Friday, 1 July 2016

The likelihood ratio and why its use in forensic analysis is often flawed

FORREST 2016 (for details see here)

I am giving the opening address at the Forensic Institute 2016 Conference (FORREST 2016) in Glasgow on 5 July 2016. The talk is about the benefits and pitfalls of using the likelihood ratio to help understand the impact of forensic evidence. The powerpoint slide show for my talk is here.

While a lot of the material is based on our recent Bayes and the Law paper, there is a new simple example of the danger of using the likelihood ratio (LR) when the defence hypothesis is not the negation of the prosecution hypothesis. Recall that the LR for some evidence E is the probability of E given the prosecution hypothesis divided by the probability of E given the defence hypothesis. The reason the LR is popular is because it is a measure of the probative value of the evidence E in the sense that:
  • LR>1 means E supports the prosecution hypothesis
  • LR<1 means  E supports the defence hypothesis
  • LR=1 means E has no probative value
This follows from Bayes Theorem but only when the defence hypothesis is the negation of the prosecution hypothesis. The problem is that there are Forensic Science Guidelines* that explicitly state that this requirement is not necessary. But if the requirement is not met then it is possible to have LR<1 even though E actually supports the prosecution hypothesis. Here is the example:


A raffle has 100 tickets numbered 1 to 100

Joe buys 2 tickets and gets numbers 3 and 99

The ticket is drawn but is blown away in the wind.

Joe says the ticket drawn was 99 and demands the prize, but the organisers say 99 was not the winning ticket. In this case the prosecution hypothesis H is “Joe won the raffle”.
Suppose we have the following evidence E presented by a totally reliable eye witness:
 
E: “winning ticket was an odd nineties number (i.e. 91, 93, 95, 97, or 99)”

Does the evidence E support H? let's do the calculations:
  • Probability of E given H = ½
  • Probability of E given not H = 4/98
So the LR  is  (1/2)/(4/98) = 12.25

That means the evidence CLEARLY supports H. In fact, the probability of H increases from a prior of 1/50 to a posterior of 1/5, so thee is no doubt it is supportive.

But suppose the organisers’ assert that their (defence) hypothesis is:

H’: “Winning ticket was a number between 95 and 97”

Then in this case we have:
  • Probability of E given H = ½
  • Probability of E given H’ = 2/3
So the LR  is  ( 1/2)/(2/3) = 0.75

That means that in this case the evidence supports H’ over H. The problem is that, while the LR does indeed 'prove' that the evidence is more supportive of H' than H that is actually irrelevant unless there is other evidence that proves that H' is the only possible alternative to H (i.e. that H' equivalent to 'not H').  In fact, the  'defence' hypothesis has been cherry picked. The evidence E supports H irrespective of which cherry-picked alternative is considered.  
Norman Fenton, 1 July 2016
 

*Jackson G, Aitken C, Roberts P. 2013. Practitioner guide no. 4. Case assessment and interpretation of expert evidence: guidance for judges, lawyers, forensic scientists and expert witnesses. London: R. Stat. Soc. http://www.maths.ed.ac.uk/∼cgga/Guide-4-WEB.pdfPage 29: "The LR is the ratio of two probabilities, conditioned on mutually exclusive (but not necessarily exhaustive) propositions."

See also:

6 comments:

  1. Thank you so much you have given the great blogs site
    insurance life cycle

    ReplyDelete
    Replies
    1. BRING BACK THE GOOD TIMES, THINK ABOUT THE HAPPIEST TIME IN YOUR RELATIONSHIP, DR OGUDU CAN MAKE IT HAPPEN AGAIN, YOU DESERVE TO BE HAPPY, TODAY BRING BACK LOST LOVE INSTANTLY USING HIS EFFECTIVE SPELLS

      Are you looking for ultimate spells that works effectively same time on your problems, ranges from Love spells, marriage spells, and carrier related problems, Gay and lesbian extreme love / attraction spells, women of the night Norton accruing powders and oil for extreme ecstasy and protection with in working ordeals. How to get your ex back permanently? Is this what you are asking yourself? Have you been dumped? Can't you just move on? Did he/she chose someone else over you? Your lover shows no interest in you anymore? You might have been asking yourself how to get your ex lover back permanently and you have been looking for unanswered questions about it, Well today is the day for your worries to be eliminated for good. Dr Ogudu have assisted me in getting my ex lover back,Are you going through emotional torture contact him now so he can use his birth gift of casting strong love spells and his super natural magical powers that mean no harm but motivated by peace, wellness and love. The fact that you ask how to get your lover back permanently is the reason why you should no longer face sorrow on your own, and that is because you are in a perfect condition to win over your ex lover and make him or her fall in love with you all over again. It is a great pain to be in love with someone who does not show the same affection back to you as you hope for. However, it is never too late to have all that you wish for and deserve in a lover. Love spells by (DR OGUDU) are pure nature of magic, they are inspired by true mystery of the beauty of the planet earth and they will do well for you as well. CONTACT HIM NOW AND BE HAPPY AGAIN""""


