19th Ave New York, NY 95822, USA

# 数学代写|统计计算作业代写Statistical Computing代考|Reversible Jump Markov Chain Monte Carlo

my-assignmentexpert™统计计算Statistical Computing作业代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。my-assignmentexpert™， 最高质量的统计计算Statistical Computing作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此统计计算Statistical Computing作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

my-assignmentexpert™ 为您的留学生涯保驾护航 在统计计算Statistical Computing作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计计算Statistical Computing代写服务。我们的专家在统计计算Statistical Computing代写方面经验极为丰富，各种统计计算Statistical Computing相关的作业也就用不着 说。

• 随机微积分 Stochastic calculus
• 随机分析 Stochastic analysis
• 随机控制理论 Stochastic control theory
• 微观经济学 Microeconomics
• 数量经济学 Quantitative Economics
• 宏观经济学 Macroeconomics
• 经济统计学 Economic Statistics
• 经济学理论 Economic Theory
• 计量经济学 Econometrics

## 数学代写|统计计算作业代写Statistical Computing代考|Description of the method

Due to the complex structure of the state space used in RJMCMC methods, more mathematical formalism is required to state the RJMCMC algorithm than was necessary in the previous sections. This section introduces the required notation and states the general RJMCMC algorithm.

We start the exposition by giving a mathematical description of the state space: Let $I$ be a finite or countable set and let $d_{k} \in \mathbb{N}{0}$ for all $k \in I$ be given. Define $$S{k}={k} \times \mathbb{R}^{d_{k}}$$
for all $k \in I$ and
$$S=\bigcup_{k \in I} S_{k}$$

Then the elements $z$ of the space $S$ have the form $z=(k, x)$, where $x \in \mathbb{R}^{d_{k}}$ and $k \in I$. Since the index $k$ is included as the first component of all elements in $S_{k}$, the spaces $S_{k}$ are disjoint and each $z \in S$ is contained in exactly one of the subspaces $S_{k}$. For a value $(k, x) \in S$, the first component, $k$, indicates which of the spaces $\mathbb{R}^{d_{k}}$ a point is in while the second component, $x$, gives the position in this space. The space $S$ is the state space our target distribution will live on and the Markov chain constructed by the RJMCMC algorithm will move in.

## 数学代写|统计计算作业代写STATISTICAL COMPUTING代考|Bayesian inference for mixture distributions

In this section we illustrate the RJMCMC algorithm $4.36$ with the help of an example: we consider a Bayesian inference problem for mixture distributions. For the example, we assume the following model: observations $Y_{1}, \ldots, Y_{n}$ are given from a twodimensional mixture distribution
$$\mu=\frac{1}{k} \sum_{a=1}^{k} \mathcal{N}\left(\mu_{a}, r_{a}^{2} I_{2}\right),$$
where $I_{2}$ is the two-dimensional identity matrix. We assume that the number $k$ of modes, the means $\mu_{a}$ and the standard deviations $r_{a}$ are all random, with distributions given by
$$k \sim \operatorname{Pois}(3)+1$$
as well as
$$\mu_{a} \sim \mathcal{U}([-10,+10] \times[-10,+10])$$
and
$$r_{a} \sim \mathcal{U}\left[\frac{1}{2}, \frac{5}{2}\right]$$
for all $a \in{1, \ldots, k}$. Our aim is to generate samples from the posterior distribution of $k, \mu_{a}$ and $r_{a}$, given the data $Y_{1}, \ldots, Y_{n}$.

In this section we will use the RJMCMC algorithm to generate the required samples. In order to do so we first have to determine the state space $S$ and the target distribution on this state space, and then we have to choose a set of moves which allows the algorithm to efficiently explore all of the state space.

## 数学代写|统计计算作业代写STATISTICAL COMPUTING代考|DESCRIPTION OF THE METHOD

F○r一种一世一世$到∈一世$一种nd
S=\bigcup_{k \in I} S_{k}


## 数学代写|统计计算作业代写STATISTICAL COMPUTING代考|BAYESIAN INFERENCE FOR MIXTURE DISTRIBUTIONS

μ=1到∑一种=1到ñ(μ一种,r一种2一世2),

μ一种∼ü([−10,+10]×[−10,+10])

r一种∼ü[12,52]