INTRODUCTION

I have read through many of the files here on the Crucible
regarding UFO's and the possible involvement of the United
States government with the same. Many of the documents (
such as the statement by John Lear and the Fenwick
interviews) make a number of claims, but seem to offer
little data to support those claims. What data is offered
seems inconclusive to me. With the scarcity of data on one
hand and a number of claims on the other hand, I am faced
with a dilemma.

I can reject the arguments put forth by Lear and others
that the U.S. government is involved with UFO's. To reject
thes arguments I must dismiss some evidence that is both
plausible and has no other explanation. I find this option
undesireable because some of the evidence supports the
claims of Lear et al and is hard to refute.

My alternative is to accept the claims of U.S. government
involvement with UFO's. To accept these arguments I must
accept some statements that have little supporting evidence.
I find such leaps of faith distasteful.

What other choices do I have? As I see it, I can use an
existing technique for examining the claims and the evidence
supporting them. That technique is Bayesian analysis. If
we convert the Lear statements into hypotheses, we can then
apply Bayes to the data. This process involves several
steps.


STEP 1

The only requirement for the hypotheses is that they be
mutually exclusive (one hypothesis can't encompass another)
and collectively exhaustive (taken together, the hypotheses
account for all possible explanations).

For example, the basic argument put forward by Lear is
that the U.S. government has had contact with UFO's since
the late 1940's and is not telling the truth about its
involvement. I would break this into several hypotheses:

1. The U.S. government has had contact with UFO's, is
providing no accurate information on its activities, and is
producing disinformation on the subject.

2. The U.S. government has had contact with UFO's, is
providing some accurate information on its activities, and
some disinformation on the subject.

3. The U.S. government has had contact with UFO's and
is providing totally accurate information on its activities.

4. The U.S. government has had no contact with UFO's,
is providing no accurate information on its activities, and
producing disinformation on the subject.

5. The U.S. government has had no contact with UFO's,
is providing some accurate information on its activities,
and some disinformation on the subject.

6. The U.S. government has had no contact with UFO's
and is providing totally accurate information on its
activities.

I think these six hypotheses are independent of one
another (mutually exclusive) and cover the range of
explanations (collectively exhaustive). Would anyone care
to add to, modify, or replace these hypotheses?


STEP 2

Now that we have some hypotheses, we must make an initial
assessment of their accuracy. The hypotheses must each be
assigned a value between zero and one. The sum of the
values for all of the hyotheses must equal one. [If you
aren't familiar with Bayes, most textbooks on statistics
have a section on it.] These values are then used with the
incoming data.

If you want to work on this yourself, use a columnar
worksheet (paper) or a spreadsheet (computer). Assign each
hypothesis on a row of the sheet. In the first column to
the right of the hypothesis, put your initial value. Set
aside the next column for your first piece of data.


STEP 3

With initial hypotheses in hand, we can now take each
piece of data and compare it to each hypothesis. We assign
a value between zero and one to the data for each
hypothesis. A value of zero for a given piece of data means
that it absolutely denies a hypothesis. A value of one
means that it absolutely supports a hypothesis. As you can
see, very few pieces of data will fit either extreme.
Instead, most data falls in between. [An example of a "one"
value piece of data might be the President of the United
States saying on national television that the U.S.
government has been in contact with EBE's and that until now
the government has been lying about it. This would rate a
1.0 for Hypothesis 1 above and a zero for Hypothesis 6.]

With six hypotheses, each datum must be evaluated six
times and assigned six value (once for each hypothesis). On
your worksheet (spreadsheet) put the value you have chosen
into the column to the right of the initial value (as
mentioned in Step 2 above). Multiply the initial value (
Column 1) by the new value (Column 2) and place the product
in the next column (Column 3). Add up the numbers in Column
3 and put the sum at the bottom of the column. [As you can
see, a spreadsheet becomes handy very quickly.] Now divide
each of the numbers in Column 3 by that sum at the bottom of
the column and place the quotient in Column 4. What you
should have should look something like this:

Hypotheses Initial Datum Product Revised
Value One Value
Hyp 1 0.2 0.4 0.08 0.24
Hyp 2 0.3 0.5 0.15 0.44
Hyp 3 0.1 0.2 0.02 0.06
Hyp 4 0.1 0.3 0.03 0.09
Hyp 5 0.2 0.1 0.02 0.06
Hyp 6 0.1 0.4 0.04 0.12
___ ____ ____
SUM 1.0 0.34 1.01*

* [Note round-off error. This sum should also equal 1.0]

This process can be continued for each new piece of data,
using the revised product of the previous datum as the
starting value for the next datum.


SUMMARY

I have participated in and led group problem-solving
efforts with these techniques. Bayesian analysis is
particularly useful for this type of problem. I can set up
this sort of spreadsheet in either Lotus 1-2-3 (.WKS) or
Microsoft format (SYLK). I think Tom will welcome this sort
of exchange on the Crucible. Let me know if you are
interested in helping.

I think this approach has considerable merit for the type
of problems that are presented by the Lear/Krill/Fenwick
statements. I welcome any individual or group efforts to
isolate and evaluate the data available. Without the sort
of approach I have described, I believe no serious
assessment and cooperation is possible. Ufology will
continue to spin its wheels with inconclusive data and
unproveable theories.

- Bill Badger

PART 2

The method I described in BAYES.TXT is intended as a tool for evaluating how
consistent various data are with a given set of hypotheses. It is not an
evaluation tool for the data itself. Data inputs must be accurate and
reliable, otherwise you are likely to get garbage.

For example, take President Reagan's remarks in Dec 1985 about, "Well, I
don't suppose we can wait for some alien race to come down and threaten
us...." Since this remark was widely reported, we can take it as both
accurate (it reflects what Reagan said) and reliable (checking it from several
sources gives the same answer). The issue then is consistency with our
hypotheses (from BAYES.TXT).

Hypothesis 1: US gov't contact, no disinformation. Reagan's remarks are
very inconsistent (20% correlation).

Hypothesis 2: US gov't contact, some disinformation. Reagans remarks are
very consistent (80% correlation).

Hypothesis 3: US gov't contact, all disinformation. Reagan's remarks are
fairly consistent (60% correlation).

Hypothesis 4: No US gov't contact, no disinformation. Reagan's remarks are
fairly consistent (60% correlation).

Hypothesis 5: No US gov't contact, some disinformation. Reagan's remarks
are somewhat consistent (40% correlation).

Hypothesis 6: No US gov't contact, all disinformation. Reagan's remarks
very inconsistent (20% correlation).

Let's apply these judgements to our model (I picked the initial values for
the sake of argument, not because I necessarily endorse them).

Hypotheses Initial Datum Product Revised
Value One Value
Hyp 1 10% 20% 2% 3.45%
Hyp 2 30% 80% 24% 41.38%
Hyp 3 25% 60% 15% 25.86%
Hyp 4 20% 60% 2% 20.69%
Hyp 5 10% 40% 4% 6.90%
Hyp 6 5% 20% 1% 1.72%

TOTAL 100% 0.58