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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.

A hidden Markov model (HMM) is a useful tool for modeling dependent heterogeneous phenomena. It can be used to find factors that affect real-world events, even when those factors cannot be directly observed. HMMs differ from traditional methods by using state variables and mixture distributions to model the hidden states. This allows HMMs to find relationships between variables even when the variables cannot be directly observed. HMM can be extended, allowing the transition probabilities to depend on covariates. This makes HMMs more flexible and powerful, as they can be used to model a wider range of sequential data. Modeling covariates in a hidden Markov model is particularly difficult when the dimension of the state variable is large. To avoid these difficulties, Markovian properties are achieved by implanting the previous state variables to the logistic regression model. We apply the proposed method to find the factors that affect the hidden state of matsutake mushroom growth, in which it is hard to find covariates that directly affect matsutake mushroom growth in Korea. We believe that this method can be used to identify factors that are difficult to find using traditional methods.

Currently, more than 30% of the fine dust generated in the Seoul metropolitan area is a pollutant emitted from automobiles such as diesel vehicles, and air pollution caused by this is becoming increasingly serious. In addition, the importance of electric vehicle distribution is increasing due to the strengthening of international environmental regulations on automobile exhaust gas and increasing the possibility of depletion of petroleum resources. This manuscript proposes a method for selecting an optimal electric vehicle charging station location in expanding charging facilities to activate electric vehicle distribution. For the sake of illustration, directions will be provided on how to select the best location for electric vehicle charging stations using data from Seoul, which has the best access. As the features, the number of living population and work force people and the number of guest facilities, which are determined to affect demand for quick charging, are considered. The missing values of the observed data are imputed based on the kriging technique from spatial correlation, and by segmenting the data through clustering, a representative technique of unsupervised learning, the characteristics of each cluster are examined and the characteristics of the clusters are identified. In addition, machine learning techniques such as the elastic net, random forest, support vector machine, and extreme gradient boosting are applied to examine the influence of the features used in predicting classes of data. In clustering analysis, the optimal number of clusters was determined to be 3 based on the heuristic and information-theoretic methods, and all the machine learning techniques considered showed that the number of work force population is the most important feature in predicting classes of data. All things considered from our results, it is reasonable to install quick electric vehicle charging stations in the places with the highest concentration of work force population and guest facility.

In environmental studies, it is important to assess how regulatory standards for air pollutants affect public health. High ozone levels contribute to harmful air pollutants. The EPA regulates ozone levels by setting ozone standards to protect public health. It is thus crucial to assess how various regulatory ozone standards affect non-accidental mortality related to respiratory deaths during the ozone season. The original rollback approach provides an adjusted ozone process under a new regulation scenario in a deterministic fashion. Herein, we consider a statistical rollback approach to allow for uncertainty in the rollback procedure by adopting the quantile matching method so that it provides flexible rollback sets. Hierarchical Bayesian models are used to predict the potential effects of different ozone standards on human health. We apply the method to epidemiologic data.

Large quantities of air pollutants are released into the atmosphere and hence, must be monitored and routinely assessed for their health implications. This paper proposes a stochastic technique to predict unobserved hazardous air pollutants (HAPs), especially Benzo[a]pyrene (BaP), which can have negative effects on human health. The proposed approach constructs a nearest-neighbor structure by incorporating the linkage between BaP and meteorology and meteorological effects. This approach is adopted in order to predict unobserved BaP concentrations based on observed (or forecasted) meteorological conditions, including temperature, precipitation, wind speed, and air quality. The effects of BaP on human health are examined by characterizing the cancer risk. The efficient prediction provides useful information relating to the optimal monitoring period and projections of future BaP concentrations for both industrial and residential areas within Korea.

Recently, the area of sea ice is rapidly decreasing due to global warming, and since the Arctic sea ice has a great impact on climate change, interest in this is increasing very much all over the world. In fact, the area of sea ice reached a record low in September 2012 after satellite observations began in late 1979. In addition, in early 2018, the glacier on the northern coast of Greenland began to collapse. If we are interested in record values of sea ice area, modeling relationships of these values and predicting future record values can be a very important issue because the record values that consist of larger or smaller values than the preceding observations are very closely related to each other. The relationship between the record values can be modeled based on the pivotal quantity and canonical and drawable vine copulas, and the relationship is called a dependence structure. In addition, predictions for future record values can be solved in a very concise way based on the pivotal quantity. To accomplish that, this article proposes an approach to model the dependence structure between record values based on the canonical and drawable vine. To do this, unknown parameters of a probability distribution need to be estimated first, and the pivotal-based method is provided. In the pivotal-based estimation, a new algorithm to deal with a nuisance parameter is proposed. This method allows one to reduce computational complexity when constructing exact confidence intervals of functions with unknown parameters. This method not only reduces computational complexity when constructing exact confidence intervals of functions with unknown parameters, but is also very useful for obtaining the replicated data needed to model the dependence structure based on canonical and drawable vine. In addition, prediction methods for future record values are proposed with the pivotal quantity, and we compared them with a time series forecasting method in real data analysis. The validity of the proposed methods was examined through Monte Carlo simulations and analysis for Arctic sea ice data.

In models with nuisance parameters, Bayesian procedures based on Markov Chain Monte Carlo (MCMC) methods have been developed to approximate the posterior distribution of the parameter of interest. Because these procedures require burdensome computations related to the use of MCMC, approximation and convergence in these procedures are important issues. In this paper, we explore Gibbs sensitivity by using an alternative to the full conditional distribution of the nuisance parameter. The approximate sensitivity of the posterior distribution of interest is studied in terms of an information measure, including Kullback–Leibler divergence. As an illustration, we then apply these results to simple spatial model settings.

In many case-control genetic association studies, a secondary phenotype that may have common genetic factors with disease status can be identified. When information on the secondary phenotype is available only for the case group due to cost and different data sources, a fitting linear regression model ignoring supplementary phenotype data may provide limited knowledge regarding genetic association. We set up a joint model and use a Bayesian framework to estimate and test the effect of genetic covariates on disease status considering the secondary phenotype as an instrumental variable. The application of our proposed procedure is demonstrated through the rheumatoid arthritis data provided by the 16th Genetic Analysis Workshop.