Vampires And Zombies, Oh My!

I just submitted my newest paper to the Journal of Spatial and Spatio-temporal Epidemiology. I know, I’m excited too.

This makes paper number 5 submitted in the last year, three of which have been published, 1 is currently under revision, and, well, I just submitted this one. W00t!

Sadly, I don’t think I’m going to be able to hit item #4 on my Not-So-Bucket-List list; that is, publish 5 papers in a year. But no worries, as I have several other papers in various stages of production. My aim is to get at least 2-3 of these finished by the end of the year and submitted to appropriate journals.

Anyway, for your entertainment I offer you the first four lines of the introduction:

Imagine a post-apocalyptic world divided into R geopolitical regions that have become overrun by diseased creatures who are neither alive or dead, who survive only on human flesh and blood, and who spread their disease to the uninfected with a single bite. We label each case of disease as undead (U). We also know that a case labeled as U is the result of one of two diseases; zombie-ism (Z), or vampirism (V). That is, we assume that there are multiple diseases (e.g., Z and V) leading to the same diagnosis (e.g., U).

That’s right folks, I opted to stick with my Vampire-Zombie example. Hopefully the reviewers enjoy this and don’t outright reject it based on a little tongue-in-cheek motivation.

For those wondering, this particular introduction leads to the following posterior distribution:

\begin{array}{ll}  \ln{p({\Theta,\Pi,\Omega}|Y,Z,X)} & \propto \displaystyle{\sum_{i,j,k=1}^{2,18,n}}\left\{z_{ijk}y_{ijk}(\gamma_{1}+\beta_{1}x_{ijk}+\Lambda_{1}u_{1j}+\Lambda_{2}u_{2j})\right.\\  {} & - z_{ijk}N_{ijk}\exp{(\gamma_{1}+\beta_{1}x_{ijk}+\Lambda_{1}u_{1j}+\Lambda_{2}u_{2j})}\\  {} & +(1-z_{ijk})y_{ijk}(\gamma_{2}+\beta_{2}x_{ijk}+\Lambda_{3}u_{2j})\\  {} & - (1-z_{ijk})N_{ijk}\exp{(\gamma_{2}+\beta_{2}x_{ijk}+\Lambda_{3}u_{2j})}\\  {} & \left.+ z_{ijk}\ln{\pi_{1}} + (1-z_{ijk})\ln{(1-\pi_{1})}\right\}\\  {} & -\frac{1}{2}\ln{\left|{\Sigma}_{\gamma}\right|}-\frac{1}{2}({\gamma}-{\mu}_{\gamma})^{t}{\Sigma}_{\gamma}^{-1}({\gamma}-{\mu}_{\gamma})\\  {} & -\frac{1}{2}\ln{\left|{\Sigma}_{\beta}\right|}-\frac{1}{2}({\beta}-{\mu}_{\beta})^{t}{\Sigma}_{\beta}^{-1}({\beta}-{\mu}_{\beta})\\  {} & -\frac{1}{2}\displaystyle{\sum_{i=1}^{2}\sum_{j=1}^{18}}\ln{(1-\zeta_{i}\xi_{j})}\\  {} & +\frac{1}{2}\displaystyle{\sum_{j,j^{\prime}}^{18}}(g_{1}^{2}+g_{2}^{2})u_{1,j}u_{1,j^{\prime}}{W}_{j,j^{\prime}}\\  {} & +\displaystyle{\sum_{j,j^{\prime}}^{18}}g_{2}g_{3}u_{1,j}u_{2,j^{\prime}}{W}_{j,j^{\prime}}\\  {} & +\frac{1}{2}\displaystyle{\sum_{j,j^{\prime}}^{18}}g_{3}^{2}u_{2,j}u_{2,j^{\prime}}{W}_{j,j^{\prime}}+2\ln{g_{3}}+\ln{g_{1}}\\  {} & -(\nu+3)\ln{(g_{1}g_{3})}-\frac{\nu}{20}\left(\frac{g_{1}^{2}+g_{2}^{2}+g_{3}^{2}}{g_{1}^{2}g_{3}^{2}}\right)+2\ln{g_{3}}\\  {} & -(\nu+3)\ln{(\Lambda_{1}\Lambda_{3})}-\frac{\nu}{20}\left(\frac{\Lambda_{1}^{2}+ \Lambda_{2}^{2}+ \Lambda_{3}^{2}}{\Lambda_{1}^{2} \Lambda_{3}^{2}}\right)+2\ln{\Lambda_{3}}\\  {} & +\ln{g_{1}}+\ln{\Lambda_{1}}.  \end{array},

Pretty, isn’t it?


3 Comments Add yours

  1. Beth says:

    Your posterior is very pretty.

    1. dangillis says:

      Why thank you. Thank you very much.

  2. Michael says:

    In a meta-post sense, this is a very interesting post as it concludes with: “…the following posterior distribution…said distribution…Pretty, isn’t it?…Thank You Mr. Oxycodone”.
    My posterior doesn’t look anything like that and thus, I must be missing Mr. Oxycodone.

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