Hi,

The present work is aimed to show how **bayesian inference** methods can be used to infer (= to assess) **the probabilility that a person detected infected by the SARS-Cov2 has to die** (remark I did not write "has to die if it" because one never be sure of the reason of the death).

A lot of details are avaliable in the attached pdf file (I tried to be pedagogic enough so that the people not familiar with bayesian inference can get a global understanding of the subject, many links are provided for quick access to the different notions).

In particular, I explain why simple mathematics cannot provide a reliable estimate of this probability of death (sometimes referred to as the "death rate") as long as the epidemic continues to spread.

Even if the approach presented here is rather original, this is not the purpose of this post.

Since a long time I had in mind to post here an application concerning bayesian methods. The CoVid19 outbreak has only provided me with the most high-profile topic to do so.

I will say no more about the inference procedure itself (all the material is given in the attached pdf file) and I will only concentrate on the MAPLE implementation of the solution algorithm.

Bayesian Inference uses generally simple algorithms such as MCMC (Markov Chain Monte Carlo) or ABC (Approximate Bayesian Computation) to mention a few, and their corresponding pseudo code writes generally upon a few tens of lines.

This is something I already done with other languages but I found the task comparatively more difficult with Maple. Probably I was to obsess not to code in Maple as you code in Matlab or R for instance.

At the very end the code I wrote is rather slow, this because of the allocated memory size it uses.

In a question I posed weeks ago (How can I prevent the creation of random variables...) Preben gave a solution to limit the burst of the memory: the trick works well but I'm still stuked with memory size problems (Acer also poposed a solution but I wasn't capable to make it works... maybe I was too lazzy to modify deeply my code).

Anyway, the code is there, in case anyone would like to take up the challenge to make it more efficient (in which case I'll take it).

Note 1: this code contains a small "Maplet" to help you choose any country in the data file on which you would like to run the inference.

Note 2: Be careful: doing statistics, even bayesian statistics, needs enough data: some countries have history records ranging over a few days , or no recorded death at all; infering something from so loos date will probably be disappointing

The attached files:

- The pdf file is the "companion document" where all or most of it is explained.It has been written a few days ago for another purpose and the results it presents were not ontained from the lattest data (march 21, 2020 coronavirus)
- xls files are data files, they were loaded yesterday (march 28, 2020) from here coronavirus
- the mw file... well, I guess you know what it is.

Bayesian_inference.pdf

total-cases-covid-19_NF.xls

total-deaths-covid-19_NF.xls

Bayesian_Inference_ABC+MCMC_NF_2.mw