# Bayes decision rule - Basic

Good day,

I'm having a problem with an exercise I have for in class.

What is given for this example is the likelihood of an event happening and vice versa. Other details I have is only what the cost will be of the event occurring.

However, from examples I can locate in my class book there's at least more variables needed to use the Bayes rule.

How can I use the Bayes decision rule with only the likelihood given?

The question is should the homeowner have insurance for earthquake activity; There's a 7% chance an earthquake happens within the year, 93% it will not.

There's also given the cost of the insurance as well as the loss if it happens(Covered with insurance).

The two decision are between either to buy insurance or not.

• Could you tell us what exactly does the exercise say? Also, please add the [self-study] tag.
– Tim
Commented Apr 17, 2021 at 16:04

I don't think that Bayes is needed here, this is just an expected value problem.

There are 2 cases, you buy the insurance or you do not.

If you buy the insurance then the cost is just the price of the premium(s) (no cost due to earthquake because the insurance will pay any cost if it occurs (unless there is a deductable)).

If you do not buy the insurance then there is a 93% chance of 0 cost (no earthquake) and a 7% chance of the cost of the loss.

So the expected cost when you do not buy the insurance is $$0.07 \times loss + 0.93 \times 0$$.

The question is just which is lower?

• That's what I had figured, but the exercise states: Which option should you pick in regards with Bayes decision rule. I had put this in Treeplan previously and figured the the best route to go. I'm wondering if the question simply is flawed. Commented Apr 17, 2021 at 16:44