贝叶

Limit theorems, asymptotic methods, asymptotic efficiency and efficiency bounds for estimation, maximum likelihood estimation, Bayes methods, asymptotics via derivatives of functionals, sample-based estimates of variability:; robustness; estimation for dependent data, nonparametric estimation and testing.

高级统计推断理论：极限理论，渐进方法，渐进有效和估计的效率，加大似然估计，贝叶斯方法，泛函数的微商渐进性，基于样本的估计：(bootstrap 和 jackknife方法)；稳健性；独立数据的估计，非参数估计和经验。

Limit theorems, asymptotic methods, asymptotic efficiency and efficiency bounds for estimation, maximum likelihood estimation, Bayes methods, asymptotics via derivatives of functionals, sample-based estimates of variability:; robustness; estimation for dependent data, nonparametric

高级统计推断理论：极限理论，渐进方法，渐进有效和估计的效率，加大似然估计，贝叶斯方法，泛函数的微商渐进性，基于样本的估计：（bootstrap 和 jackknife方法）；稳健性；独立数据的估计，非参数估计和经验。

STAT 581 Advanced Theory of Statistical Inference (3) Limit theorems, asymptotic methods, asymptotic efficiency and efficiency bounds for estimation, maximum likelihood estimation, Bayes methods, asymptotics via derivatives of functionals, sample-based estimates of variability:; robustness; estimation for dependent data, nonparametric estimation and testing.

高级统计推断理论：极限理论，渐进方法，渐进有效和估计的效率，加大似然估高级统计推断理论：计，贝叶斯方法，泛函数的微商渐进性，基于样本的估计：(bootstrap 和 jackknife 方法)；稳健性；独立数据的估计，非参数估计和经验。

In the first chapter, using fragments of COI gene, we studied the phylogenetic relationships among species of five familes of Acridoidea with MP and Bayesian methods. The results were as follows:(1) Species of Acrididae, Gomphoceridae and all the Arcypterinae species of Arcypteridae are monophyletic. Species of Oedipodidae are supported as a monophyleticgroup, Ceracrinae species of Arcypteridae cluter together to make a monophyletic group. Epistaurus aberrans and Xenocatantops humilis is a phylogenetic group, Stenocatantops splendens and Hieroglyphus banian is also a phylogenetic group.

我们首先利用COI基因序列片段，使用最大简约法、贝叶斯法研究了斑腿蝗科、剑角蝗科、斑翅蝗科、网翅蝗科和槌角蝗科5个科42种的系统发育关系，得到如下结果：（1）由所有网翅蝗亚科的物种与剑角蝗科绿洲蝗亚科和槌角蝗科的物种组成一个单系群；斑翅蝗科的物种组成一个单系群；网翅蝗科的竹蝗亚科的黄脊雷蓖蝗和青脊竹蝗聚在一起形成单系群；斑腿蝗科的长翅十字蝗和大斑外斑腿蝗亲缘关系较近，形成一个单系群；长角直斑腿蝗和等歧蔗蝗始终聚在一起，形成一个单系群。

The formula of total probability ,conditional probability and bayes formula are elementary formulas of probability theory.

指出了全概率公式、条件概率及贝叶斯公式在实际应用中与其理论上的矛盾，从应用的角度重新叙述并精确论证了这些公式，弥补了原理论上的不

This thesis try to use the risk decision, Bayes formula and game theory to analyze the utility of the traffic information, and put forward the corresponding static and dynamic model.

本论文在总结国内外交通信息效用研究理论与方法的基础上，系统地对不考虑交通信息有效性反馈和考虑交通信息有效性反馈两种条件下交通信息的作用机理进行研究，尝试采用风险决策、贝叶斯推理、博弈论等理论和方法建立了相应的模型，并对影响交通信息效用的交通信息质量、交通系统稳定性、出行者的出行经验等因素进行了分析，提出了增加交通信息有效性的方法。

Born in London 1702, the son of a minister, Thomas Bayes developed a formula which allowed him to determine the probability of an event occurring based on the probabilities of two or more independent evidentiary events.

生于1702年的伦敦，一名部长的儿子，托马斯贝叶斯公式，使他形成了以确定一个事件发生的概率基于两个或两个以上的独立概率事件的证据。

Keywords:Markov chain, the analytic approach of the first step , Bayes formula

用。关键词：马尔可夫链，首步分析法，贝叶斯公式

Then we use the diagram of Venn to analyse and predigest the theorem proof. And it is also used in probability addition and multiply、conditional probability、total probability formula、 Bayes formula to simplify the calculation of probability. So it is easy to understand and master.

进而利用Venn图分析、简化概率性质的证明以及Venn图在概率的加法与乘法、条件概率、全概率公式和贝叶斯公式中的应用，简化概率的计算，便于学习者理解和掌握。

Bayes Formula probability trees probability theory probability tree method

贝叶斯公式；概率树；概率论；概率树法

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。