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Prediction variables of the regression model are grouped in many application problems. For example, a factor in an analysis of variance can have several levels or each original prediction variable in additive models can be expanded into different order polynomials or a set of basis functions. It is essential to select important groups and individual variables within the selected groups. In this study, we propose the objective Bayesian group and individual variable selections within the selected groups in the regression model to reduce the computational cost, even though the number of regression variables is large. Besides, we examine the consistency of the proposed group variable selection procedure. The proposed objective Bayesian approach is investigated using simulation and real data examples. The comparisons between the penalized regression approaches, Bayesian group lasso and the proposed method are presented.

In this paper, we consider some objective priors for the ratio of variabilities in a bivariate normal distribution. We develop the first and second order matching priors and reference priors. We obtain that the second order matching prior matches the alternative coverage probabilities up to the same order. It is also an HPD matching priors. It turns out that the derived reference priors do not satisfy a second order matching criterion. The simulation result shows that the second order matching prior performs better than reference priors based on matching the target coverage probabilities in a frequentist sense. Finally, we show that the second order matching prior and reference priors produce confidence sets with an expected length shorter than the Cox and Reid adjustment.

This study considers the problem of multiple change-points detection. For this problem, we develop an objective Bayesian multiple change-points detection procedure in a normal model with heterogeneous variances. Our Bayesian procedure is based on a combination of binary segmentation and the idea of the screening and ranking algorithm (Niu and Zhang in Ann Appl Stat 6:1306–1326, 2012). Using the screening and ranking algorithm, we can overcome the drawbacks of binary segmentation, as it cannot detect a small segment of structural change in the middle of a large segment or segments of structural changes with small jump magnitude. We propose a detection procedure based on a Bayesian model selection procedure to address this problem in which no subjective input is considered. We construct intrinsic priors for which the Bayes factors and model selection probabilities are well defined. We find that for large sample sizes, our method based on Bayes factors with intrinsic priors is consistent. Moreover, we compare the behavior of the proposed multiple change-points detection procedure with existing methods through a simulation study and two real data examples.

In this work, we suggest new spatial precipitation interpolation schemes using compressed sensing (CS), which is a new framework for signal acquisition and smart sensor design. Using CS, the precipitation maps are recovered in high resolution by obtaining sparse coefficients of radial basis functions(RBFs). Two types of methods are designed according to the construction methods of CS matrix. In the first type, the CS matrix is derived as the product of an m × n (n ≫ m) weights matrix of inverse distance weighting (IDW) and an n × n radial basis function (RBF) matrix. The second type of CS matrix consists of an m × n RBF matrix that depends on a few observation vectors and a number of n unknown vectors. The advantage of the proposed CS methods is that it can be represented at a high resolution because it is interpolated based on a large number of bases (or degrees of freedom). This prevents the variance value from being much smaller than the actual value due to interpolation using a few observation scales. To test our CS interpolation schemes, interpolation results were compared with IDW, Ordinary Kriging (OK) and RBF interpolation methods for analytic test function and some actual rainfall data. In the case of an analytic test function, when the proposed method is compared at high resolution, the error from the true value is the smallest. In real rainfall data, comparison with real values is not possible at high resolutions, but the error with the observed data is the smallest in terms of ‘spatial variogram’. In addition, the proposed CS method generates hight resolution data from rainfall cases, showing promising results when identifying peaks.

New technologies for the classification of convective cloud lifecycles and the prediction of their movements are needed to detect severe convective weather and to support objective cloud guidance. Satellites enable earlier detection of severe weather over larger coverage areas than ground-based observations or radar. The use of satellite observations for nowcasting is thus likely. In this study, convective initiation (CI) data are paired with a modified rapid-development thunderstorm (RDT) algorithm for the analysis of new data from the Geostationary Korea Multi-Purpose Satellite-2A (GEO-KOMPSAT-2A, GK2A). The RDT algorithm is further modified to accommodate the additional GK2A satellite channels, and new satellite data are used to continuously analyze thunderstorms associated with severe weather in Korea. The logistic regression (LR) machine learning approach is used to optimize the criteria of interest fields and weighting coefficients of the RDT algorithm for convective detection. In addition, auxiliary data (cloud type, convective rainfall rate, and cloud top temperature/height) calculated from RDT sub-module is replaced with GK2A derived products. The fully modified RDT algorithm (K-RDT) is quantitatively verified using lightning data from summer convection cases. The probability of detection (POD) for convective clouds is increased by 30–40%, and the threat score (TS) for average lightning activity is improved by 10–30%. The channel properties of Japan Himawari-8 satellite are similar to those of the GK2A satellite. Due to the lack of GK2A satellite data during the development period, CI data from the Himawari-8 satellite are used as proxies.

