Thursday, 28 January 2016

Misleading DNA evidence and the current damaged winning lottery ticket story


Norman Fenton, 28 January 2016

This post is primarily about how DNA match evidence is often presented in a way that is highly misleading (it is an important issue in an ongoing case I'm involved with). But in order to illustrate the point it turns out that we can use a simple analogy based loosely on the current lottery story that is getting a lot of media attention in the UK. This concerns an unverified £33 million winning ticket from a recent draw. About 200 people are claiming to have bought the (single) winning ticket but, until today*, none had actually provided proof of possessing such a ticket. The claim of one - Miss Susan Hinte - is the one that has grabbed media attention because she has produced a ticket in which key identifying information cannot be read because, she claims, the ticket was put through a washing machine.

But first let's look at the DNA issue, which is concerned with the following generic problem:
  • The prosecution claims that defendant Joe was at the crime scene. This hypothesis is denoted as Hp.
  • A tiny trace of DNA from the crime scene has been analysed and found to match the profile of Joe. This evidence (of the match) is denoted E
Typically the defence will argue that Joe was not at the crime scene and that any DNA matching Joe - especially as it was a tiny trace - got there through secondary transfer or other means. So the defence hypothesis Hd is simply the negation of Hp.

The DNA experts have correctly recognised that, in determining the probative value of the evidence E,  they have to use the ‘likelihood ratio’ approach [1]. This means they have to consider both of the following probabilities:
  1. The probability that E is the result of the prosecution hypothesis Hp being true  - formally we write this as P(E given Hp)
  2. The probability that E is the result of the defence hypothesis Hd being false  -  formally we write this as P(E given Hd) 
If probability 1 is greater than probability 2 then the evidence E supports  Hp over Hd and vice versa. The likelihood ratio is simply 1 divided by 2 and provides a simple and compelling measure of probative value of evidence. If the ratio is greater than one the evidence E supports Hp, with higher values indicating stronger support. If the ratio is less than one the evidence E supports Hd, with smaller values indicating stronger support. However, for reasons explained in [1], this whole notion of probative value is not meaningful if the defence hypothesis Hd is not the negation of the prosecution hypothesis Hp. One of the common errors made by DNA experts is to replace Hd with a different hypothesis, namely Hd':  "DNA from Joe got there by secondary transfer".  In this case Hd' excludes other possibilities of observing E even though Joe was not at the crime scene (such as errors or contamination during the DNA testing, or the DNA belonging to a different person with the same profile etc) and is not even mutually exclusive to Hp since Joe may have been at the crime scene even though the trace sample was there through secondary transfer. But, while this common error is serious, it is not the real concern I wish to raise here. In fact, let's suppose that no such error is made and that the expert considers the correct Hd.

The real concern is how a jury member reacts when the DNA expert now makes the following assertions:
  1. “The findings are what I would have expected if Hp were true.” i.e. P(E given Hp) is very high
  2. “The probability of the findings are considerably more likely to have been the result of Hp rather than Hd”  i.e. P(E given Hp) is much higher than P(E given Hd)
Notwithstanding the unnecessary redundancy of statement 1, these assertions sound very important and suggest very strong support for the prosecution hypothesis, especially as most people would already have assumed (wrongly) that the DNA 'match' means the trace certainly belongs to Joe.

But to demonstrate how misleading they are I will return now to the lottery example. For simplicity I will assume the old 6-ball lottery with 49 numbers. Suppose the winning numbers were:
1, 7, 21, 28, 40, 46

Mrs Smith has a damaged ticket that she claims has the winning numbers. The evidence E is that the first number (which is the only number clearly visible) is 1.

Our hypotheses are:
  • Hp: “Mrs Smith's ticket is the winning ticket”
  • Hd: “Mrs Smith ticket is not the winning ticket”
In this case we know the following:
  • P(E given Hp) = 1  (it is certain that the first number on the ticket would be 1 if it was the winning ticket)
  • P(E given Hd) is 0.122 (this is the proportion of non-winning tickets that have 1 as the first number) 
So we could certainly make exactly the same assertions in this case as the DNA experts above:
  1. “The findings are what I would have expected if Hp were true.” (since the probability of E given Hp is 1)
  2. “The probability of the findings are considerably more likely to have been the result of Hp rather than Hd” (since 1 is considerably greater than 0.122).
However, despite these (correct) assertions it is almost certain that Hd rather than Hp is true - Mrs Smith's ticket is not the winning ticket. In fact, the probability of Hp being true is less than one in 1.7 million (because there are over 1.7 million non-winning combinations in which the first number is 1).

