Statistique bayésienne, théorie de la décision et méthodes de simulation par chaînes de Markov

巴耶统计、马尔可夫链决策理论和模拟方法

• 批准号: RGPIN-2018-04661
• 负责人: Perron, Francois
• 金额: $ 1.31万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=712125
• 关键词: Statistique; bay; sienne; th; orie

I want to develop an algorithm that is going to help the companies when they have to offer new products to the customers. The algorithm is a Bayesian procedure giving predictive probabilities on rank statistics. The theory of copula is used in the model and a Markov Chain Monte Carlo simulation is going to be constructed for the numerical evaluations. The acceptance-rejection sampler is an algorithm for sampling from a target density f using a proposal density g. In this algorithm some of the sample values generated by g will be rejected when they fail a test. When the rejection rate is large the sampling is slow. I want to develop better samplers. In particular, I propose to use a Markov chain related to the acceptance-rejection sampler. In want to work on an existing variation of the acceptance-rejection sampler showing that this variation works under weaker conditions than the ones proposed in Caffo, Booth and Davison (2002). In the theory of copula I want to answer the questions raised in Carley's (2002) paper. These questions are about copula extensions of a subcopula. In the theory of extreme values the copula is characterized by a function called the Pickands function. The Pickands function is also related to something called the spectral measure. In Guillotte and Perron (2016) we have characterized all of the polynomial Pickands functions for a 2-dimensional problem. I want to do the same for the spectral measure in a 3-dimensional problem. I want to develop a Bayesian nonparametric estimator for the spectral measure in a 3-dimensional problem. This problem is related to the estimation of a cumulative distribution function. The solution will be based on Polya trees. In Pham Gia, Turkkan and Marchand (2006) the density of the ration X_1/X_2 where the distribution of (X_1,X_2) is a mixture of normal distributions is expressed through special functions like the 1F1 function. I want to exploit a new representation involving a mixture. In the mixture the weights follow a mixed Poisson distribution. The mixed Poisson distributions are very important in mathematical finance.

我想开发一种算法，当公司不得不向客户提供新产品时，它将帮助公司。该算法是一个贝叶斯过程，给出了关于秩统计量的预测概率。模型中使用了Copula理论，并将构建一个马尔可夫链蒙特卡罗模拟来进行数值评估。 拒绝接受采样器是一种使用建议密度g从目标密度f进行采样的算法。在该算法中，g生成的一些样本值在测试失败时将被拒绝。当拒绝率较大时，采样速度较慢。我想开发更好的采样器。特别是，我建议使用与接受-拒绝采样器相关的马尔可夫链。我想要研究接受拒绝采样器的一个现有变体，表明这个变体在比Caffo，Booth和Davison(2002)提出的条件更弱的条件下工作。 在联结理论中，我想回答Carley(2002)论文中提出的问题。这些问题是关于次Copula的Copula扩张的。 在极值理论中，Copula的特征是一个称为Pickands函数的函数。Pickands函数也与所谓的谱度量有关。在Guillotte和Perron(2016)中，我们已经刻画了二维问题的所有多项式Pickands函数。我想对三维问题中的谱测量做同样的事情。我想为三维问题中的谱测量开发一个贝叶斯非参数估计量。这个问题与累积分布函数的估计有关。该解决方案将基于Polya树。 在Pham Gia，Turkan和Marchand(2006)中，当(X_1，X_2)的分布是正态分布的混合时，比X_1/X_2的密度通过类似于1F1函数的特殊函数来表示。我想利用一种涉及混合的新表示法。在混合物中，权重服从混合泊松分布。混合泊松分布在数学金融中是非常重要的。