Matching priors in principle provide a possible compromise between frequentist and Bayesian and default priors for routine use in Bayesian inference in that posterior probability of the parameter also provides an interpretation as confidence statements. Here we introduce a matching prior for the ratio of two log-normal means which is nontrivial because the derivation of matching prior requires the elicitation of a suitable orthogonal parameterization on the nuisance parameters and the computation of the marginal posterior distribution requires multidimensional integration over the nuisance parameter. Numerical integrations and approximation techniques could be used but they are difficult to use in general. Thus, we derive a matching prior based on a modification of the profile likelihood to avoid the elicitation of priors for the entire parameter and integration on the nuisance parameter. The proposed method is illustrated by real data examples and simulation studies under several configurations.

This study introduces a modified hybrid gamma and generalized Pareto distribution. Prior to this, we define a general spliced distribution and its corresponding gamma distribution, which is part of the head, and a generalized Pareto (GP) distribution, which is part of the tail. We then examine the threshold conditions for the modified hybrid gamma and GP distribution and defined probability density function. Also, we derive the negative log-likelihood function of the modified hybrid gamma and GP distribution and estimate approximate maximum likelihood estimates using the differential evolution algorithm for each simulation to minimize it. Moreover, by presenting the mean square error for each sample size, the model is evaluated according to the size of the sample. Finally, we use daily observed summer precipitation for Seoul, Korea, from 1961 to 2011, which includes 4692 data sets. We use 2051 data sets corresponding to wet conditions. As a result, the estimated threshold of the modified hybrid gamma and GP distribution is 0.1455. After deriving Fisher information through the Hessian matrix, we also present the standard error of the maximum likelihood estimator.

For normal populations with unequal variances, we develop matching priors and reference priors for a linear combination of the means. Here, we find three second-order matching priors: a highest posterior density (HPD) matching prior, a cumulative distribution function (CDF) matching prior, and a likelihood ratio (LR) matching prior. Furthermore, we show that the reference priors are all first-order matching priors, but that they do not satisfy the second-order matching criterion that establishes the symmetry and the unimodality of the posterior under the developed priors. The results of a simulation indicate that the second-order matching prior outperforms the reference priors in terms of matching the target coverage probabilities, in a frequentist sense. Finally, we compare the Bayesian credible intervals based on the developed priors with the confidence intervals derived from real data.

From a statistical perspective, the Fieller–Creasy problem which involves inference about the ratio of two normal means has been quite challenging. In this study, we consider some solutions to this problem, based on an objective Bayesian model selection procedure. First, we develop the objective priors for testing the ratio of two normal means, based on measures of divergence between competing models. We then propose the intrinsic priors and the fractional priors for which the Bayes factors and model selection probabilities are well defined. In addition, we prove that the Bayes factors based on divergence-based priors, as well as intrinsic and fractional priors, are consistent for large sample sizes. Finally, we derive the Bayesian reference criterion from the Bayesian decision theory framework, based on the intrinsic discrepancy loss function. The behaviors of the Bayes factors are compared by undertaking a simulation study and using a case study example.

In this paper, we develop a matching prior for the common mean in several log-normal distributions. For this problem, assigning priors appropriately for the common log-normal mean is challenging owing to the presence of nuisance parameters. Matching priors, which are priors that match the posterior probabilities of certain regions within their frequentist coverage probabilities, are commonly used in this problem. However, a closed form posterior under the derived first order matching prior is not available; further, the second order matching prior is difficult to be derived in this problem. Thus, alternatively, we derive a matching prior based on a modification of the profile likelihood. Simulation studies show that this proposed prior meets the target coverage probabilities very well even for small sample sizes. Finally, we present a real example.

Time series of daily weather such as precipitation, minimum temperature and maximum temperature are commonly required for various fields. Stochastic weather generators constitute one of the techniques to produce synthetic daily weather. The recently introduced approach for stochastic weather generators is based on generalized linear modeling (GLM) with covariates to account for seasonality and teleconnections (e.g., with the El Nino). In general, stochastic weather generators tend to underestimate the observed interannual variance of seasonally aggregated variables. To reduce this overdispersion, we incorporated time series of seasonal dry/wet indicators in the GLM weather generator as covariates. These seasonal time series were local (or global) decodings obtained by a hidden Markov model of seasonal total precipitation and implemented in the weather generator. The proposed method is applied to time series of daily weather from Seoul, Korea and Pergamino, Argentina. This method provides a straightforward translation of the uncertainty of the seasonal forecast to the corresponding conditional daily weather statistics.

This paper considers the problem of testing on the common mean of several normal distributions. We propose a solution based on a Bayesian model selection procedure in which no subjective input is considered. We construct the proper priors for testing hypotheses about the common mean based on measures of divergence between competing models. This method is called the divergence-based priors (Bayarri and Garcia-Donato in J R Stat Soc B 70:981---1003, 2008). The behavior of the Bayes factors based DB priors is compared with the fractional Bayes factor in a simulation study and compared with the existing tests in two real examples.

