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  • Originally posted by Trevor Marriott View Post

    Hi Jeff
    I am just kidding and I know you mean well, but the reality is we are never going to know, even with those who say that based on the witness testimony it could be after 5am, as keeps getting said both Phillips and the witness testimony are "unsafe" to totally rely on to prove a conclusive TOD, what else can be said?

    www.trevormarriott.co.uk
    Hi Trevor,

    We agree! (yes I'm back from quizz - we came 4th, so close until the last round; but I digress). And,to be clear, I fully agree with your concerns about what I presented. I hope everyone has noted that I have been clear in that the data I'm working from is not suitable. Why?

    I'm using as a model of "complete rigor" times to decide if Annie Chapman, specifically, fits that model. Well, guess what, there are so many things about Annie Chapman's murder that make her unilke the data I'm using that - those conclusions are as unsafe as Dr. Phillips. I'm comparing apples with oranges.

    Look, we know, low temperatures slow rigor mortis progression, and we know Chapman was not kept at the temperatures that the data set I've used would have been, so that alone should make you question the inferences I've suggested (though I warned you; I have been careful to say, a few times, this data is not a good comparison).

    If the rate of rigor, and therefore the time that Annie Chapman reaches full rigor, depends upon temperature, slowing the time to full rigor, then the "time to reach full rigor" data I have won't apply, so all bets are off.
    ,
    But if murder by cut throat, etc, speeds up rigor onset, then again, the data I've used still isn't a good model for this case.

    We do not know when she reached full rigor (so we are missing critical data).
    We do not know if temperature (slowing rigor) or other factors (speeding up rigor) has the bigger effect in this case, so we do not know the actual expected progression (so we're also missing more critical information).

    I want to restate, to make it very clear, the previous analyses are not "real", they are just "what would need to be done", if we had the information. But we're not going to find research on "death by throat cutting with disembolwed bodies partially exposed to cold temperatures", which is really what we need to do anything that won't have a margin of error so wide as to be not worth the time (unless, like me, it's worth it for the enjoyment of trying to extract something out of real data).

    Change, however, one thing (believe that with Annie Chapman rigor progressed faster than in the data set I've presented), and nothing that it may appear I've suggested "works".

    But I want to once again emphasize, I'm not saying the previous is "true", I'm trying to demonstrate what sort of analysis would allow us to draw inferences. But without date from cases similar to Chapman's, we can't do that.

    Basically, if I came across as suggesting "this is true", shake your head, that's smoke and mirrors. What I presented only works if - all the factors that suggest rigor should progress faster are cancelled exactly by all the factors that suggest it should progress more slowly. And that situation is so unlikely that it makes my analyse nothing more than "playing", as Trevor rightly noted. I am playing, I'm not proselytizing.

    However, to explain why I spent time on this, it does tell us that that rigor seems to follow a "log normal" progression over time. That gives us reason to expect that if Annie Chapman's specific case leads to a faster or slower progression of rigor, that it would still follow a log normal type of equation. I just don't know how to adjust the model to fit that, and how the model gets adjusted to fit this specific case is critical with respects of the conclusions one draws. I'm basically using a model that is based upon the idea that the factors that speed up rigor progression (which we know there are some) are pretty much cancelled by the factors that slow it down (which we also know there are some). If one side of that balance scale is greater than the other, then what I've presented is rubbish.

    It's a highly qualified analysis, and I don't want anyone, on either side of the debate, to view it as anything other than that.

    - Jeff
    Last edited by JeffHamm; 09-18-2019, 11:53 AM.

