Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs

We study a Bayesian approach to nonparametric estimation of the periodic drift function of a one-dimensional diffusion from continuous-time data. Rewriting the likelihood in terms of local time of the process, and specifying a Gaussian prior with precision operator of differential form, we show that the posterior is also Gaussian with the precision operator also of differential form. The resulting expressions are explicit and lead to algorithms which are readily implementable. Using new functional limit theorems for the local time of diffusions on the circle, we bound the rate at which the posterior contracts around the true drift function.     

On the Convergence of Successive Substitution Sampling

Abstract

The problem of finding marginal distributions of multidimensional random quantities has many applications in probability and statistics. Many of the solutions currently in use are very computationally intensive. For example, in a Bayesian inference problem with a hierarchical prior distribution, one is often driven to multidimensional numerical integration to obtain marginal posterior distributions of the model parameters of interest. Recently, however, a group of Monte Carlo integration techniques that fall under the general banner of successive substitution sampling (SSS) have proven to be powerful tools for obtaining approximate answers in a very wide variety of Bayesian modeling situations. Answers may also be obtained at low cost, both in terms of computer power and user sophistication. Important special cases of SSS include the “Gibbs sampler” described by Gelfand and Smith and the “IP algorithm” described by Tanner and Wong. The major problem plaguing users of SSS is the difficulty in ascertaining when “convergence” of the algorithm has been obtained. This problem is compounded by the fact that what is produced by the sampler is not the functional form of the desired marginal posterior distribution, but a random sample from this distribution. This article gives a general proof of the convergence of SSS and the sufficient conditions for both strong and weak convergence, as well as a convergence rate. We explore the connection between higher-order eigenfunctions of the transition operator and accelerated convergence via good initial distributions. We also provide asymptotic results for the sampling component of the error in estimating the distributions of interest. Finally, we give two detailed examples from familiar exponential family settings to illustrate the theory.     

Regulation of Content of Malondialdehyde by Siqi Decoction via Increasing Activity of Superoxide Dismutase in Blood Serum of Rats with Myocardial Ischemia

Effect of Siqi decoction on myocardial ischemia is to prevent cardiac myocyte membrane from damage associated with oxygen free radicals related to NO. To research the regulatoin of the content of malondialdehyde by Siqi decoction, an index of lipid peroxidation, via increasing activity of superoxide dismutase in blood serum of rats with Myocardial Ischemia, the model of myocardium ischemia was made in Wistar rats with posterior pituitary injection through vein in tail. Siqi decoction, Diaoxinxuekang(DK) and...     

三段直线回归模型的贝叶斯分析

对于三段直线回归模型，本文利用贝叶斯观点，给出了转换点和参数的边沿后验分布，参数的条件后验分布和它的点估计     

基于Gibbs抽样算法的贝叶斯动态面板数据模型分析

针对现有动态面板数据分析中存在偶发参数和没有考虑模型参数的不确定性风险问题,提出了基于Gibbs抽样算法的贝叶斯随机系数动态面板数据模型.假设初始值服从平稳分布,自回归系数服从Logit正态分布的条件下,设计了Markov链Monte Carlo数值计算程序,得到了模型参数的贝叶斯估计值.实证研究结果表明:基于Gibb...     

Nanostructured lipid carriers for triamcinolone acetonide delivery to the posterior segment of the eye

Triamcinolone acetonide (TA) is a corticosteroid drug currently administered by intravitreal injection for a broad spectrum of inflammatory, edematous and angiogenic ocular diseases. To increase the drug's bioavailability by ocular instillation, TA was encapsulated in nanostructured lipid carriers (NLC), previously optimized by our group using a factorial design approach. In the present paper, nanometric (∼200 nm), unimodal and negatively charged NLC loaded with the fluorescent lipid marker Nile red (NR-NLC) and drug (TA-NLC) were produced by high pressure homogenization. Based on the selected formulations, in vivo tests were carried out by eye-drop instillation of NR-NLC in mice, revealing the systems’ ability of delivering lipophilic actives to the posterior segment of the eye via the corneal and non-corneal pathways. Short and long-term stability of TA-NLC was assessed by high performance stability analysis using the Turbiscan^®. The results showed a backscattering of less than 1.5% and during a period of 6 months, anticipated the low tendency of these particles for aggregation during shelf life when stored at room temperature.     

Bayesian Inference with Wavelets: Density Estimation

Abstract

We propose a prior probability model in the wavelet coefficient space. The proposed model implements wavelet coefficient thresholding by full posterior inference in a coherent probability model. We introduce a prior probability model with mixture priors for the wavelet coefficients. The prior includes a positive prior probability mass at zero which leads to a posteriori thresholding and generally to a posteriori shrinkage on the coefficients. We discuss an efficient posterior simulation scheme to implement inference in the proposed model. The discussion is focused on the density estimation problem. However, the introduced prior probability model on the wavelet coefficient space and the Markov chain Monte Carlo scheme are general.     

基于Tikhonov正则参量后验选择策略的PCS颗粒粒度反演方法

采用基于Morozov偏差原理的后验策略来选择最优正则参量,并采用此方法对单峰和多峰分布颗粒系的模拟电场自相关函数进行了反演,结果表明,对于单峰颗粒体系,当电场自相关函数的扰动误差小于0.05时,反演得到的峰值准确,当电场自相关函数的扰动误差大于0.05时,反演得到的峰值偏离所模拟的颗粒粒径.正则参量初始值在0.000 02～2范围内,在反演所得的峰值准确的基础上,正则参量初始值越小,反演得到的分布宽度越窄.收敛误差在0.000 05～50范围内,在保持反演结果稳定的基础上,收敛误差取值越大,反演得到的分布宽度越窄.对于多峰颗粒体系,当颗粒系中的颗粒粒径差别较小时,峰值向平均值偏移,当颗粒系中的颗粒粒径差别较大时,小颗粒粒径分布以噪音的形式出现.     

Range of the posterior probability of an interval for priors with unimodality preserving contaminations

Range of the posterior probability of an interval over the -contamination class ={=(1–)₀+q:qQ} is derived. Here, ₀ is the elicited prior which is assumed unimodal, is the amount of uncertainty in ₀, andQ is the set of all probability densitiesq for which =(1–)₀+q is unimodal with the same mode as that of ₀. We show that the sup (resp. inf) of the posterior probability of an interval is attained by a prior which is equal to (1–)₀ except in one interval (resp. two disjoint intervals) where it is constant.     

The Towne-Heuer reading passage—A reliable aid to the evaluation of voice

The science of voice evaluation and assessment has profited from technological advancement and objective measurement of voice parameters has become an integral part of the voice examination, however, subjective voice evaluation remains a vital component of any voice examination. The Towne-Heuer Reading Passage was developed in 1970 to provide a reading sample that would facilitate subjective voice evaluation. The reliability of the passage was established using three judges listening to 15 normal Philadelphia speakers and 15 vocal abuse-misuse clients with verified vocal nodules. The frequency of hard glottal attack (HGA) was determined for the two groups and high interjudge and intrajudge correlation was found. A difference in the frequency of HGA was found between the two groups.