So what is the moral of this story? The likelihood ratio of the evidence might often suggest the evidence is highly probative in favour of one of the hypotheses, but if the prior probability of the alternative hypothesis was much higher to start with then the evidence will not ‘overturn’ the prior belief in favour of the alternative.

Lay people ignore this in connection to DNA evidence. Because the random match probability associated with a DNA match is typically less than one in a billion, the very fact that the evidence E is a "DNA match" already puts into their mind the notion that this 'must tie the defendant to the crime scene'. But the random match probability is almost irrelevant in this case - it only accounts for a tiny proportion of P(E given Hp). Lay people can also easily be tricked into believing that the (redundant) assertion 1 “The findings are what I would have expected if Hp were true” provides additional weight to assertion 2.

Unfortunately, this type of evidence is increasingly prejudicing juries and, I believe, leading to serious miscarriages of justice.

*The real winner has now been found, and since their ticket was not damaged it can not have been Miss Hinte

[1] Fenton, N. E., D. Berger, D. Lagnado,  M. Neil and A. Hsu, (2014). "When ‘neutral’ evidence still has probative value (with implications from the Barry George Case)",  Science and Justice, 54(4), 274-287 http://dx.doi.org/10.1016/j.scijus.2013.07.002. (pre-publication draft here)

42 comments:

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    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
  13. Here is my testimony of how i win the lottery,I have been playing the lottery for the past 20yrs and i have never won anything i keep on trying hoping one day i will win but i still could not win anything. So i decide to go for more research on the internet if i could get some tips to improve my chances of winning,there i saw a comment of how Dr Kumar help a woman name carina gomez to win $50million and i just said let me give him a try and i contacted him on the email that was provided on the comment (spellcasttemple@gmail.com) and i explain my problem to him and Dr Kumar cast spell on the winning numbers and gave them to me to play, I pick up my ticket and tick the numbers he gave to me and i won the sum of $110m. I am so grateful to Dr Kumar for helping me to win the lottery and if you also need his help,email him at: spellcasttemple@gmail.com and also Whatsapp him on +2347051705853 and he will also help you win and make you happy like me today.

    ReplyDelete
  14. I am very happy today because i never thought i would be able to leave up till this day.i am Benson Tanaka from Zimbabwe i was infected with h i v by my wife who later died of it and this disease has been with me for the past 6 years now i have gone to several hospitals to seek for cures but all they give to me are some drugs which has taking almost all my savings i had,i was on Facebook on Saturday morning then there was an health group which i was asked to join by a friend immediately after i joined it i saw some post of people giving tanks to this doctor that he has cured them of their hiv disease i was so surprised about this i collected the doctors contact and i thought of it for about 5 good days then i concluded in giving him a try because there was no harm in trying.when i contacted doctor prince he tolled me he was going to prepare an herbal medicine for me which i was going to take for 2 weeks and after that i should go for a test at any of the hospital,after i did every thing which he asked me to do i received the medicine the next two days from a courier company which i started taking immediately after about a week plus i felt some strange moves in me,i felt like i was getting better when i completed the medicine i went for a test at the Bulawayo Central Hospital were i was tested (-)negative i thought i was dreaming i went for another test at the St anne's hospital it was still the same then i believed i was really free from this disease today i have got-in a new job and i am also married to a beautiful wife all tanks to doctor prince here is his contact details for any one who is passing true any kind of sickness or disease he will be willing to help you too.dr.princearataabraham@gmail.com you can also call or whatsapp him on +2348163241499

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  15. It continuously amazes me i am Julie Leach from Michigan, i really do not have much to say but to send my gratitude to Priest Andrew who help me with his spiritual prayers on my winning ticket and i won my Power-ball Jackpot lottery in September in the sum of $310 Million USD. I am amazed and totally indebted to him for elevating me financially, you can contact him on his private email: priestandrew91@yahoo.com for your spiritual help, winning of lottery and all other problems.