    Comment


    • Unless rigor can begin between 5:15 and 5:50, then this discussion is a waste of time and Phillips was wrong. He misread what he saw, simple. Instead of having Richardson as some near sighted fool and Cadosche as someone who could tell his left from his right, and because its almost certain Phillips had never before faced the type of murder in the outdoors that he did that morning.
      Michael Richards

      Comment


      • Just noticed I should have written Cadosche "couldn't" last post.
        Michael Richards

        Comment


        • Originally posted by Michael W Richards View Post
          Unless rigor can begin between 5:15 and 5:50, then this discussion is a waste of time and Phillips was wrong. He misread what he saw, simple. Instead of having Richardson as some near sighted fool and Cadosche as someone who could tell his left from his right, and because its almost certain Phillips had never before faced the type of murder in the outdoors that he did that morning.
          Unless the temperature is low enough to halt the chemical reactions that produce rigor, rigor begins at the point of death (for all intents and purposes). The rate at which those chemical reactions proceed determines, in part, the point at which an observer will "detect them" by touch (i.e. by finding that the limbs are "stiff", actually, eyelids are the best place to check for onset it appears; small muscles are easier to detect rigor in than larger ones). Also, "detecting rigor" will also depend upon who is checking, because it is a decision, and we all set a different criterion. You and I might be presented with the same body, and I might say "yes, rigor has started" and you might, with the same information, say "no it hasn't", because it is within some boundary zone and our thresholds are different. Annie Chapman's murder has a lot of factors about it that are know to influence how rigor sets in and progresses, but we are missing the vital details to allow us to work out what we should expect (should it be slower, faster, about typical?). Add on to that the wide range of times that rigor type "evidence" gives us, there's not much we can do (mind you, if I had the right data set as a model for her murder, I could work magic! ) From what we have, and using a typical progression of rigor, things land on the side of the witnesses. Change that model, though, and it could fall the other way. But then, we would still have their statments, which keep pushign towards 5:25 ish.

          By the way, Long testified she set the time by the Brewer's clock after she passed the couple she saw. So even if she correctly remembers the chime as the half hour chime, it was 5:30 after she passed that couple - so she saw them before 5:30 (closer to Cadosch's time). And if she heard that chime only 5-7 minutes after walking passed them, there is no problem with her testimony as given.

          - Jeff

          Comment


          • Originally posted by Michael W Richards View Post
            Unless rigor can begin between 5:15 and 5:50, then this discussion is a waste of time and Phillips was wrong. He misread what he saw, simple. Instead of having Richardson as some near sighted fool and Cadosche as someone who could tell his left from his right, and because its almost certain Phillips had never before faced the type of murder in the outdoors that he did that morning.
            Itís simply game over Michael.

            The witnesses far outweigh dodgy Forensic guesswork.

            Unless you happen to have a theory that depends on Phillips of course.

            Comment


            • Originally posted by JeffHamm View Post
              By the way, Long testified she set the time by the Brewer's clock after she passed the couple she saw. So even if she correctly remembers the chime as the half hour chime, it was 5:30 after she passed that couple - so she saw them before 5:30 (closer to Cadosch's time). And if she heard that chime only 5-7 minutes after walking passed them, there is no problem with her testimony as given.
              It's a small point (my speciality), but most papers reported her as saying she heard the chimes just before passing the couple, I think only the Morning Advertiser has it the other way around.

              Eg the Telegraph;
              "I heard the brewer's clock strike half-past five just before I got to the street"

              and later;
              "You are certain about the time? - Quite.
              What time did you leave home? - I got out about five o'clock, and I reached the Spitalfields Market a few minutes after half-past five."

              ​​​​​​​The clock on Spitalfields church (from which Cadosche noted his time) can clearly be seen from the market side of Commercial Street. However, since she doesn't mention actually seeing a clock, Long may have simply inferred her arrival time from the chimes she heard a couple of minutes earlier.

