This study investigated the application of Bayesian multiple change-point detection techniques in the context of piecewise polynomial signals. Given the limited number of existing methodologies for identifying change-points in such signals, we proposed an objective Bayesian change-point detection approach that accommodated heterogeneous error distributions. Our methodology was grounded in a piecewise polynomial regression framework and employed binary segmentation. Initially, we identified change-points across various signals using Bayesian binary segmentation. Subsequently, we applied Bayesian model selection to ascertain the most suitable polynomial order for the identified segments. This approach facilitated a change-point detection method that minimized reliance on subjective inputs. We incorporated intrinsic priors that allowed for the formulation of Bayes factors and model selection probabilities. To evaluate the efficacy of the proposed change-point detection techniques, we conducted a simulation study alongside two empirical case studies: one involving the Goddard Institute for space studies surface temperature analysis and the other concerning the daily closing stock prices of Samsung Electronics Co.

The application of a doubly Type-Ⅱ censoring scheme, where observations are censored at both the left and right ends, is often used in various fields including social science, psychology, and economics. However, the observed sample size under this censoring scheme may not be large enough to apply a likelihood-based approach due to the occurrence of censoring at both ends. To effectively respond to this difficulty, we propose a pivotal-based approach within a doubly Type-Ⅱ censoring framework, focusing on two key aspects: Estimation for parameters of interest and prediction for missing or censored samples. The proposed approach offers two prominent advantages, compared to the likelihood-based approach. First, this approach leads to exact confidence intervals for unknown parameters. Second, it addresses prediction problems in a closed-form manner, ensuring computational efficiency. Moreover, novel algorithms using a pseudorandom sequence, which are introduced to implement the proposed approach, have remarkable scalability. The superiority and applicability of the proposed approach are substantiated in Monte Carlo simulations and real-world case analysis through a comparison with the likelihood-based approach.

In many applications, modeling based on a normal kernel is preferred because not only does the normal kernel belong to the family of stable distributions, but also it is easy to satisfy the stationary condition in the stochastic process. However, the characteristic of the data, such as count or proportion, is a major obstacle to complete modeling based on a normal distribution. To solve a limited boundary or non-normal distribution problem, we provided a novel transformation method and proposed a nonparametric Bayesian approach based on a normal kernel of the transformed variable. In particular, the provided transformation transforms any probability space into a real space and is free from the constraints of the previous transformation, such as skewness, presence of power, and bounded domains. Another advantage was that it was possible to use the Dirichlet process mixture model with full conditional posterior distributions for all parameters, leading to a fast convergence rate in the Markov chain Monte Carlo. The proposed methodology was illustrated with simulated datasets and two real datasets with non-normal distribution problems. In addition, to demonstrate the superiority of the proposed methodology, the comparison with the transformed Bernstein polynomial model was made in the real data analysis.

The generalized half-normal distribution is notable for its flexibility in modeling diverse hazard rate shapes, including ones that are monotonically increasing or decreasing, and bathtub forms, determined by the value of the shape parameter. To facilitate Bayesian comparative analyses of these shape parameters, we have proposed noninformative priors for the ratio of shape parameters within generalized half-normal distributions. We derived probability matching priors and reference priors, identifying a second-order matching prior that satisfies all specified matching criteria. Our findings show that both the two-group and three-group reference priors meet the first-order matching criterion, whereas Jeffreys' prior does not. However, the one-at-a-time reference prior successfully satisfies the stricter second-order matching criterion. Additionally, we established conditions ensuring posterior propriety under general priors, particularly highlighting the derived noninformative priors. A simulation study demonstrated that the one-at-a-time reference prior achieves accurate alignment with target frequentist coverage probabilities. Finally, we provided two real-world examples to illustrate and reinforce our theoretical results.