Probability study of airplane crash on Kartini Reactor site area

Probability study of airplane crash at Kartini Reactor site has been carried out. Objective of this study is to determine probability of airplane crash coming from airports around Kartini Reactor site to Kartini Reactor Site. This study was carried out in several stages, namely identification of airports around Kartini Reactor site, initial screening using SDV values (10 km for small airport and 16 km for large airport), probability calculation of airplane crash at Kartini Reactor site and comparing the calculation result with applicable regulations. Based on the identification results there are four airports / runways around the Kartini Reactor site, they are Adi Sutjipto Airport, Adi Sumarmo Airport, Depok Runway, and Yogyakarta International Airport where distance from airport to the site between 2.26-48.23 km. After screening using SDV value, that is known only Adi Sutjipto Airport which is inside SDV radius of Kartini Reactor, so that probability of airplane crash from Adi Sutjipto Airport is calculated, i.e. 3,769x10-8 events/year is. This value is still under the provisions in BAPETEN Regulation No. 4 of 2018 i.e. maximum 10-7 events/year. So it can be concluded that Kartini Reactor is safe from the possibility of airplane crash.

Probability Theory and Its Models

This paper argues for the status of formal probability theory as a mathematical, rather than a scientific, theory. Some remarks are made about the historical transition from Hilbert’s view of probability as a scientific theory to Kolmogorov’s view of probability as a mathematical theory. A process is provided that bridges abstract probability theory with concrete systems via mathematical models. This demonstrates that empirical content is injected into formal models via the mapping from those formal models on to elements of the concrete systems. David Freedman and Philip Stark’s concept of model-based probabilities is examined and is used as a bridge between the formal theory and applications.

Response to Johnson: A random sample versus the radical event

Timothy Johnson’s working hypothesis in his review of my latest book, The Medium of Contingency, is that I (as well as the ‘quants’ involved in the derivative pricing industry) do not understand the foundations of abstract probability theory. In this response, I show that this is not the case. On the contrary, rules and protocols which are common in the derivative pricing industry, the result of which can be an extension of abstract probability theory as it now stands, seem to elude Johnson. To address these failings, I provide theoretical reflections on probability theory and its formalisms.

Infinite secret sharing – Examples

The motivation for extending secret sharing schemes to cases when either the set of players is infinite or the domain from which the secret and/or the shares are drawn is infinite or both, is similar to the case when switching to abstract probability spaces from classical combinatorial probability. It might shed new light on old problems, could connect seemingly unrelated problems, and unify diverse phenomena. Definitions equivalent in the finitary case could be very much different when switching to infinity, signifying their difference. The standard requirement that qualified subsets should be able to determine the secret has different interpretations in spite of the fact that, by assumption, all participants have infinite computing power. The requirement that unqualified subsets should have no or limited information on the secret suggests that we also need some probability distribution. In the infinite case events with zero probability are not necessarily impossible, and we should decide whether bad events with zero probability are allowed or not. In this paper, rather than giving precise definitions, we enlist an abundance of hopefully interesting infinite secret sharing schemes. These schemes touch quite diverse areas of mathematics such as projective geometry, stochastic processes and Hilbert spaces. Nevertheless our main tools are from probability theory. The examples discussed here serve as foundation and illustration to the more theory oriented companion paper [arXiv:1310.7423].

Rare events, temporal dependence, and the extremal index

Classical extreme value theory for stationary sequences of random variables can to a large extent be paraphrased as the study of exceedances over a high threshold. A special role within the description of the temporal dependence between such exceedances is played by the extremal index. Parts of this theory can be generalized not only to random variables on an arbitrary state space hitting certain failure sets, but even to a triangular array of rare events on an abstract probability space. In the case of M4 (maxima of multivariate moving maxima) processes, the arguments take a simple and direct form.

Rare events, temporal dependence, and the extremal index

Classical extreme value theory for stationary sequences of random variables can to a large extent be paraphrased as the study of exceedances over a high threshold. A special role within the description of the temporal dependence between such exceedances is played by the extremal index. Parts of this theory can be generalized not only to random variables on an arbitrary state space hitting certain failure sets, but even to a triangular array of rare events on an abstract probability space. In the case of M4 (maxima of multivariate moving maxima) processes, the arguments take a simple and direct form.

NONSTANDARD APPROACH TO POSSIBILITY MEASURES

Possibility measures have been conceived by Zadeh [1], and developed by, e. g., Dubois, Prade and others, as very simple, if compared with, e.g., probability theory, but still nontrivial and reasonable uncertainty measures. The relatively poor descriptional and operational abilities of possibility measures seem to be closely related to the standard linear ordering relation and the corresponding supremum and infimum operations defined over the unit interval of real numbers. Having discussed, very briefly, the possibilities how to overcome these limitations, we propose and investigate possibility measures taking their values in the well-known Cantor subset of the unit interval but defined with respect to a nonstandard operation of supremum resulting from a nonstandard partial ordering of real numbers from the Cantor set. Such a nonstandard possibility measure is proved to be a sufficient tool to define an infinite sequence of probability measures defined over countable sets, consequently, the distribution of each continuous real-valued random variable defined over a general abstract probability space can be defined by an appropriate nonstandard possibility measure.