              Comment


              • Originally posted by JeffHamm View Post

                Unless the temperature is low enough to halt the chemical reactions that produce rigor, rigor begins at the point of death (for all intents and purposes). The rate at which those chemical reactions proceed determines, in part, the point at which an observer will "detect them" by touch (i.e. by finding that the limbs are "stiff", actually, eyelids are the best place to check for onset it appears; small muscles are easier to detect rigor in than larger ones). Also, "detecting rigor" will also depend upon who is checking, because it is a decision, and we all set a different criterion. You and I might be presented with the same body, and I might say "yes, rigor has started" and you might, with the same information, say "no it hasn't", because it is within some boundary zone and our thresholds are different. Annie Chapman's murder has a lot of factors about it that are know to influence how rigor sets in and progresses, but we are missing the vital details to allow us to work out what we should expect (should it be slower, faster, about typical?). Add on to that the wide range of times that rigor type "evidence" gives us, there's not much we can do (mind you, if I had the right data set as a model for her murder, I could work magic! ) From what we have, and using a typical progression of rigor, things land on the side of the witnesses. Change that model, though, and it could fall the other way. But then, we would still have their statments, which keep pushign towards 5:25 ish.

                By the way, Long testified she set the time by the Brewer's clock after she passed the couple she saw. So even if she correctly remembers the chime as the half hour chime, it was 5:30 after she passed that couple - so she saw them before 5:30 (closer to Cadosch's time). And if she heard that chime only 5-7 minutes after walking passed them, there is no problem with her testimony as given.

                - Jeff
                To believe Long...in any shape or form... you must disbelieve Cadosche, there is no middle ground there. He heard a sound which must have come from 29's yard, and then heard another sound from the same spot around 10 minutes later, its highly unlikely that Annie and her killer arrived after that time, (time to kill, mutilate and then wildly confuse Phillips), and there would be no-one standing over an already dead Annie when "no" or the thud was heard. I would back Cadosche over Long in a second, if for no other reason than what his statement includes are human sounds on the spot where Annie is found less than an hour before she is found there.

                People oddly seem to believe that there were dramatic differences in the way people dressed or looked, using Annies ID by Long as the example. Annie was not attired in anything unusual. That might have added some credence to her statement if she had been. Same goes for Lawende, and he didn't even see Kates face.
                Michael Richards

                Comment


                • Originally posted by Joshua Rogan View Post

                  It's a small point (my speciality), but most papers reported her as saying she heard the chimes just before passing the couple, I think only the Morning Advertiser has it the other way around.

                  Eg the Telegraph;
                  "I heard the brewer's clock strike half-past five just before I got to the street"

                  and later;
                  "You are certain about the time? - Quite.
                  What time did you leave home? - I got out about five o'clock, and I reached the Spitalfields Market a few minutes after half-past five."

                  ​​​​​​​The clock on Spitalfields church (from which Cadosche noted his time) can clearly be seen from the market side of Commercial Street. However, since she doesn't mention actually seeing a clock, Long may have simply inferred her arrival time from the chimes she heard a couple of minutes earlier.
                  Hi,

                  Hmm, yes, I think that's probably right. The Times reads "She was certain of the time, as the brewers' clock had just struck that time when she passed 29, Hanbury Street.", which I had read as striking when she was past it, but yes, re-reading it I see that it in all likelihood is her meaning at about the time she was walking by #29.

                  That just leaves us with either the couple being two other people (making her identification of Chapman, erroneous), or she's misremembered hearing the quarter hour chime as the half hour chime. I'm not saying she would have made that error at the time, only that when she thought back about it to recall the events, her memory for the chime was wrong.

                  - Jeff

                  Comment


                  • Originally posted by Michael W Richards View Post

                    To believe Long...in any shape or form... you must disbelieve Cadosche, there is no middle ground there. He heard a sound which must have come from 29's yard, and then heard another sound from the same spot around 10 minutes later, its highly unlikely that Annie and her killer arrived after that time, (time to kill, mutilate and then wildly confuse Phillips), and there would be no-one standing over an already dead Annie when "no" or the thud was heard. I would back Cadosche over Long in a second, if for no other reason than what his statement includes are human sounds on the spot where Annie is found less than an hour before she is found there.