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  16. Wow i never thought i will happy in my life ever again, i want you all to thank DR OGUDUGU of GREATOGUDUGU@GMAIL.COM, he is a father that takes care of his children the spell caster of our time, he has saved me from a very ugly situation that almost made my life miserable and i want you all to thank him for me,my husband and i have be married for so many years now with children and the relationship was being threatened by a small girl in his working place,she was almost destroying my home i met so many spell casters but to no avail until i met a friend who came from africa and she told me about DR OGUDUGU, and i decided to contact him and try him out as i was losing faith in all spell casters, but he told not to worry that now am in his temple everything will be alright he assured me 100% that his spell has no side effects and that it will work straight and save my home and my marriage and after he has performed the sacrifices and casted the spell, my husband came back to us with love and affection and he loved us more and more and he never looked back or none did his love for me waiver, if you are also experiencing this sort of your situation in your home, if your husband is drifting away, if you are experiencing a broken home or you have lost your husband to a young woman outside there then look no further help is here as GREATOGUDUGU@GMAIL.COM is ready to help you out okay for any of your problem is it financial needs, revenge spell,Hiv cure, job spell, promotion spell what kind of spell do you need DR OGUDUGU is going to solve it for you okay i have promised him to always talk of his good works to the world in general and to any body who cares to listen, you can email him on his personal email on GREATOGUDUGU@GMAIL.COM or his website @ www.greatdrogudugusolutiontemple.webs.com and he will attend to you as soon as possible okay once again his email is GREATOGUDUGU@GMAIL.COM.

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  17. This is my testimony on how i won $66 million dollars. I am from USA I want to use this opportunity to thank Great PAPA for helping me to win the lottery of $66 million lottery ticket.I have been playing the lottery for the past 5 years now and i have never won. Ever since then i have not been able to win and i was so upset and i need help to win the lottery. so i decided to go online and search for help,there i saw so many good testimony about this man called Great PAPA of how he have cast lucky spell lotto for people to win the lottery.I contact him also and tell him i want to win a lottery, he cast a spell for me which i use and i play and won $66 million dollars. I am so grateful to this man, just in-case you also need him to help you win,you can contact him through his Email> greatpapax@gmail.com and he will surely help you
    Email> greatpapax@gmail.com
    http://greatpapax.wixsite.com/website-1

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  18. good day everyone out there my name is marie holmes I want to use this opportunity to thanks to [ the great OGUN] for helping me to win the lottery .I have been playing the lottery for the past 10 years now and the only big money i have ever won was $800 dollar.Ever since then i have not been able to win again and i was so upset and i need help to win the lottery so i decided to go online and search for help,there i saw so many good talk about this man called [the great OGUN] of how he have cast a spell for people to win the lottery.I contact him also and tell him i want to win a lottery he cast a spell for me which i use and i play and won $188 million million GBP.I am so greatful to this man just incase you also need him to help you win,you can contact him through his email: ogundola38@gmail.
    combest regard
    Marie Holmes

    ReplyDelete
  19. Hello my name is JOHN,I know a great spell
    caster who helped me when I
    had problem with my wife if you need a
    right place to solve your
    problems contact chiwakaspelltemple@gmail.com
    is the right choice. he is a great
    man that have been casting spells with years
    of experience. he cast spells
    for different purposes like.
    Contact.chiwakaspelltemple@GMAIL.COM
    (1) If you want your ex back.
    (2) if you always have bad dreams.
    (3) You want to be promoted in your office.
    (4) You want women/men to run after you.
    (5) If you want a child.
    (6) You want to be rich.
    (7) You want to tie your husband/wife to be
    yours forever.
    (8) If you need financial assistance.
    (9) Herbal care.
    (10) you want your hiv/aids cure forever. Contact . WISE DOCTOR
    on:chiwakaspelltemple@outlook.com

    ReplyDelete
  20. HELLO FRIENDS,i really dont have much to say but first my name is Perry maggie from usa,i am a loving mother of two,i want to thank the man that make it possible to get my husband back, i am happy with my lovely husband, i am saying thank you to the greatest spell caster that made it possible thank you sir, DR,IMONITIE,for what you have done in my life and in the life of my husband and family for bring back my husband to me thank you,if you have any problem at all you can report it to him reach him on this email:Miraculoussolutionhome@yahoo.com... and get your problems solve or you can call his cell phone on +2348058802667 Dr SAMSON CAN AS WELL CURE THE FOLLOWING DISEASES:-
    1. HERPES
    2. LASSA FEVER
    3. GONORRHEA
    4. HIV/AIDS
    5. LOW SPERM COUNT
    6. MENOPAUSE DISEASE
    7. EPILEPSY
    8. ASEPSIS
    9. CANCER
    10. ANXIETY DEPRESSION
    11. PREGNANCY PROBLEM
    12. SHORT SIGHTEDNESS PROBLEM
    14. Male menopause
    15. Menopause – male
    16. Menopause – peri
    17. Menstruation problems
    18. Mercury Poisoning
    19. Migraine
    20. Miscarriage
    21. Mites (demodex mites)

