Bayesian analysis for quantile smoothing spline

In Bayesian quantile smoothing spline[Thompson,P.,Cai,Y.,Moyeed,R.,Reeve,D.,&Stander,J.(2010).Bayesian nonparametric quantile regression using splines.Computational Statistics and Data Analysis,54,1138-1150.],a fixed-scale parameter in the asymmetric Laplace likelihood tends to result in misleading fitted curves.To solve this problem,we propose a new Bayesian quantile smoothing spline(NBQSS),which considers a random scale parameter.To begin with,we justify its objective prior options by establishing one sufficient and one necessary condition of the posterior propriety under two classes of general priors including the invariant prior for the scale component.We then develop partially collapsed Gibbs sampling to facilitate the compu-tation.Out of a practical concern,we extend the theoretical results to NBQSS with unobserved knots.Finally,simulation studies and two real data analyses reveal three main findings.Firstly,NBQSS usually outperforms other competing curve fitting methods.Secondly,NBQSS consid-ering unobserved knots behaves better than the NBQSS without unobserved knots in terms of estimation accuracy and precision.Thirdly,NBQSS is robust to possible outliers and could provide accurate estimation.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

Mapping Near-surface Air Temperature, Pressure, Relative Humidity and Wind Speed over China's Mainland with High Spatiotemporal Resolution

As part of a joint effort to construct an atmospheric forcing dataset for China's Mainland with high spatiotemporal reso- lution, a new approach is proposed to construct gridded near-surface temperature, relative humidity, wind speed and surface pressure with a resolution of 1 km× 1 km. The approach comprises two steps： （1） fit a partial thin-plate smoothing spline with orography and reanalysis data as explanatory variables to ground-based observations for estimating a trend surface; （2） apply a simple kriging procedure to the residual for trend surface correction. The proposed approach is applied to observations collected at approximately 700 stations over China's Mainland. The generated forcing fields are compared with the corresponding components of the National Centers for Environmental Predic- tion （NCEP） Climate Forecast System Reanalysis dataset and the Princeton meteorological forcing dataset. The comparison shows that, both within the station network and within the resolutions of the two gridded datasets, the interpolation errors of the proposed approach are markedly smaller than the two gridded datasets.

A Spatial-Nonparametric Approach for Prediction of Claim Frequency in Motor Insurance

Spatial modeling has largely been applied in epidemiology and disease modeling. Different methods such as Generalized linear models (GLMs) have been made available to prediction of the claim frequencies. However, due to heterogeneity nature of policies, the methods do not generate precise and accurate claim frequencies predictions;these parametric statistical methods extensively depend on limiting assumptions (linearity, normality, independence among predictor variables, and a pre-existing functional form relating the criterion variable and predictive variables). This study investigates how to derive a spatial nonparametric model estimator based on smoothing Spline for predicting claim frequencies. The simulation results showed that the proposed estimator is efficient for prediction of claim frequencies than the kernel based counterpart. The estimator derived was applied to a sample of 6500 observations obtained from Cooperative Insurance Company, Kenya for the period of 2018-2020 and the results showed that the proposed method performs better than the kernel based counterpart. It is worth noting that inclusion of the spatial effects significantly improves the estimator prediction of claim frequency.

Spatiotemporal variation in forest fire danger from 1996 to 2010 in Jilin Province,China

We evaluated the spatial and temporal patterns of forest fires in two fire seasons (March to June and September to November) from 1996 to 2010 in Jilin Province, China, using the Canadian Forest Fire Weather Index System. Fire data were obtained from the Provincial Fire Agency, and historical climate records of daily weather observations were collected from 36 weather stations in Jilin and its neighboring provinces. A linear regression model was used to analyze linear trends between climate and fire weather indices with time treated as an independent variable. Correlation analysis was used to detect correlations between fire frequency, areas burned, and fire weather indices. A thin-plate smooth spline model was used to interpolate the point data of 36 weather stations to generate a surface covering the whole province. Our analyses indicated fire frequency and areas burned were significantly correlated with fire weather indices. Overall, the Canadian Forest Fire Weather Index System appeared to be work well for determining the fire danger rating in Jilin Province. Also, our analyses indicated that in the forthcoming decades, the overall fire danger in March and April should decrease across the province, but the chance of a large fire in these months would increase. The fire danger in the fall fire season would increase in the future, and the chance of large fire would also increase. Historically, because most fires have occurred in the spring in Jilin Province, such a shift in the future fire danger between the two fire seasons would be beneficial for the province's fire management.

