bayesian statistics. We
argue that the most successful forms of Bayesian statistics do not actually
support that particular philosophy but rather accord much better with
sophisticated forms of hypothetico-deductivism. We examine the actual role
played by prior distributions in Bayesian models, and the crucial aspects of
model checking and model revision, which fall outside the scope of Bayesian
confirmation theory. We draw on the literature on the consistency of Bayesian
updating and also on our experience of applied work in social science.
Clarity about these matters should benefit not just philosophy of science,
but also statistical practice. At best, the inductivist view has encouraged
researchers to fit and compare models without checking them; at worst,
theorists have actively discouraged practitioners from performing model
checking because it does not fit into their framework.Comment: 36 pages, 5 figures. v2: Fixed typo in caption of figure 1. v3:
Further typo fixes. v4: Revised in response to referee
Technology assessment of advanced automation for space missions
Six general classes of technology requirements derived during the mission definition phase of the study were identified as having maximum importance and urgency, including autonomous world model based information systems, learning and hypothesis formation, natural language and other man-machine communication, space manufacturing, teleoperators and robot systems, and computer science and technology
Space exploration: The interstellar goal and Titan demonstration
Automated interstellar space exploration is reviewed. The Titan demonstration mission is discussed. Remote sensing and automated modeling are considered. Nuclear electric propulsion, main orbiting spacecraft, lander/rover, subsatellites, atmospheric probes, powered air vehicles, and a surface science network comprise mission component concepts. Machine, intelligence in space exploration is discussed
Where do statistical models come from? Revisiting the problem of specification
R. A. Fisher founded modern statistical inference in 1922 and identified its
fundamental problems to be: specification, estimation and distribution. Since
then the problem of statistical model specification has received scant
attention in the statistics literature. The paper traces the history of
statistical model specification, focusing primarily on pioneers like Fisher,
Neyman, and more recently Lehmann and Cox, and attempts a synthesis of their
views in the context of the Probabilistic Reduction (PR) approach. As argued by
Lehmann [11], a major stumbling block for a general approach to statistical
model specification has been the delineation of the appropriate role for
substantive subject matter information. The PR approach demarcates the
interrelated but complemenatry roles of substantive and statistical information
summarized ab initio in the form of a structural and a statistical model,
respectively. In an attempt to preserve the integrity of both sources of
information, as well as to ensure the reliability of their fusing, a purely
probabilistic construal of statistical models is advocated. This probabilistic
construal is then used to shed light on a number of issues relating to
specification, including the role of preliminary data analysis, structural vs.
statistical models, model specification vs. model selection, statistical vs.
substantive adequacy and model validation.Comment: Published at http://dx.doi.org/10.1214/074921706000000419 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Re-reading Jevons's Principles of Science - Induction Redux
In this paper I try to substantiate the thesis that Jevons may have been too harsh on the vices of induction and generously optimistic about the virtues of deduction, as discussed, primarily, in his magnum opus, The Principles of Science [6]. With this aim in mind the paper attempts to suggest (modern), recursion theoretic, theoretical technologies that could reduce and, under conditions that I claim would be acceptable to Jevons, even eliminate the inductive indeterminacies that he had emphasised.Jevons, Inductiion, Inductive Inference, Bayes's Rule
Keynes and the logic of econometric method
This paper analyzes the controversy between Keynes and Tinbergen on econometric testing of business cycle theories. In his writings, Keynes repeatedly emphasizes a logical objection to Tinbergen s work. It is clarified what exactly this logical objection is, and why it matters for a statistical analysis of investment. Keynes arguments can be traced back to his Treatise on Probability, where the principle of limited independent variety is introduced as the basic requirement for probabilistic inference. This requirement is not satisfied in case of investment, where expectations are complex determinants. Multiple correlation, sometimes thought to take care of required ceteris paribus clauses, does not help to counter Keynes critiqueBusiness Cycles;Econometrics;Testing;business cycle
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