This study considers objective Bayesian testing for the linear combinations of the means of several normal populations. We propose solutions based on a Bayesian model selection procedure to this problem in which no subjective input is considered. We first construct suitable priors to test the linear combinations of means based on measuring the divergence between competing models (so-called divergence-based priors). Next, we derive the intrinsic priors for which the Bayes factors and model selection probabilities are well defined. Finally, the behavior of the Bayes factors based on the DB priors, intrinsic priors, and classical test are compared in a simulation study and an example.

In this study, we address inference problems for Gumbel distribution when the available data are lower record values. We first derive unbiased estimators of unknown parameters, and then, we construct an exact confidence interval for the scale parameter and a predictive interval for the next lower value by deriving certain properties and pivotal quantities. These are compared with the results for existing inference. For Bayesian inference, we derive noninformative priors such as the Jeffreys and reference priors for unknown parameters and examine whether they satisfy the probability matching criteria; then, we apply them to develop objective Bayesian analysis.

Even under assumption of normality, likelihood-based inferences are often difficult for large and irregularly spaced spatial datasets. Exact calculations of the likelihood for a Gaussian spatial process observed in n locations require O ( n 3 ) operations. Instead of Whittle’s approximation to the Gaussian log likelihood for large spatial datasets, this paper introduces an approximated likelihood function of spatial parameters based on the correlogram, which involves no calculation of determinants and is computationally feasible. The proposed likelihood approximation method for spatial parameter is applied to the estimation of the spatial structure of changes in the average summer temperature based on 30 years of data by using an regional climate model (RCM) with a particular global climate model (GCM) boundary condition. The results verify the benefits and the performance of the proposed method.

Statistical downscaling is based on the fact that the large-scale climatic state and regional/local physiographic features control the regional climate. In the present paper, a stochastic weather generator is applied to seasonal precipitation and temperature forecasts produced by the International Research Institute for Climate and Society (IRI). In conjunction with the GLM (generalized linear modeling) weather generator, a resampling scheme is used to translate the uncertainty in the seasonal forecasts (the IRI format only specifies probabilities for three categories: below normal, near normal, and above normal) into the corresponding uncertainty for the daily weather statistics. The method is able to generate potentially useful shifts in the probability distributions of seasonally aggregated precipitation and minimum and maximum temperature, as well as more meaningful daily weather statistics for crop yields, such as the number of dry days and the amount of precipitation on wet days. The approach is extended to the case of climate change scenarios, treating a hypothetical return to a previously observed drier regime in the Pampas.

The Weibull distribution is widely used in survival analysis, reliability engineering, and failure analysis. In this paper, we develop noninformative priors such as probability matching priors for the common shape parameter of Weibull models using the asymptotic matching of coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. Here, various matching criteria, such as quantile matching, matching of distribution function, highest posterior density matching, and matching via inversion of test statistics, are considered. Next, we derive the reference priors for groups of ordering. It also shows that most reference priors do not satisfy the first order matching criterion, but the one-at-a-time reference prior is the second order matching priors. A simulation study is performed and a real example is given.

In Bayesian statistics, a model can be assessed by checking that the model fits the data, which is addressed by using the posterior predictive distribution for a discrepancy, an extension of classical test statistics to allow dependence on unknown (nuisance) parameters. Posterior predictive assessment of model fitness allows more direct assessment of the discrepancy between data and the posited model. The sensitivity analysis revealed that the effect of priors on parameter inferences is different from their effect on marginal density and predictive posterior distribution. In this paper, we explore the effect of the prior (or posterior) distribution on the corresponding posterior predictive distribution. The approximate sensitivity of the posterior predictive distribution is studied in terms of information measure including the Kullback–Leibler divergence. As an illustration, we applied these results to the simple spatial model settings.

The diffusion process is a widely used statistical model for many natural dynamic phenomena but its inference is very complicated because complete data describing the diffusion sample path is not necessarily available. In addition, data is often collected with substantial uncertainty and it is not uncommon to have missing observations. Thus, the observed process will be discrete over a finite time period and the marginal likelihood given by this discrete data is not always available. In this paper, we consider a class of nonstationary diffusion process models with not only the measurement error but also discretely time-varying parameters which are modeled via a state space model. Hierarchical Bayesian inference for such a diffusion process model with time-varying parameters is applied to financial data.

Studies of the behaviors of glaciers, ice sheets, and ice streams rely heavily on both observations and physical models. Data acquired via remote sensing provide critical information on geometry and movement of ice over large sections of Antarctica and Greenland. However, uncertainties are present in both the observations and the models. Hence, there is a need for combining these information sources in a fashion that incorporates uncertainty and quantifies its impact on conclusions. We present a hierarchical Bayesian approach to modeling ice-stream velocities incorporating physical models and observations regarding velocity, ice thickness, and surface elevation from the North East Ice Stream in Greenland. The Bayesian model leads to interesting issues in model assessment and computation.