Lapshyn Ye., Shevchenko O. Relative probabilities of hypotheses in the Bayesian approach
- Details
- Parent Category: Geo-Technical Mechanics, 2025
- Category: Geo-Technical Mechanics, 2025, Issue 175
Geotech. meh. 2025, 175, 94-100
https://doi.org/10.15407/geotm2025.175.094
RELATIVE PROBABILITIES OF HYPOTHESES IN THE BAYESIAN APPROACH
M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine
UDC [519.226:519.233.3:519.246]:004
Language: English
Abstract. Bayesian networks are widely used in various fields of science and industry, in particular geotechnical mechanics, ecology. They are applied to support decision making under risk conditions, under which is understood as the product of the probability of danger seriousness of the consequences if it is implemented. A Bayesian network allows you to establish cause-and-effect relationships between events and determine the probability of a particular situation when receiving new information about a change in the state of any network variable. It allows you to consistently refine the probabilities of a complete group of events based on the results of observations based on the intermediate results of a stochastic experiment. In other words, Bayes' theorem provides the possibility of determining the posterior probabilities of hypotheses taking into account the priors based on additional experience results. It is known that Bayes' theorem implies: the ratio of the posterior probability of a hypothesis to the prior probability is equal to the ratio of the probability of an event under a given hypothesis to the total probability of the event. However, there is no information on how much the posterior probability of hypotheses changes compared to the prior probability with the appearance of new data. Such a need arises when planning experiments, the conduct of which is associated with large financial and time costs, and most importantly, is associated with unacceptable risks. As a result of the research, an analysis of the influence of additional data on the probabilities of events that depend on hypotheses on the ratio of the posterior and prior ones was carried out. The ratio of probabilities (relative posterior probability of hypotheses) shows how many times the posterior probability will change compared to the prior. The dependence of the ratio on probabilities is shown on graphs in 3d and 2d form. The relative posterior probability of hypotheses allows you to identify the hypothesis that reacts most strongly to additional data and, on this basis, determine the least expensive experiments to refine the prior probability. To demonstrate the simplicity of calculations that allow you to rank hypotheses in terms of sensitivity to new data, a model example is given. As a result of the research, the following was obtained. The relative posterior probability of hypotheses is proposed, which shows how many times the posterior probability will change compared to the prior when receiving additional data related to the occurrence of events caused by the hypotheses. The relative posterior probability of hypotheses is equal to the ratio of the conditional probability of the occurrence of an event under a given hypothesis to the probability of this event. The relative posterior probability of hypotheses allows us to rank hypotheses in terms of sensitivity to new data. The greatest sensitivity was found for an event probability of less than 0.1.
Key words: hypothesis, event, probability, a priori, a posteriori
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About the authors
Lapshyn Yevhen, Doctor of Technical Sciences (D.Sc.), Senior Researcher, Principal Researcher in Department Ecology of Natural Resources Development, M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine (IGTM of the NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it. , ORCID 0000-0002-5443-5566
Shevchenko Oleksandr, Doctor of Technical Sciences (D.Sc.), Senior Researcher, Senior Researcher in Department of Geomechanical Basis of Open-Pit Technology, M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Science of Ukraine (IGTM of the NAS of Ukraine), Dnipro, Ukraine, This email address is being protected from spambots. You need JavaScript enabled to view it. (Corresponding author), ORCID 0000-0003-2630-0186