先验分布

First, the concept emergence probability is assumed to be a random variable with a priori Beta distribution. Second, its priori parameters are designated by the distance-based similarity algorithm, calculated by Bayesian Estimation.

该算法首先假定概念出现概率是符合Beta分布的随机变量，然后基于语义距离的相似度算法计算先验参数，并根据统计样本计算该先验分布下基于最小风险的贝叶斯估计后验参数。

In order to avoid that a small amount of field test information would be obliterated by a large amount of prior information,a Bayesian method with mixed Beta distribution was used.

为避免少量的现场试验信息被大量的先验信息淹没，使用了以混合贝塔分布为先验分布的贝叶斯方法。

Methods According to the Bayesian conjugate prior distribution principle, the estimating methods of prior parameters of the conjugate beta distribution Be of the binomial distribution was given by writing the SAS programs.

根据贝叶斯共轭先验分布原理，对二项分布的共轭贝塔分布中的α、β两个先验参数的确定方法进行分析比较，编写SAS程序确定先验参数。

In mathematical that is to say,after obtaining the sampleχ,we may obtain the conditional distribution Hwhen X=χ.

在传统的Bayes估计中，参数λ的先验分布都是已知的，但有时候我们不一定能得到λ的精确的先验分布，于是就产生了新的Bayes估计方法，比如E Bayes估计和多层Bayes估计。

In classical method, the author has generalized the results of Chen, Sun and Li (1995), and given classical lower confidence limit of average life, reliability and reliable life of exponential distribution.

最后，介绍了本文的主要创新点：(1)提出了先验分布、多层先验分布的构造方法——减函数法、增函数法，并给出了它们在无失效数据问题中的应用。

Especially since Lindley and Smith (1972) addressed the thought of hierarchical prior distribution and Han (1997) provided the methods to construct hierarchical prior distribution, more achievements have been made on hierarchical Bayesian methods to be used for solving zero-failure data problem.

所谓λ的多层先验分布的构造方法——减函数法，主要是选取λ的减函数作为λ的第一层先验密度函数的核，第二层先验分布——第一层先验分布中超参数的先验分布取均匀分布。

Then, we choose suitable classes of mean θ for normal distribution.

文中以正态分布为例，给出了均值参数θ的先验分布及先验分布族的选择方法。

Results Under the condition of the conjugate prior distribution, the prior parameters computed by three methods were similar.

结果在共轭先验分布的条件下，先验矩、分位数、众数与分位数三种方法确定的先验分布参数结果一致。

The noninformative prior of the standard deviation of error terms was introduced for Bayesian analysis. Then, given the prior density of the random coefficients in the degradation path model, the Markov Chain Monte Carlo method was adopted to generate samples of joint posterior distribution of random coefficients and unknown standard deviation.

为了处理未知的误差项方差，引入相应的标准差的无信息先验分布，并进一步结合退化轨道模型中随性参数的先验分布，利用马尔可夫链蒙特卡罗方法得到随机参数及误差项标准差的联合后验分布的采样值，进而实时预测产品在未来一段时间内的可靠度。

The last section of chapter 3 discusses the local sensitivityof the Bayes VaR when the contaminated probability ε close to zero. Consider adifferent contaminated class 〓,where Q consists ofsuch functions q that π can be regulized to be a proper probability distribution.

当〓是由定义在参数空间上的所有概率分布组成的分布类时，在没有观测数据和存在观测数据两种情况下，我们分别得到了基准先验分布〓下BayesVaR在ε污染类上对应概率水平的变化范围，该范围越小，表示基准先验分布下BayesVaR的稳健性越好，该范围越大意味着稳健性越差。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。