Proceedings of the 18th Conference on Computer Science and Intelligence Systems

DOI: http://dx.doi.org/10.15439/2023F1144

Citation: Proceedings of the 18th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 35, pages 1223–1227 (2023)

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Abstract. Regarding the parameter estimation task, besides the time effectiveness of the simulation, parameter estimates are required to be precise enough. Usually, the estimates are Monte Carlo-simulated using a prior estimated variability within a small sample. However, the problem with pre-estimated variability is that it can be estimated imprecisely or, even worse, underestimated, resulting in estimation bias. In this work, we address the abovementioned issue and suggest estimating all parameters as probabilities. Since the probability is not only finite but has its theoretical maximum as $1$, using outcomes of Bernoulli and binomial distribution's upper-bounded variance and Chebyshev's inequality, the estimator's variability is theoretically upper-bounded within the Monte Carlo simulation and estimation process. It cannot be underestimated or estimated inaccurately; thus, its precision is ensured till a given decimal digit, with very high probability. If there is a known process that treats the parameter of interest in terms of probability, we can estimate how many iterations of the Monte Carlo simulation are needed to ensure parameter estimate on a given level of precision. Also, we analyze the asymptotic time complexity of the proposed estimation strategy and illustrate the approach on a short case study of $\pi$ constant estimation.

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