                    People oddly seem to believe that there were dramatic differences in the way people dressed or looked, using Annies ID by Long as the example. Annie was not attired in anything unusual. That might have added some credence to her statement if she had been. Same goes for Lawende, and he didn't even see Kates face.
                    To believe Long in every detail is to disbelieve Cadosch. However, all it takes is one error of memory (Long misremembers hearing the quarter hour chime as the half hour chime), and suddenly she and Cadosch fit together nicely.

                    Obviously, it can't be proven that her memory for the chime was incorrect, but if we take her time as correct, then we have to disregard her identification of Chapman's body (and she did see Chapman's face, it was the man who was back on to her). That, to me, seems a bigger stretch than a memory error for the time, but it is also possible of course.

                    - Jeff

                    Comment


                    • Originally posted by JeffHamm View Post

                      To believe Long in every detail is to disbelieve Cadosch. However, all it takes is one error of memory (Long misremembers hearing the quarter hour chime as the half hour chime), and suddenly she and Cadosch fit together nicely.

                      Obviously, it can't be proven that her memory for the chime was incorrect, but if we take her time as correct, then we have to disregard her identification of Chapman's body (and she did see Chapman's face, it was the man who was back on to her). That, to me, seems a bigger stretch than a memory error for the time, but it is also possible of course.

                      - Jeff
                      I think what you've not factored in is the proximity to the actual murder site factor Jeff. Which is what tips the scales towards Cadosche. If someone was alive in that yard at 5:15, then it was almost certainly Annie and her killer. That would eliminate Long, even with "allowances".
                      Michael Richards

                      Comment


                      • Originally posted by JeffHamm View Post

                        Hi Trevor,

                        We agree! (yes I'm back from quizz - we came 4th, so close until the last round; but I digress). And,to be clear, I fully agree with your concerns about what I presented. I hope everyone has noted that I have been clear in that the data I'm working from is not suitable. Why?

                        I'm using as a model of "complete rigor" times to decide if Annie Chapman, specifically, fits that model. Well, guess what, there are so many things about Annie Chapman's murder that make her unilke the data I'm using that - those conclusions are as unsafe as Dr. Phillips. I'm comparing apples with oranges.

                        Look, we know, low temperatures slow rigor mortis progression, and we know Chapman was not kept at the temperatures that the data set I've used would have been, so that alone should make you question the inferences I've suggested (though I warned you; I have been careful to say, a few times, this data is not a good comparison).

                        If the rate of rigor, and therefore the time that Annie Chapman reaches full rigor, depends upon temperature, slowing the time to full rigor, then the "time to reach full rigor" data I have won't apply, so all bets are off.
                        ,
                        But if murder by cut throat, etc, speeds up rigor onset, then again, the data I've used still isn't a good model for this case.

                        We do not know when she reached full rigor (so we are missing critical data).
                        We do not know if temperature (slowing rigor) or other factors (speeding up rigor) has the bigger effect in this case, so we do not know the actual expected progression (so we're also missing more critical information).

                        I want to restate, to make it very clear, the previous analyses are not "real", they are just "what would need to be done", if we had the information. But we're not going to find research on "death by throat cutting with disembolwed bodies partially exposed to cold temperatures", which is really what we need to do anything that won't have a margin of error so wide as to be not worth the time (unless, like me, it's worth it for the enjoyment of trying to extract something out of real data).

                        Change, however, one thing (believe that with Annie Chapman rigor progressed faster than in the data set I've presented), and nothing that it may appear I've suggested "works".

                        But I want to once again emphasize, I'm not saying the previous is "true", I'm trying to demonstrate what sort of analysis would allow us to draw inferences. But without date from cases similar to Chapman's, we can't do that.

                        Basically, if I came across as suggesting "this is true", shake your head, that's smoke and mirrors. What I presented only works if - all the factors that suggest rigor should progress faster are cancelled exactly by all the factors that suggest it should progress more slowly. And that situation is so unlikely that it makes my analyse nothing more than "playing", as Trevor rightly noted. I am playing, I'm not proselytizing.

