\@doanenote {1}
macro:->One
of
us
(LH)
has
a
personal
story
about
how
statisticians
believe
you
can't
do
anything
without
an
explicitly
stated
stochastic
model.
He
was
giving
a
paper
in
the
1990s
(in
Switzerland,
no
less)
on
how
an
additive-tree
representational
structure
could
be
fit
to
a
proximity
matrix
based
on
an
$L_{1}$
criterion
(i.e.,
the
sum
of
absolute
differences
between
the
given
proximities
and
the
obtained
additive-tree
distances
was
minimized).
It
was
an
elegant
approach
(or,
so
he
thought),
based
on
a
recursive
dynamic
programming
algorithm
guaranteeing
global
optimality
for
the
obtained
solution.
In
fact,
he
believed
this
to
be
quite
the
coup
given
that
local
optimality
has
plagued
proximity
representations
forever.
The
first
question
from
the
audience
after
he
was
done,
and
from
a
close
colleague
at
one
of
his
academic
stops:
``and
do
you
have
a
stochastic
model
for
the
generation
of
the
proximities,
where
the
additive-tree
structure
could
be
characterized
through
parameters
that
could
then
be
estimated,
preferably,
through
maximum
likelihood?''
This
was
before
the
time
algorithmic
modelers
could
be
emboldened
by
Leo
Breiman's
``Two
Cultures''
paper.
So,
LH
softly
said
``no''
--
and
quietly
slinked
off
the
stage
and
back
into
his
seat.
\@endanenote
\@doanenote {2}
macro:->A
(slightly)
amusing
story
told
in
some
of
our
beginning
statistics
sequences
reflects
this
practice
of
postulating
a
\emph
{deus
ex
machina}
to
carry
out
statistical
interpretations.
Three
academics
--
a
philosopher,
an
engineer,
and
a
statistician
--
are
walking
in
the
woods
toward
a
rather
large
river
that
needs
to
be
crossed
The
pensive
philosopher
stops,
and
opines
about
whether
they
really
need
to
cross
the
river;
the
engineer
pays
no
attention
to
the
philosopher
and
proceeds
immediately
to
chop
down
all
the
trees
in
sight
to
build
a
raft;
the
statistician
yells
to
the
other
two:
``stop,
assume
a
boat.''
\@endanenote