The d-risk of Bayesian estimation for the probability of success in Bernoulli trials
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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2022-12-01
|
| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://kpfu.ru/uz-eng-phm-2022-4-1.html |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846095183804891136 |
|---|---|
| author | N.F. Bilalova |
| author_facet | N.F. Bilalova |
| author_sort | N.F. Bilalova |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-91c46bcf37bf4e8895659fda09a7ff9b |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2022-12-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-91c46bcf37bf4e8895659fda09a7ff9b2025-01-02T11:25:55ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982022-12-01164427128410.26907/2541-7746.2022.4.271-284The d-risk of Bayesian estimation for the probability of success in Bernoulli trialsN.F. Bilalova0Kazan Federal University, Kazan, 420008 RussiaThis 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.https://kpfu.ru/uz-eng-phm-2022-4-1.htmlbernoulli trialsbayesian probability estimationbeta prior distributiond-risk estimation |
| spellingShingle | N.F. Bilalova The d-risk of Bayesian estimation for the probability of success in Bernoulli trials Учёные записки Казанского университета: Серия Физико-математические науки bernoulli trials bayesian probability estimation beta prior distribution d-risk estimation |
| title | The d-risk of Bayesian estimation for the probability of success in Bernoulli trials |
| title_full | The d-risk of Bayesian estimation for the probability of success in Bernoulli trials |
| title_fullStr | The d-risk of Bayesian estimation for the probability of success in Bernoulli trials |
| title_full_unstemmed | The d-risk of Bayesian estimation for the probability of success in Bernoulli trials |
| title_short | The d-risk of Bayesian estimation for the probability of success in Bernoulli trials |
| title_sort | d risk of bayesian estimation for the probability of success in bernoulli trials |
| topic | bernoulli trials bayesian probability estimation beta prior distribution d-risk estimation |
| url | https://kpfu.ru/uz-eng-phm-2022-4-1.html |
| work_keys_str_mv | AT nfbilalova thedriskofbayesianestimationfortheprobabilityofsuccessinbernoullitrials AT nfbilalova driskofbayesianestimationfortheprobabilityofsuccessinbernoullitrials |