Biology Reference
In-Depth Information
,
because as the coin is flipped more and more times, the observed
proportions of heads become on average closer and closer to
experiment, the probability that a coin will come up heads is
φ
φ
. In
the Bayesian view, a coin does not pose as a constant
; instead, the
probability that a coin should come up heads is viewed as a current
state of knowledge, like, for example, the physics of the situation
and a number of test flips. Cox
15
gives a short comparative intro-
duction to the two schools.
One can also differentiate between parametric and nonpara-
metric statistics. In parametric statistical modeling, one assumes
that the variables being determined belong to known parametric
probability distributions such as, for example, the normal distribu-
tion. In contrast, nonparametric models do not rely on assump-
tions that the data are a realization of a particular distribution.
A histogram is an example of a nonparametric estimate of a
probability distribution.
Given the number of possible approaches to tree building, it is
no surprise that there is a great and increasing number of tree
building methods. In the following, we review some popular ones.
φ
•
Unweighted pair group method using arithmetic averages
(
UPGMA
).
UPGMA is a classic, greedy, bottom-up clustering algo-
rithm. It is a very fast distance method and produces ultrametric trees.
At the beginning of the algorithm, each object is in its own cluster.
At each step, the two closest clusters are merged and the distances are
updated. The distance between clusters
U
and
V
is taken to be the
average of all distances between pairs of objects in
U
and
V
. UPGMA
does not use a statistical method. It is designed to construct the cor-
rect tree given that the input data are ultrametric and exact. If the
data do not behave like a molecular clock, then UPGMA may pro-
duce the wrong tree, even for simple quartets and exact distances.
Here is an example. Given the pairwise distances of the tree UPGMA
A
C
2
2
1
6
6
D
B