                        However, to explain why I spent time on this, it does tell us that that rigor seems to follow a "log normal" progression over time. That gives us reason to expect that if Annie Chapman's specific case leads to a faster or slower progression of rigor, that it would still follow a log normal type of equation. I just don't know how to adjust the model to fit that, and how the model gets adjusted to fit this specific case is critical with respects of the conclusions one draws. I'm basically using a model that is based upon the idea that the factors that speed up rigor progression (which we know there are some) are pretty much cancelled by the factors that slow it down (which we also know there are some). If one side of that balance scale is greater than the other, then what I've presented is rubbish.

                        It's a highly qualified analysis, and I don't want anyone, on either side of the debate, to view it as anything other than that.

                        - Jeff
                        Actually, I think there are some things we can infer, with caution, even if the rate of Annie's rigor differs from the normal progression (which is what the analysis is based upon).

                        First, we do have to make one assumption, which is, that if the rate of progression is sped up or slowed down, it still follows a log normal function. I've changed the model to produce a hypothetical faster and slower progression series (basically, in the function =NORMSDIST((LN(A1-0.648)-1.38)/0.527), the -1.38 is changed to -1.6 to produce a slower rate, and to -1.2 to produce a faster rate, all the other values are kept the same. These are pretty arbitrary changes just to illustrate, but I chose values where all series had a high likelihood of reaching full rigor in the 8 hours between when she was found around 6 and when Dr. Phillips noted it at 2 (and these functions give 77%, 88%, and 93% for slower, normal, and faster progressions. And given she must have died earlier than that, those would go up to 84%, 92%, 96% from the witness time, and 89%, 95%, 97% for Dr. Phillips time. So while the faster and slower functions are made up, I did want them to be something that isn't terribly unrealistic. All of them produce a high probability that full rigor would be observed by 2.

                        But as you can see, things don't change much in terms of which time window is the more likely of the two when we use "time of full rigor" to work backwards to estimate the likely ToD. So, while we don't know the exact rate we should be considering with respect to Annie Chapman's case, it is mostly likely a rate that follows a log normal distribution. And depending upon when she did reach full rigor (which we don't know of course), determines which of the times is the more probable (basically, until you shift the curves to about the point where the peaks line up with Dr. Phillips time, the witness time window is the more likely.

                        Now, it would be a bit more complicated then that, as we also would have to take into the account the fact that reaching full rigor by 2 is more probable based upon Dr. Phillips time. Working out the relatively likelihoods needs to factor in both the probability of reaching full rigor by 2 (which favors Dr. Phillips time), and the probability of ToD on the bases of having reached full rigor by 2 (which favor the Witness time).

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                        As I say, the "faster and slower" functions are illustrative only.

                        - Jeff

                        Comment


                        • Iím 99% convinced that Cadosch and Richardson were correct. Long appears to be a creditable witness who actually saw Chapmanís at the mortuary and had no reason to lie but obviously there is a clash of times but, for me, a far from an insurmountable clash. We all know from knowledge of the times that timings shouldn't be considered concrete. We have to allow for an error factor with people that didnít own watches or clocks. All we have to concede is that both Long and Cadosch could easily have been 7 or 8 minutes out. Giving us the possibility of:

                          Long sees Chapman and her killer at 5.25(approx)

                          As soon as she passes they enter the yard.

                          Cadosch hears the Ďnoí at 5.26 (approx)

                          Cadosch hears the noise at 5.30 (approx)

                          He leaves the house at 5.31 (approx)

                          He passed the Church just before 5.40 (instead of just before 5.35)


                          These arenít exactly massive changes. I think itís plausible. No certainties of course but plausible.













