Use Map with OptionValue
Evaluation of OptionValue[]
I want to calculate the posterior distribution given a gamma-prior and a poisson likelihood. The task is from a textbook and I just have the solutions (without a walkthrough). Please find all given information in the following:  Given information:  $m$ countries each with a population of $n_i$; $y_i$ is the number of people having a disease; $y_i$ is a poisson random variable with mean $\frac{n_i*\lambda}{100}$  The prior distribution for $\lambda$: $\lambda \sim Gamma(a_0,b_0)$  Task:  Show that the posterior distribution is also a gamma distribution with $a_m = a_0 + \sum_{i = 1}^{m}y_i$ and $b_m = b_0 + \sum_{i = 1}^{m} \frac{n_i}{100}$  My solution:  $Posterior \propto Likelihood \times Prior$  $p(\theta|y) \propto \prod_{i=1}^{m}(\theta^{y_i}e^{-\theta})\times \theta^{a_0-1}e^{-b_0\theta}$  $p(\theta|y) \propto \theta^{\sum_{i = 1}^{m}y_i}e^{-m\theta}\times \theta^{a_0-1}e^{-b_0\theta}$  $p(\theta|y) \propto \theta^{\sum_{i = 1}^{m}y_i+a_0-1}e^{-\theta(m+b_0)}$  $a_m = a_0 + \sum_{i = 1}^{m}y_i$  $b_m = b_0 + m \neq b_0 + \sum_{i = 1}^{m} \frac{n_i}{100}$  I think I am doing a mistake, because I don't know how to incorporate the information that the mean of $y_i$ is given as $\frac{n_i*\lambda}{100}$. Or do I just have to transform $b_m$ somehow? Can someone may give me a hint?   Thank you already in advance!  Edit 1: Considering first advices  $Likelihood: p(y | \theta) \propto \prod_{i=1}^{m}(\frac{n_i\lambda}{100})^{y_i}e^{-\frac{n_i\lambda}{100}}$  $\propto \prod_{i = 1}^{m} ((\frac{n_i}{100})^{y_i})\lambda^{\sum_{i=1}^{m}y_i}e^{-\lambda\sum_{i=1}^{m}\frac{n_i}{100}}$  $\propto \lambda^{\sum_{i=1}^{m}y_i}e^{-\lambda\sum_{i=1}^{m}\frac{n_i}{100}}$  Is the transformation of $\prod_{i=1}^{m}$ I did from the first to the second step correct? Where can the viewport clipping parameters be changed? Every word is marked as misspelled in TeXstudio Mandatory excerpt for custom post type Drive shape key based on relative camera orientation? 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A simple flag counter added to the header next to the notification counter and linked to the tools page (which automatically opens the full version anyway right now) would fix this. This week we rolled out a series of changes to  of the question close workflow.  You can read more about the details of these changes .    For context, the overall effort to improve the question close experience will be optimized for Stack Overflow. Given Stack Overflow’s scale, many of the pain points we hear about with question closing and reopening are unique to Stack Overflow and won’t make sense for other network sites. However some  changes are general improvements that should improve usability and guidance overall. Wherever possible, we plan to roll these changes out network wide as well. Any time we roll out a change network wide, we’ll make sure to cross-post here. This first phase is being rolled out to the network and is why I’m posting today.  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When asking about , people sometimes refer to the strict aliasing rule. What are they talking about?