    ReplyDelete
  21. I have heard of him before, but after watching his documentary “healing spell” I was turned on to the full story



    about Dr uwa. He is a man who has the Cure for AIDS,Cancer, Sickle Cell, Herpes,warts,HPV,ALS Diabetes and every kind of



    illness, through a whole foods vegetarian diet and natural herbs, what he calls Electric Foods. He went to herbal school college,



    and has thousands of testimonials of healing people with Herpes, HIV AIDS, and HPV several other



    illnesses. Lisa “Left Eye” Lopes of TLC was cured of Herpes by him and she was so moved by his knowledge that she went on



    to spread the word about him in every way she could. She also opened a Cultural/Healing Center for Children in USA



    before she passed away tragically. This all inspired me that i had to contact Dr uwa, because i was having Herpes



    which could not be cure but was only managed, when i contacted Dr. uwa, he sent me some herbs which i took, and now i can tell you, i have be totally cured of Herpes, My Name is Jasmine, I am from the South Carolina, Please if you have any form



    of illness especially STD,Infertility,HIV etc. you can contact him immediately through his Email Address







    Name: Jasmine Jennifer



    Email: druwaherbalcenter@gmail.com



    PHONE/WHATS APP : +2348063930531

    ReplyDelete
  22. Words are not enough to express my profound gratitude for the wonderful thing that Dr. Ovasaraki did for me.Hi everybody,My name is Kesley Zachow from Brooks New York, USA, Life has not been easy for me and my family and I have been trying to help out with my little salary which is not enough to pay my bills and that of my old parents. I have spent more than 35000 dollars buying lottery tickets all to no avail. I was on the internet one day when I saw testimonies on how Dr. Ovasaraki has helped many people to win big in lottery. After contacting Dr. Ovasaraki and I explained my condition to him he cast a lottery spell fro me which made me win big, (66,000,000 dollars) All what he said and what he promised to do really happened.I guess never believed in magic or spells because I thought they were mostly scam acts or tricksters until I met him,everything changed,it exists but only in the right hands and with it everything is possible.I don't know how to pay him for this but I really hope I can do something important and special for him by telling the world on how I became rich now with his magic lottery spell,I now have a house and a car of my own.He his good in love spell, get your ex back, HIV spell, Pregnancy Spell And other spell if you are in need of any help contact him here ( dr_ovasaraki@yahoo.com ) or
    whatsapp number +2349057779106

    ReplyDelete

  23. i am here to give testimony of how i got back my husband, we got married for more than 9 years and have gotten two kids. thing were going well with us and we are always happy. until one day my husband started to behave in a way i could not understand, i was very confused by the way he treat me and the kids. later that month he did not come home again and he called me that he want a divorce, i asked him what have i done wrong to deserve this from him, all he was saying is that he want a divorce that he hate me and do not want to see me again in his life, i was mad and also frustrated do not know what to do,i was sick for more than 2 weeks because of the divorce. i love him so much he was everything to me without him my life is incomplete. i told my sister and she told me to contact a spell caster, i never believe in all this spell casting of a thing. i just want to try if something will come out of it. i contacted (24hourslovespell@gmail.com ) for the return of my husband to me, they told me that my husband have been taken by another woman, that she cast a spell on him that is why he hate me and also want us to divorce. then they told me that they have to cast a spell on him that will make him return to me and the kids, they casted the spell and after 1 week my husband called me and he told me that i should forgive him, he started to apologize on phone and said that he still live me that he did not know what happen to him that he left me. it was the spell that he traditional spell hospital casted on him that make him comeback to me today,me and my family are now happy again today. thank you for what you have done for me i would have been nothing today if not for your great spell. i want you my friends who are passing through all this kind of love problem of getting back their husband, wife , or ex boyfriend and girlfriend to contact 24hourslovespell@gmail.com . call or whatsapp +2347059073543 and you will see that your problem will be solved without any delay.

    ReplyDelete
  24. This is Angel Sean from USA, am sharing this article to give thanks to Dr.Vanisa, who helped me to bring back my EX lover that broke up with me for 2 months. I was searching for advise on what to do to get back my EX lover and i came across a post of a woman in USA called Angela Shuane giving thanks to Dr.Vanisa, for helping her to get back her lost HUSBAND who left her for years with her kids. I contacted the spell caster for help due to the fact that i needed my EX lover desperately because he is my lover and my life. To God be the glory, my EX lover came back to me within 12 to 16 after Dr.Vanisa, finished preparing the spell and i want the world to join me to give thanks to Dr.Vanisa, for helping me. Viewers reading my article that also need his help should contact Dr.Vanisa, with his email : [vanisaspellcaster@gmail.com]...he do cure nerve problem.....

