# 贝叶斯推理和计算|MATH5960 Bayesian Inference and Computation代写

We revisit the On/Off problem but this time from a Bayesian perspective, which fully and automatically accounts for uncertainty in the background rate estimate.

We consider first the “off” measurement, which collects $n_{\text {off }}$ photons in a time $t_{\text {off. }}$.

(i) Assuming a uniform prior on the background rate $b$, find the posterior distribution for $b$ from the off measurement.
(ii) Now consider the “on” measurement, which collects a number $n_{\text {on }}$ of photons during a time $t_{\mathrm{on}}$. This is a measurement for the combined rate $s+b$ (where $s$ denotes the source rate). Write down the likelihood function for this measurement.
(iii) Assume again a uniform prior on $s$, and a prior on $b$ given by the posterior of the “off” measurement $”$, find the (unnormalized) joint posterior distribution for $s, b$, and show that is is given by the expression:
$$p\left(s, b \mid n_{\mathrm{on}}, t_{\mathrm{on}}\right) \propto(s+b)^{n_{\mathrm{on}}} b^{n_{\mathrm{off}}} \exp \left(-s t_{\mathrm{on}}\right) \exp \left(-b\left(t_{\mathrm{on}}+t_{\mathrm{off}}\right)\right) \text { for } s, b \geq 0$$
(iv) Compute analytically the marginal posterior pdf for the signal, $s$, by integrating the joint posterior over $b$, i.e.
$$p\left(s \mid n_{\mathrm{on}}, t_{\mathrm{on}}\right)=\int_{0}^{\infty} p\left(s, b \mid n_{\mathrm{on}}, t_{\mathrm{on}}\right) d b$$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: