Geodesic
The $d $-risk of Bayesian estimation for the probability of success in Bernoulli trials
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 164 (2022) no. 4, pp. 271-284

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This article considers the problem of estimating the probability $p$ of success in Bernoulli trials when it is a priori the smallest. Using the $d$-posterior approach to the problem of guaranteed statistical inference, a Bayesian estimation of $p$ was performed for a special loss function of type $1$-$0$ with the relative error restriction and the beta prior distribution of the estimated parameter. The $d$-risk of the Bayesian estimation was calculated, and the impossibility to design a $d$-guaranteed estimation procedure for a fixed amount of tests was revealed.
Keywords: Bernoulli trials, Bayesian probability estimation, beta prior distribution, $d$-risk estimation. 
@article{UZKU_2022_164_4_a0,
     author = {N. F. Bilalova},
     title = {The $d $-risk of {Bayesian} estimation for the probability of success in {Bernoulli} trials},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {271--284},
     publisher = {mathdoc},
     volume = {164},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2022_164_4_a0/}
}
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N. F. Bilalova. The $d $-risk of Bayesian estimation for the probability of success in Bernoulli trials. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 164 (2022) no. 4, pp. 271-284. http://geodesic.mathdoc.fr/item/UZKU_2022_164_4_a0/