# Bayes and Likelihood Ratio (crime, ethnicity, blood types)

#### mathyou

##### New member

A crime occurs within an isolated community. A bloodstain is left at the crime scene. Within the adult male population, 71% is White, 16% are Afro-Caribbean and the remainder are Asian.

The offender is male according to a witness and no other information was given.
The bloodstain has genotype ABC12.
Probabilities of someone from the ethnic groups within the relevant population having this genotype are: White, p=0.025; Afro-Caribbean, p= 0.023 and Asian, p=0.012.

A suspect has been arrested: a white male with matching DNA evidence to the scene of the crime.

1) What are the prior odds that an White male committed the crime?

2) Using the information and DNA evidence, what is the Likelihood Ratio in this case?

3) Assume no match between the crime sample and the suspect’s sample. What would the Likelihood Ratio be?

Thanks,

M.

#### tkhunny

##### Moderator
Staff member
Really, #1 is too easy. Your lack of response is not encouraging.

71%

For #2, you'll have to define "Liklihood Ratio". It should be in your book. What does it say? Is it in a section on Bayes Theorem? Is it in the Neyman-Pearson section? How about F-test or t-test? How sure are you the definition is consistent across text books?

Without real discussion, it's very hard to know what is wanted.

Please feel free to make discussions public, rather than PM.