                          Comment


                          • Hi all,

                            Ok, I'm having way too much fun with this, but I wanted to try a Bayesian type analysis. Basically, what you end up with is a value something like a probability, which indicates which of two theories is considered more strongly supported by the evidence (meaning, given we have a particular piece of evidence which of two options should we believe is more strongly supported). Now, we've been tossing around ideas about the factors that speed up and slow down the progression of rigor, and in Chapman's case we know we have things that should slow it down (low temperature) and speed it up (things like cut throat death, and others that have been mentioned). Now, her actual rate of rigor progression will depend upon how all of those factors combine, and they could either result in a slower than typical rate (the cold has greater influence than the others), a faster rate (the cold has less of an influence than the others), or end up being typical after all (the two sets of forces tend to cancel each other).

                            Now, I've been drawing from a published table of data that gives us a model of the typical progression of rigor in terms of the amount of time after death that full rigor is reached. Dr. Phillips examined her at 6:30 (ish) and notes that he detected rigor beginning, but she was not in a full state of rigor, while at 2 o'clock she was.

                            The data allows me to work out the probability of reaching full rigor after various amounts of time have passed since death under the typical circumstances, and I made some hypothetical models to simulate slower and faster rates. I'll only show the results based upon the typical rate of progression because the end results lead to the same conclusion.

                            Now, we have 2 competing theories for the ToD; 4:30 or 5:30 (Dr. Phillips and Witness times, respectively). When Dr. Phillips examined Annie at 6:30, that point in time is either 2 hours or 1 hour after she died, pending upon which time window is correct. Very very few cases typically reach full rigor in 2 hours (about 2%), but far fewer reach full rigor after only 1 hour (0.0002%). So, if she actually were in full rigor at that time that would be far more supportive of Dr. Phillips because 2% is 10,000 times more probable than 0.0002%. That 10,000:1 odds is converted to a probability type value by simply going (10000/(10000+1), so we end up with something that's pretty much 1, and that would be very strong support for Dr. Phillips' time. (the converse, say 1:10,000 would be support for the Witness time, as then the probability ends up being 0.0001/(0.0001+1), which is very close to 0 (so Dr. Phillips time would be rejected in that case.

                            Now, when that probability value is 0.5, it means the data is "non-informative", it's equivocal and either theory is able to account for it equally well. In my own research publications I've recommended that anything between 47.5 and 52.5 should be viewed as equivocal. Then others (Raftery), have suggested ranges such as 0.25-0.75 would be viewed as weak evidence, 0.05-0.95 would be positive evidence, 0.01-0.99 would be strong evidence, and 0-1.00 is very strong (I hope it's obvious these are bands, so something that has a value of 0.51 is in the equivocal band only, it's not in "all of them"; start with equivocal and work your way "up" until you locate the band that contains your value, and then stop.

                            Anyway, using the typical progression I compared the probabilities of reaching full rigor from 6:30 on based upon a ToD of either 4:30 or 5:30.

                            Now, there is always going to be a larger probability for reaching full rigor as more time passes, so the onset of rigor can never actually support the witness time since the probability will always be greater if you have an additional hour. However, that doesn't mean the evidence can't become equivocal, (if the probability of rigor is 99.8% vs 99.9% one would hardly say there's a difference after all).

                            So to be clear, what we're looking at is a measure of the weight of the evidence, and the closer it gets to 1 the more strongly it supports Dr. Phillips, and once it gets close to .5 it becomes non-informative. I've marked the eqivical range in red, the change from weak to positive in blue, and the change from positive to strong in yellow. I've not put the "very strong" in as it's hard to see anyway.

                            Also, these values represent what it would mean IF she reached full rigor at the corresponding time. So had Dr. Phillips found her at 6:30 to be in full rigor, that would have been strong support for his time window (not that rigor was detectable, but in full rigor). We know she wasn't, so I've marked that point in red.

                            now at 2, when he did note she was in full rigor, that's easily explainable by either ToD estimate, there's been more than enough time go by that both times would expect her to be in full rigor. (And basically, for the fast and slow hypothetical models I posted earlier, the exact some thing happens, though faster rigor onset does lower the values a bit and slower progression raises them a bit (so slower progression supports Dr. Phillips and faster progression favors the Witness time line; but regardless, by 2 o'clock she is expected to be in full rigor so that data does not help us - its always equivocal by 2; the green marker).

