BN node probabilities calculation

Question

In the paper The use of Bayes and causal modelling in decision making, uncertainty and risk by Norman Fenton and Martin Neil following BN is presented:

Quote from the paper: "Once we have supplied the priors probability values a BN tool will run the model and generate all the measures of risk that you need". So I assume that given "Meteor on collision" and "Explode meteor" priors, "Meteor strikes Earth" could be calculated.

How are probabilities of Meteor strikes Earth node are calculated given priors?

Answer 1

As posted, it's not possible to answer this question because we're missing a crucial piece of information. Per the table on page 14, if we explode the meteor, there's still a 20 percent chance that it strikes earth. To quote the explanation of the table,"For example, if the meteor is on a collision course then the probability of it striking the earth is 1, if it is not destroyed, and 0.2, if it is."

So given the trigger there are two ways that earth can be struck: 1) It's on a collision course and the attempt to explode it is unsuccessful or 2) It's on a collision course, the attempt to explode it is successful, but it still strikes earth. These probabilities are given by

$$ 0.999 \cdot 0.99 + 0.999 \cdot 0.01 \cdot 0.2 $$

To find the probability of earth being struck we just divide this summation by the sum of all the possibilities.

Calculating this in R

( (.999 * .99 ) + (.999 * 0.01 * 0.2) )  /  
( (.999 * .99) + (.999 * 0.01 * 0.2) + (.999 * 0.01 * 0.8) + (0.001 * 0.01) + (0.001 * .99) )

gives us 0.991008 which is ~ 0.99101 or 99.101 percent.