The article “Asymptotic Confidence Interval for Conditional Probability at Decision Making” by Yu. S. Kan and V. R. Sobol is a statistics based paper in which the authors discuss the problems related to unilateral asymptotic confidence intervals for unknown conditional probabilities that are independent of the said distribution (Kan, Y. S. & Sobol, V. R., 2017, p. 2). Within the article, the authors propose a method of constructing confidence intervals that is “computationally simpler” and “not less precise” than other methods previously used to complete this task (Kam, Y. S. & Sobol, V. R., 2017, p. 2). They begin by offering prior information that relates to the history of the unknown conditional probability and why it is relevant to their research. The real word relation that the authors give is that estimates of the conditional probability are required when attempting to apply mathematical analysis to railroad safety monitoring (Kam, Y. S. & Sobol, V. R., 2017, p. 1). Hence, they are attempting to find the first steps of creating a simpler and more reliable method of doing so.

Deeper in the article, the methods that the authors used during their experimentations and research come to light. The authors first establish basis and reason by giving readers benchmarks and parameters to follow the authors’ thought process with. One of the ways in which this is demonstrated is on page 3 when the authors create the scenario of a transport accident and how the variables found within a related equation relate to the occurrence of the scenario. Secondly, the authors introduce the frequency ratio to be the estimate of a conditional event’s probability. In their use of the frequency ratio, and other variables, the authors find that they were able to obtain expressions for the boundaries of asymptotic confidence intervals for unknown conditional probabilities.

Later on in the article, the authors begin to create their basic results and start by representing the difference of the left and right sides of the probably and, then, the independence and mutual independence of the multiple variables that were found within their experiments and tests. After doing this, the authors find the value of n and greater n in this probability. After doing so, they then replace greater n with a condition that is transformed into an unknown constant that depends on the values of probabilities P (AB) and P (B). Going further into the article, the authors perform more math work and discover more facts and details about the inequalities in question. The authors come to another milestone when they find that a priori restriction on the probability of event P (A) actually improves the accuracy of estimates pertaining to the unknown conditional probability P (A|B) (Kam, Y. S. & Sobol, V. R., 2017, p. 7). Their math and formulas were extremely detailed, but they were able to concisely present a formula that found a confidence interval of 0.0243 in the left boundary of the interval that is not “worse in precision” than the previous results found with the use of other methods (Kam, Y. S. & Sobol, V. R., 2017, p. 7).

In their conclusions statement, the authors mention that the results of various experiments demonstrate the availability of restrictions of events that would allow one to greatly improve the accuracy of one’s estimate of the unknown conditional probability (Kam, Y. S. & Sobol, V. R., 2017, p. 7). However, the authors also mentioned that a joint occurrence of events A and B often take place at an extremely rare rate. The authors have plans to use the results that they presented in this article to construct new criteria for the dangers of the aforementioned transport accidents.