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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.

In radiation epidemiology, the excess relative risk (ERR) model is used to determine the dose–response relationship. In general, the dose-response relationship for the ERR model is assumed to be linear, linear-quadratic, linear-threshold, quadratic, and so on. However, since none of these functions dominate other functions for expressing the dose-response relationship, a Bayesian semiparametric method using splines has recently been proposed. Thus, we improve the Bayesian semiparametric method for the selection of the tuning parameters for splines as the number and location of knots using a Bayesian knot selection method. Equally spaced knots cannot capture the characteristic of radiation exposed dose distribution which is highly skewed in general. Therefore, we propose a nonparametric Bayesian knot selection method based on a Dirichlet process mixture model. Inference of the spline coefficients after obtaining the number and location of knots is performed in the Bayesian framework. We apply this approach to the life span study cohort data from the radiation effects research foundation in Japan, and the results illustrate that the proposed method provides competitive curve estimates for the dose-response curve and relatively stable credible intervals for the curve. [ABSTRACT FROM AUTHOR]

The Bayesian approach is a suitable alternative in constructing appropriate models for observed record values because the number of these values is small. This paper provides an objective Bayesian analysis method for upper record values arising from the Rayleigh distribution. For the objective Bayesian analysis, the Fisher information matrix for unknown parameters is derived in terms of the second derivative of the log-likelihood function by using Leibniz's rule; subsequently, objective priors are provided, resulting in proper posterior distributions. We examine if these priors are the PMPs. In a simulation study, inference results under the provided priors are compared through Monte Carlo simulations. Through real data analysis, we reveal a limitation of the appropriate confidence interval based on the maximum likelihood estimator for the scale parameter and evaluate the models under the provided priors. [ABSTRACT FROM AUTHOR]

In this paper, we provide an entropy inference method that is based on an objective Bayesian approach for upper record values having a two-parameter logistic distribution. We derive the entropy that is based on the i-th upper record value and the joint entropy that is based on the upper record values. Moreover, we examine their properties. For objective Bayesian analysis, we obtain objective priors, namely, the Jeffreys and reference priors, for the unknown parameters of the logistic distribution. The priors are based on upper record values. Then, we develop an entropy inference method that is based on these objective priors. In real data analysis, we assess the quality of the proposed models under the objective priors and compare them with the model under the informative prior. [ABSTRACT FROM AUTHOR]

This paper considers the multiple comparisons problem for normal variances. We propose a solution based on a Bayesian model selection procedure to this problem in which no subjective input is considered. We construct the intrinsic and fractional priors for which the Bayes factors and model selection probabilities are well defined. The posterior probability of each model is used as a model selection tool. The behaviour of these Bayes factors is compared with the Bayesian information criterion of Schwarz and some frequentist tests. [ABSTRACT FROM AUTHOR]

This manuscript summarized advances in bootstrap methods for long-range dependent time series data. The stationary linear long-memory process is briefly described, which is a target process for bootstrap methodologies on time-domain and frequency-domain in this review. We illustrate time-domain bootstrap under long-range dependence, moving or non-overlapping block bootstraps, and the autoregressive-sieve bootstrap. In particular, block bootstrap methodologies need an adjustment factor for the distribution estimation of the sample mean in contrast to applications to weak dependent time processes. However, the autoregressive-sieve bootstrap does not need any other modification for application to long-memory. The frequency domain bootstrap for Whittle estimation is provided using parametric spectral density estimates because there is no current nonparametric spectral density estimation method using a kernel function for the linear long-range dependent time process. [ABSTRACT FROM AUTHOR]

The authors develop statistical data models to combine ensembles from multiple climate models in a fashion that accounts for uncertainty. This formulation enables treatment of model specific means, biases, and covariance matrices of the ensembles. In addition, the authors model the uncertainty in using computer model results to estimate true states of nature. Based on these models and principles of decision making in the presence of uncertainty, this paper poses the problem of superensemble experimental design in a quantitative fashion. Simple examples of the resulting optimal designs are presented. The authors also provide a Bayesian climate modeling and forecasting analysis. The climate variables of interest are Northern and Southern Hemispheric monthly averaged surface temperatures. A Bayesian hierarchical model for these quantities is constructed, including time-varying parameters that are modeled as random variables with distributions depending in part on atmospheric CO2 levels. This allows the authors to do Bayesian forecasting of temperatures under different Special Report on Emissions Scenarios (SRES). These forecasts are based on Bayesian posterior distributions of the unknowns conditional on observational data for 1882–2001 and climate system model output for 2002–97. The latter dataset is a small superensemble from the Parallel Climate Model (PCM) and the Community Climate System Model (CCSM). After summarizing the results, the paper concludes with discussion of potential generalizations of the authors’ strategies. [ABSTRACT FROM AUTHOR]