the gipster: JFK Witness Deaths: Calculating the Probabilities

Saturday, May 18, 2013

JFK Witness Deaths: Calculating the Probabilities

JFK Witness Deaths: A Guide to the Probability Calculations
Richard Charnin
May 15, 2013
An actuary engaged by London Sunday Times calculated 100,000 TRILLION to 1 odds of 18 JFK material witness deaths from Nov. 1963 to Feb. 1967. In dismissing the calculation as invalid, the House Select Committee on Assassinations (HSCA) made a number of fundamental errors:
1) considered just 21 of 46 deaths in the three years, failing to include Oswald, Ruby, Ferrie, etc.
2) did not specify that the deaths were UNNATURAL
3) did not consider witness CONNECTIONS to the case and MOTIVATION for their elimination
4) ignored the need to utilize UNNATURAL MORTALITY RATES
5) falsely stated that the UNIVERSE of witnesses was UNKNOWABLE
6) ignored the KNOWN UNIVERSE of 552 Warren Commission witnesses:14 unnatural, 10 suspicious deaths
7) ignored the SUSPICIOUS deaths in 1977 of 7 top FBI officials called to testify at HSCA
8) did not question why no one at the London Times knew the actuary’s name
9) failed to show the actuary’s ASSUMPTIONS and calculation METHOD
10) did not consider using the POISSON distribution function to calculate probabilities
The HSCA succeeded in misinforming the public by falsely claiming that the actuary’s calculation was invalid and therefore did not prove a conspiracy.

The key to calculating the probability of a given number (n) of unnatural deaths occurring in a given group (N) in a given time period (T) is to recognize that it is based on the difference between expected and actual unnatural deaths. The larger the discrepancy between the actual observed and expected number of deaths, the lower the probability.
These are the relevant probability input parameters:
N= total number of witnesses
n= number of observed unnatural deaths
T= time period in years
R= unnatural mortality rate
These tables in the JFK Witness Spreadsheet Database display unnatural death probabilities for 552 Warren Commission and 1400 material witnesses based on unnatural, weighted and homicide mortality rates over 3, 7 and 14 year time intervals.

In 1963, the annual national homicide rate was 6 per 100,000 (0.00006). At least 4 of the 552 Warren Commission witnesses were murdered in the first 3 years after the assassination. The equivalent Warren Commission rate was 0.0024 =4/(552*3) or 240 per 100,000 (40 times the national rate).
If the 5 accidental deaths and 1 suicide in the three year period were actually homicides, then the equivalent Warren Commission rate was 0.006038 = 10/(552*3) or 603 per 100,000 (100 times the national average).

The Poisson Distribution calculates the probabilities of rare events over time.
We must first calculate E, the expected number of unnatural deaths: E= N*R*T
The probability of EXACTLY n unnatural deaths is: P = POISSON (n, E, false).
The probability of AT LEAST n deaths is P = 1- POISSON (n-1, E, true)
EXAMPLE:
The probability of AT LEAST 14 Warren Commission witness homicides in the 14 years from 1964-77:
E = 0.479 = N*T*R = 552*14*0.000062
P = 1 – Poisson (13, 0.479, true)
P = 4.44E-16 = 1 in 2,251,799,813,685,248
P = 1 in 2251 trillion

According to the reference “Who’s Who in the Kennedy Assassination”, there were approximately 1400 material witnesses connected in any way to the assassination. It is a fact that 552 witnesses testified at the Warren Commission.

The published unnatural mortality rates are:
homicide 0.000062 (in 1963)
suicide 0.000107
accident 0.000359
Unknown 0.000014
Total 0.000542 (unweighted rate)
The unnatural mortality rates used in the probability calculations are:
1) 0.000542 total unweighted rate (national rate – conservative)
2) 0.000163 weighted average rate (based on official cause of JFK witness unnatural death)
3) 0.000062 homicide rate (assumes all suicides and accidents were actually homicides)
Of the 72 unnatural deaths in the 107 JFK-related material witness database, 39 were homicides, 10 suicides and 23 accidents. The weighted unnatural mortality rate is calculated as:
R = 0.000163 = (39 * 0.000062 + 10 * 0.000107 + 23 * 0.000359) / 72
If the JFK unnatural deaths were in the same proportion as the national death rates, the 0.000542 unweighted rate would be the one to use. But the JFK-related deaths were mostly homicides, so the 0.000163 weighted rate is more appropriate – and results in lower probabilities. If we assume all the unnatural deaths were homicides (0.000062), the probabilities are at their lowest.
Probability of AT LEAST 10 Warren Commission unnatural witness deaths over 3 years:
1) unweighted: 3.0E-08 (1 in 33 MILLION); Expected = 0.87
2) weighted: 4.4E-13 (1 in 2.2 TRILLION); Expected = 0.27
3) homicide: 3.2E-17 (1 in 31,000 TRILLION vs. actuary 1 in 100,000 TRILLION); Expected = 0.1
Probability of 72 unnatural deaths of 1,400 material witnesses over 14 years:
1) unweighted: 3.9E-36 (1 in a TRILLION TRILLION TRILLION); Expected = 10.27
2) weighted: 1.4E-69 (1 in a TRILLION TRILLION TRILLION TRILLION TRILLION); Expected = 3.19
3) homicide: 6.0E-99 (1 in a TRILLION TRILLION TRILLION TRILLION TRILLION TRILLION TRILLION TRILLION); Expected = 1.22
For Warren Commission advocates who believe the universe of witnesses exceeds 1,400, the probability of 72 unnatural deaths OVER 14 YEARS assuming 10,000 material witnesses:
1) unweighted: 4.6E-02 (1 in 22); Expected = 74
2) weighted: 1.3E-16 (1 in 8,000 TRILLION); Expected = 23
3) homicide: 1.0E-40 (1 in 9,000 TRILLION TRILLION TRILLION); Expected = 9