Posterior propriety in nonparametric mixed efects model

It is well known that spline smoothing estimator relates to the Bayesian estimate under partially informative normal prior. In this paper, we derive the conditions for the pro- priety of the posterior in the nonparametric mixed effects model under this class of partially informative normal prior for fixed effect with inverse gamma priors on the variance compo- nents and hierarchical priors for covariance matrix of random effect, then we explore the Gibbs sampling procedure.

On Convergence of Singular integral Operators With Respect to Path of Integration

Given f being Holder continuous in a region GC. For the Cauchy principal integral where G is a smooth closed contour,lt is established that,if a sequence or smooth closed contours G(n ∈N ) smoothly convergent top,then the corresponding sequence I(Γm,f)is convergent to I (,f). Furthermore,when Γ is approximated by a sequence of complex cubic splines(Γ)interpolatory to Γ,the error is estimated.

A new scheme of climate-vegetation regionalization in the Hengduan Mountains Region

The Hengduan Mountains Region(HMR) is essential for the future ecological protection, clean energy production,Sichuan-Xizang and Yunnan-Xizang railways, and other major infrastructure projects in China. The distributions of climate and vegetation exhibit significant regional differentiation and vertical zonality due to the rugged longitudinal ranges and gorges and the complex disaster-prone environments in HMR. Therefore, it is urgent to develop the climate-vegetation regionalization in HMR to effectively satisfy the national requirements such as agricultural production and ecological protection, mountain disaster risk prevention, and major project construction. We here develop a new scheme of climate-vegetation regionalization with the latest demarcation outcome of HMR, the ground observation from 122 meteorological stations in HMR and its surrounding areas during 1990–2019, and the high-precision remote sensing data of land cover types. The new scheme first constructs the regionalization index system, fully considering the extraordinarily complicated geomorphic pattern of mountains and valleys, the scarcity of meteorological observations, and the remarkable differentiation of climate and vegetation in HMR. The system consists of three primary regionalization indices(i.e., days with daily average temperature steady above 10°C, aridity index, and main vegetation types, dividing the temperature zones, moisture regions, and vegetation subregions, respectively) and three auxiliary indices of the accumulated temperature above 10°C, and the temperatures in January and July. Then, the HMR is divided into five temperature zones, 20 moisture regions, and 55 vegetation subregions. Compared with previous regionalization schemes, the new scheme optimizes the climate spatial interpolation model of thin plate smoothing spline suitable for the unique terrain in HMR. Moreover, the disputed division index threshold between different climatic zones(regions) is scientifically clarified using geographical detectors. Specifically, the stepwise downscaling pane division method is initially proposed to determine the zoning boundary, alleviating the excessive dependence of the traditional zoning method on subjective experience.Besides, the scheme considers the typical regional characteristics of the complex underlying surface and the high gradient zone of climate-vegetation distribution types in HMR. Consequently, the transition zone with quick climate changes between the plateau temperate and mid-subtropical zones is divided into mountainous subtropics, taking into account the spatial distribution characteristics of climate-vegetation regionalization indices. The regionalization scheme will provide practically theoretical support for agricultural production, ecological protection, major project construction, disaster prevention and relief efforts, and other socioeconomic activities in HMR, serving as a classic case of climate-vegetation regionalization for the alpine and canyon regions with intricate underlying surface, striking regional differences, and lack of ground observations.