一种改进的图像压缩感知稀疏恢复算法

稀疏信号的分布模型是影响基于近似信息传递（AMP）的压缩感知(CS)信号重建效果的关键因素。因实际图像的小波近似系数、各级的水平细节系数、垂直细节系数以及对角细节系数的模型参数存在较大差异,现有基于拉普拉斯、贝努力高斯(BG)和高斯混合等模型的AMP方法因未考虑此差异而影响重建效果。为了提高模型估计的准确性,将各级小波系数的BG模型参数分开估计,进而提出了一种改进的图像压缩感知稀疏重建的新方法,即期望最大分段贝努力高斯近似信息传递算法（EM-SSBG-AMP）。仿真结果表明,相同采样率下,新算法的峰值信噪比（PSNR）明显高于5阶期望最大高斯混合近似信息传递算法(EM-GM-AMP),重建时间与5阶EM-GM-AMP相当。     

基于GPR模型的中国“十三五”时期碳排放趋势预测

系统分析了中国CO2排放的影响因素,在此基础上建立了基于高斯过程回归的CO2排放预测模型,运用历史数据进行模型精度检验,并与传统的GM(1,1)模型、人工神经网络和支持向量机的预测结果比较。结合情景设计,预测了中国"十三五"时期的CO2排放量和CO2排放强度。结果表明:高斯过程回归模型具有显著的精度优势,中国能达到2020年CO2排放强度较2005年下降40%~45%的减排目标。指出:对于CO2减排,应结合各地区的实际情况灵活处理,以调整产业结构、优化能源结构、推动技术创新为重点,不可片面牺牲经济发展。     

Estimating stochastic volatility models using integrated nested Laplace approximations

Volatility in financial time series is mainly analysed through two classes of models; the generalized autoregressive conditional heteroscedasticity (GARCH) models and the stochastic volatility (SV) ones. GARCH models are straightforward to estimate using maximum-likelihood techniques, while SV models require more complex inferential and computational tools, such as Markov Chain Monte Carlo (MCMC). Hence, although provided with a series of theoretical advantages, SV models are in practice much less popular than GARCH ones. In this paper, we solve the problem of inference for some SV models by applying a new inferential tool, integrated nested Laplace approximations (INLAs). INLA substitutes MCMC simulations with accurate deterministic approximations, making a full Bayesian analysis of many kinds of SV models extremely fast and accurate. Our hope is that the use of INLA will help SV models to become more appealing to the financial industry, where, due to their complexity, they are rarely used in practice.     

规则RA码在混合信道上的高斯估计

将高斯估计方法运用到规则重复累积（RA）码在具有加性白色高斯噪声和删除干扰的混合信道上的性能分析中．导出了RA码在该信道上概率密度进化的递归等式和误码率的解析表达式。仿真结果验证了解析结果的正确性。因此解析结果可以直接用来预测RA码在混合信道上的性能。     

A Class of Gaussian Hybrid Processes for Modeling Financial Markets

This paper proposes a one-factor model of financial markets using a class of Gaussian process that can be decomposed into a Brownian motion and an Ornstein–Uhlenbeck process. It is shown that this “hybrid” process is obtained as a continuous-time scaling limit of the differenced first-order autoregressive integrated moving average (ARIMA(1,1,1)) process. Parameter estimations using an ARIMA(1,1,1) framework and its variance ratio test show the accuracy of the proposed model. Construction of the one-factor commodity futures price model is presented as an application. A multidimensional extension of the hybrid process is also presented in the Appendix.     

The History of the Dirichlet and Liouville Distributions

The Dirichlet distributions have long been the subject of intense scrutiny in statistics and probability. Despite the enormous interest in, and wide-ranging applications of, these distributions, little appears to be known about their history. In this article we review the development of the Dirichlet distributions and their companions, the Liouville distributions. After reviewing some integral formulas of Dirichlet and Liouville, we survey the theory and applications of these distributions in statistics.     

On Pooling of Data and Its Relative Efficiency

Pooling of data is often carried out to protect privacy or to save cost, with the claimed advantage that it does not lead to much loss of efficiency. We argue that this does not give the complete picture as the estimation of different parameters is affected to different degrees by pooling. We establish a ladder of efficiency loss for estimating the mean, variance, skewness and kurtosis, and more generally multivariate joint cumulants, in powers of the pool size. The asymptotic efficiency of the pooled data non‐parametric/parametric maximum likelihood estimator relative to the corresponding unpooled data estimator is reduced by a factor equal to the pool size whenever the order of the cumulant to be estimated is increased by one. The implications of this result are demonstrated in case–control genetic association studies with interactions between genes. Our findings provide a guideline for the discriminate use of data pooling in practice and the assessment of its relative efficiency. As exact maximum likelihood estimates are difficult to obtain if the pool size is large, we address briefly how to obtain computationally efficient estimates from pooled data and suggest Gaussian estimation and non‐parametric maximum likelihood as two feasible methods.     

A New Approach for Using Lévy Processes for Determining High-Frequency Value-at-Risk Predictions

A new approach for using Lévy processes to compute value-at-risk (VaR) using high-frequency data is presented in this paper. The approach is a parametric model using an ARMA(1,1)-GARCH(1,1) model where the tail events are modelled using fractional Lévy stable noise and Lévy stable distribution. Using high-frequency data for the German DAX Index, the VaR estimates from this approach are compared to those of a standard nonparametric estimation method that captures the empirical distribution function, and with models where tail events are modelled using Gaussian distribution and fractional Gaussian noise. The results suggest that the proposed parametric approach yields superior predictive performance.     

Marginal consistent dependence modelling using weak subordination for Brownian motions

We present an approach for modelling dependencies in exponential Lévy market models with arbitrary margins originated from time changed Brownian motions. Using weak subordination of Buchmann et al. [Bernoulli, 2017], we face a new layer of dependencies, superior to traditional approaches based on pathwise subordination, since weakly subordinated processes are not required to have independent components considering multivariate stochastic time changes. We apply a subordinator being able to incorporate any joint or idiosyncratic information arrivals. We emphasize multivariate variance gamma and normal inverse Gaussian processes and state explicit formulae for the Lévy characteristics. Using maximum likelihood, we estimate multivariate variance gamma models on various market data and show that these models are highly preferable to traditional approaches. Consistent values of basket-options under given marginal pricing models are achieved using the Esscher transform, generating a non-flat implied correlation surface.