    ReplyDelete
  25. Hello!! I’m indeed very happy for the great help that Dr. Zadson rendered to me, I was a herpes patient my husband also was a herpes patient, we saw a blog where Dr.Zadson cured herpes, we decided to contact him which we did,and he assured us of full recovery from this deadly disease and we did all that was necessary and required just less than 7 days Dr Zadson told us to go for a medical test which we did and to my greatest surprise we both tested negative to herpes i found it hard to beleive and we went to another hospital for confirmation and the case was similar there and then i knew this man is indeed true powerful and a man sent by God. If you require his servivces to cure herpes kindly email him on eduduzadsontemple@yahoo.com

    ReplyDelete
  26. My Heart is fill with joy after Dr Ogala cast the Lottery spell for me, I felt enveloped by the control of the spell. This spell change my life into riches,i now have my own car and a house. I am now out of debts and experiencing the most amazing good luck with lottery after i won a huge amount of money. I have more luck now than I ever had in my life. i won one million dollars (1,000,000.00 Your Lottery spell made wonders, I can’t believe it. Thank you so much sir for dedicating your time to cast the Lottery spell for me.”I am eternally grateful for the lottery spell Dr Ogala did for me. You can email him for you own lottery number.

    Ogalalotteryspell@yahoo.com or call +2348147673679
    Website http://ogalalovespell.wix.com/ogalalovespell

    ReplyDelete
  27. My Heart is fill with joy after Dr Ogala cast the Lottery spell for me, I felt enveloped by the control of the spell. This spell change my life into riches,i now have my own car and a house. I am now out of debts and experiencing the most amazing good luck with lottery after i won a huge amount of money. I have more luck now than I ever had in my life. i won one million dollars (1,000,000.00 Your Lottery spell made wonders, I can’t believe it. Thank you so much sir for dedicating your time to cast the Lottery spell for me.”I am eternally grateful for the lottery spell Dr Ogala did for me. You can email him for you own lottery number.

    Ogalalotteryspell@yahoo.com or call +2348147673679
    Website http://ogalalovespell.wix.com/ogalalovespell

    ReplyDelete
  28. I am David Carol,i am from Californian,i want to use this wonderful opportunity to thank Dr. Ogala who helped me and my wife to won lottery. We won(£33,035,323) i have spent so much money playing this game for many years,i ask myself sometimes when will i win huge amount of money,one day i came across Dr.Ogala advertisement on internet how he helped people and grant them their heart desire by winning lottery with his powerful lottery spell,so i decided to email him. He assure us that our request will be granted once he cast the lucky winning spell,i believe and follow his instructions,after the casting of the spell,he sent us the winning numbers,wish we use to play and won {Thirty three million,thirty five thousand,three hundred twenty three pounds} right now i am short of words,we are multimillionaire we won a huge amount,he is the best man on earth to work with,he take away the poverty from my generation,his direct email is Ogalalotteryspell@yahoo.com or via web site http://ogalalovespell.wix.com/ogalalovespell call him +2348147673679 just email him,he will also make you win.

    ReplyDelete
  29. AN Amazing testimony, i am MICHEAL from Canada, on a faithful day as i was walking down my street, hopeless, i meet my old friend william he was so happy to see me and he pick me up to a fast food joint in the city of Canada, he was my old time friend and class mate, but now he look different, looking good riding a big car and wearing all sort of customize shoes i was jealous but since he is my very good friend i have to ask him some few question on how come about his wealth and he say to me as a good friend and old friend of him, he told me the secret of his wealth behold i was so surprise that a voodoo spell caster can cast a lottery spell and will send you the lucky numbers to win millions of dollars, as a hopeless man i have to try all alternative to make sure i get good money and take care of my family, so believe me i contacted this Africa voodoo spell caster name Dr suka, i contacted him quickly through his mail addressat(drsukaspellhome@gmail.com) and he cast the spell and send me the hot numbers to win the lottery big, to cut the long story short i am a billionaire today, Dr. suka is truly a gifted voodoo spell caster and you can contact him today for a lottery spell lotto any kind of spell he will help you as well. because this is the only way to win the lottery and the best way as well. all thanks goes to great doc, i promise to testifier of your goodness all through my life for making me rich and famous if out there you are pool or your business is not working well contact him today at drsukaspellhome@gmail.com. or +2347036842735

    ReplyDelete