      EMAIL--[OGUDUSPELLTEMPLE@YAHOO.COM]
      WHATSAPP NUMBER +2348106058254
      Website...http://oguduspelltemple.wixsite.com/drogudu

      Delete
  2. A HEART OVER INDEBTED AND FULL OF GRATITUDE TO DR OGUDU THE MIGHTIEST LOTTERY SPELL CASTER IN THE WORLD
    My name is JOHN REHM It all started 2 years ago when i lost my job, and things became so hard for me and my family living in Florida and i decided to use my little savings to purchase a Florida lottery which never yield a result, I was now leaving in total mess and much debt i promised myself that i will never play the lottery again, After months of joblessness i was reading a tread online about{ DR OGUDU THE LOTTERY SPELL CASTER} and how he has made so many people to win the lottery, I for one don,t believe in magic and black powers but because i was very frustrated and stranded i decided to contact him through his email address, He demanded for few details about me which i gave him under 48 hours he gave me some numbers to play which have changed my life today.i was in a bar drinking when Florida Lottery announces that MR JOHN REHM is the sole winner of the 1,000,000 million POWER BALL jackpot from the drawing held on Wednesday, January 26, should claimed the prize at Lottery Headquarters in Tallahassee. if you,re in need of such winnings contact him via [OGUDUSPELLTEMPLE@YAHOO.COM] OR WHATS-APP HIM +2348106058254

    ReplyDelete
  3. Thank you for your miracle Doctor Osemu Okpamen

    This article is dedicated to the Doctor Osemu Okpamen. I have been married with my wife for 5 years and recently she broke up with me and it hurt me deeply when she told me to leave her alone and that she does not love me anymore when i was always faithful and honest to her. I tried all the ways to get her back buying her what she wants like i always did and she still left me heart broken and she even has a new boyfriend which destroyed me even more until a friend of mine from high school directed me to this genuine spell Doctor called Osemu Okpamen. This man changed my life completely. I followed everything he told me to do and my wife came back begging for me back. I was stunned everything happened exactly like he told me. I had faith in everything he told me and everything was true. Also he was there every moment until i got my happiness back and he also provides spells that cures impotence, bareness, diseases such as HIV/AID E.T.C You can contact him via email at { Doctorokpamenspelltemple@yahoo.com } or visit his website http://www.doctorokpamenspells.com. He will help you in anything you need and quick to answer once you contact him.

    You can also call me for more info +1 (914)-517-3229.

    ReplyDelete
  4. BRING BACK THE GOOD TIMES, THINK ABOUT THE HAPPIEST TIME IN YOUR RELATIONSHIP, DR OGUDU CAN MAKE IT HAPPEN AGAIN, YOU DESERVE TO BE HAPPY, TODAY BRING BACK LOST LOVE INSTANTLY USING HIS EFFECTIVE SPELLS

    Are you looking for ultimate spells that works effectively same time on your problems, ranges from Love spells, marriage spells, and carrier related problems, Gay and lesbian extreme love / attraction spells, women of the night Norton accruing powders and oil for extreme ecstasy and protection with in working ordeals. How to get your ex back permanently? Is this what you are asking yourself? Have you been dumped? Can't you just move on? Did he/she chose someone else over you? Your lover shows no interest in you anymore? You might have been asking yourself how to get your ex lover back permanently and you have been looking for unanswered questions about it, Well today is the day for your worries to be eliminated for good. Dr Ogudu have assisted me in getting my ex lover back,Are you going through emotional torture contact him now so he can use his birth gift of casting strong love spells and his super natural magical powers that mean no harm but motivated by peace, wellness and love. The fact that you ask how to get your lover back permanently is the reason why you should no longer face sorrow on your own, and that is because you are in a perfect condition to win over your ex lover and make him or her fall in love with you all over again. It is a great pain to be in love with someone who does not show the same affection back to you as you hope for. However, it is never too late to have all that you wish for and deserve in a lover. Love spells by (DR OGUDU) are pure nature of magic, they are inspired by true mystery of the beauty of the planet earth and they will do well for you as well. CONTACT HIM NOW AND BE HAPPY AGAIN""""


    EMAIL--[OGUDUSPELLTEMPLE@YAHOO.COM]
    WHATSAPP NUMBER +2348106058254
    Website...http://oguduspelltemple.wixsite.com/drogudu

    ReplyDelete