In the context of parameter estimation, Bayesian methods and frequentist methods (i.e Pluto-Tasche, classical fractional logistic regression etc) differ in the sense that Bayesian methods treat parameters as random variables. On the other hand, frequentist approaches derive point estimates using maximum likelihood estimation (MLE), whereas Bayesian methods estimate the central tendency posterior probability conditional on priors by leveraging on MAP (maximum a-posteriori method) which maximizes the posterior distribution. Eventually, MAP provides a point estimation such as mode or mean of the posterior distribution.
As in the frequentist approaches, Bayesian methods use the same statistical model structure, yet they allow to embedding the prior information (can be informative and non-informative) of the independent variables into the estimation process. A-priori information might include the probability distribution of intercept and initial values of the coefficients of risk drivers. Consequently, a generative model of an assumed distribution with parameters of the model, is simulated. After, obtaining the generative model, with risk data and priors; it is possible to obtain posterior distribution of the parameters by using MCMC (Markov Chain Monte Carlo) methods such as Metropolis, Gibbs, Hamiltonian, etc.
One advantage of using Bayesian methods in the context of LDPs is that it eliminates the need for selecting confidence intervals. In frequentist approaches, parameters are fixed but the confidence intervals are random variables, whereas in Bayesian methods, parameters are random variables and confidence bounds are fixed. With priors, if a parameter has a subjective probability that its posterior distribution lies between certain values, then these values become the confidence bounds. Another advantage is that expert opinion can be incorporated through informative priors, which can help to better address the unique features of the portfolio. In this way, the LDP transformation is less agnostic to portfolio-specific issues. Lastly, Bayesian methods can be easily adapted to accommodate correlation structures between default events.