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For radioactive nuclear data, $\beta$ decay is one of the most importantinformation and is applied to various fields. However, some of the$\beta$-decay data are not available due to experimental difficulties. Fromthis respect, theoretically calculated results have been embedded in the$\beta$-decay data to compensate the missing information. To calculate the$\beta$-decay half-lives, a proton-neutron quasi-particle random phaseapproximation on top of a Skryme energy density functional is applied with anassumption of spherical symmetry. The isoscalar pairing strength is estimatedby a Bayesian neutral network (BNN). We verify the predicted isoscalar pairingstrengths by preparing the training data and test data. It was confirmed thatthe finite-range isovector pairing ensures the $\beta$-decay half-livesinsensitive to the model space, while the zero-range one was largely dependenton it. The half-lives calculated with the BNN isoscalar pairing strengthsreproduced most of experimental data, although those of highly deformed nucleiwere underestimated. We also studied that the predictive performance on newexperimental data that were not used for the BNN training and found that theywere reproduced well. Our study demonstrates that the isoscalar pairingstrengths determined by the BNN can reproduce experimental data in the sameaccuracy as other theoretical works.

Calculation of $\beta$-decay half-lives with Skyrme Hartree-Fock-Bogoliubov+$pn$-QRPA and isoscalar pairing strengths optimized by a Bayesian method