                            Now, if we only had the actual time she did reach full rigor, if was before 11:30 then the time to reach full rigor would start to favor Dr. Phillips, and the earlier full rigor is reached before 11, the more that favors him. But we don't have that information (non filled markers), and if she reached full rigor after 11:30, then it becomes non informative.

                            In short, though too late for that really, Dr. Phillips observation that she wasn't in full rigor at 6:30 works for both times, and the fact that she was at 2 also works for both time windows. The rigor data that we have does not differentiate between them, although as you can see, it potentially could have if we had the information about when she did reach full rigor (and of course a more suitable model for its rate of progression) . But we don't have either of those. What we have is data that fits both times, even if rigor was faster or slower than typical.

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                            - Jeff

                            Comment


                            • Originally posted by Michael W Richards View Post

                              I think what you've not factored in is the proximity to the actual murder site factor Jeff. Which is what tips the scales towards Cadosche. If someone was alive in that yard at 5:15, then it was almost certainly Annie and her killer. That would eliminate Long, even with "allowances".
                              Well, yes, if someone was in the yard at 5:15 then even if Long misremembered the chime and her sighting was at 5:15 then she still saw two other people. But there's no evidence to suggest anyone was in the yard at 5:15. Cadosch testifies he got up at 5:15, so he wasn't in the yard to hear anything at that time. He went out to the toilet at some point after 5:15 and heard voices and the word "no", went back inside and came out again 3 or 4 minutes later, and heard the noise against the fence. If he got up at 5:15, give a few minutes for him to get dressed and go outside the first time, he seems to have entered the yard around 5:18 to 5:20, and returned to it to hear the thump closer to 5:25ish. But that means there's time after Long's sighting (presuming it was at 5:15 here) and before Cadosch enters the yard the first time for the couple she saw to go from the front of the house to the back yard.

                              That would fit quite well with Long's sighting if her time is wrong and she actually heard the 5:15 chime and only misremembers it as the 5:30 one. I don't know if she did misremember it, of course, but I do know that sort of memory error is very common.

                              - Jeff

                              Comment


                              • Now, doing the same thing as I did with the cumulative data, I've put together the Bayesian comparison of the time windows on the basis of assuming full rigor occurred at different times and then, using the reverse density functions, getting the probability for each time window and comparing those. And, as I mentioned earlier, if she reached full rigor shortly after Dr. Phillips examined her that would be more in line with Dr. Phillips, but at longer delays (once the "hump" is to the right of both ToD estimates) that actually favors the witnesses. And, as you can see, that's exactly what the Bayesian analysis produces. If Chapman reached full rigor before 9 am, that would favor Dr. Phillips time window, but if she reached full rigor after 9 am, that would be in favour of the witness ToD. But, it also shows that at best, this data could only provide weak support for the witness ToD window, but could have potentially provided very strong evidence in favour of Dr. Phillips. We know one of those very strong time points was actually tested and rule out (she wasn't in full rigor at 6:30 - but that's hardly surprising as that would be very rare to occur, but if it had it would be nearly impossible if she died at 5:30, but not nearly so impossible if she died at 4:30; however, that didn't happen, so I'm just trying to explain what this analysis is doing and how it works). Anyway, we know she was in full rigor by 2, and while that might look like weak evidence in favour of the witnesses, we have to remember that measurement is not when she reached full rigor, it's only when Dr. Phillips checked her out. Had he done his exam at 3 insead of 2, we would have a marker at 15 and that would be the one filled in (even though as we know, she was already in full rigor by 2).

                                What we would really like to know is, at what time did she reach full rigor as that is the point in time that we want to look at. Mind you, with our luck, it would be 9 o'clock, the one point in time that doesn't help us.

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                                - Jeff

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