3.2) Prior probability that Fido will howl
Query: P(FH)

Ordered hidden variables: NA, FM, FS, FB, NDG

Evidence set: []

Initial factors
f1(NA) = P(NA)
f2(FM) = P(FM)
f3(FS) = P(FS)
f4(FB,FS) = P(FB|FS)
f5(NDG,NA,FM) = P(NDG|NA,FM)
f6(FH,NDG,FM,FS) = P(FH|NDG,FM,FS)


Variable elimination output:

=============================

factorsWithHiddenVar: NA
==> Factor f1
Factor variables: ['NA']
Factor values:
[ 0.7  0.3]

==> Factor f5
Factor variables: ['NDG', 'FM', 'NA']
Factor values:
[[[ 1.   0.5]
  [ 0.6  0.2]]

 [[ 0.   0.5]
  [ 0.4  0.8]]]

==> Factor f7
productFactor variables: ['NA', 'NDG', 'FM']
productFactor values:
[[[ 0.7   0.42]
  [ 0.    0.28]]

 [[ 0.15  0.06]
  [ 0.15  0.24]]]

==> Factor f8
summedOutFactor variables: ['NDG', 'FM']
summedOutFactor values:
[[ 0.85  0.48]
 [ 0.15  0.52]]

=============================

factorsWithHiddenVar: FM
==> Factor f2
Factor variables: ['FM']
Factor values:
[ 0.96428571  0.03571429]

==> Factor f6
Factor variables: ['FH', 'FM', 'NDG', 'FS']
Factor values:
[[[[ 1.    0.5 ]
   [ 0.8   0.25]]

  [[ 0.6   0.1 ]
   [ 0.35  0.01]]]


 [[[ 0.    0.5 ]
   [ 0.2   0.75]]

  [[ 0.4   0.9 ]
   [ 0.65  0.99]]]]

==> Factor f8
Factor variables: ['NDG', 'FM']
Factor values:
[[ 0.85  0.48]
 [ 0.15  0.52]]

==> Factor f10
productFactor variables: ['FM', 'FH', 'NDG', 'FS']
productFactor values:
[[[[  8.19642857e-01   4.09821429e-01]
   [  1.15714286e-01   3.61607143e-02]]

  [[  0.00000000e+00   4.09821429e-01]
   [  2.89285714e-02   1.08482143e-01]]]


 [[[  1.02857143e-02   1.71428571e-03]
   [  6.50000000e-03   1.85714286e-04]]

  [[  6.85714286e-03   1.54285714e-02]
   [  1.20714286e-02   1.83857143e-02]]]]

==> Factor f11
summedOutFactor variables: ['FH', 'NDG', 'FS']
summedOutFactor values:
[[[ 0.82992857  0.41153571]
  [ 0.12221429  0.03634643]]

 [[ 0.00685714  0.42525   ]
  [ 0.041       0.12686786]]]

=============================

factorsWithHiddenVar: FS
==> Factor f3
Factor variables: ['FS']
Factor values:
[ 0.95  0.05]

==> Factor f4
Factor variables: ['FB', 'FS']
Factor values:
[[ 0.9  0.4]
 [ 0.1  0.6]]

==> Factor f11
Factor variables: ['FH', 'NDG', 'FS']
Factor values:
[[[ 0.82992857  0.41153571]
  [ 0.12221429  0.03634643]]

 [[ 0.00685714  0.42525   ]
  [ 0.041       0.12686786]]]

==> Factor f13
productFactor variables: ['FS', 'FB', 'FH', 'NDG']
productFactor values:
[[[[  7.09588929e-01   1.04493214e-01]
   [  5.86285714e-03   3.50550000e-02]]

  [[  7.88432143e-02   1.16103571e-02]
   [  6.51428571e-04   3.89500000e-03]]]


 [[[  8.23071429e-03   7.26928571e-04]
   [  8.50500000e-03   2.53735714e-03]]

  [[  1.23460714e-02   1.09039286e-03]
   [  1.27575000e-02   3.80603571e-03]]]]

==> Factor f14
summedOutFactor variables: ['FB', 'FH', 'NDG']
summedOutFactor values:
[[[ 0.71781964  0.10522014]
  [ 0.01436786  0.03759236]]

 [[ 0.09118929  0.01270075]
  [ 0.01340893  0.00770104]]]

=============================

factorsWithHiddenVar: FB
==> Factor f14
Factor variables: ['FB', 'FH', 'NDG']
Factor values:
[[[ 0.71781964  0.10522014]
  [ 0.01436786  0.03759236]]

 [[ 0.09118929  0.01270075]
  [ 0.01340893  0.00770104]]]

==> Factor f14
productFactor variables: ['FB', 'FH', 'NDG']
productFactor values:
[[[ 0.71781964  0.10522014]
  [ 0.01436786  0.03759236]]

 [[ 0.09118929  0.01270075]
  [ 0.01340893  0.00770104]]]

==> Factor f15
summedOutFactor variables: ['FH', 'NDG']
summedOutFactor values:
[[ 0.80900893  0.11792089]
 [ 0.02777679  0.04529339]]

=============================

factorsWithHiddenVar: NDG
==> Factor f15
Factor variables: ['FH', 'NDG']
Factor values:
[[ 0.80900893  0.11792089]
 [ 0.02777679  0.04529339]]

==> Factor f15
productFactor variables: ['FH', 'NDG']
productFactor values:
[[ 0.80900893  0.11792089]
 [ 0.02777679  0.04529339]]

==> Factor f16
summedOutFactor variables: ['FH']
summedOutFactor values:
[ 0.92692982  0.07307018]

=============================

factorsToMultiply: 1
==> Factor f16
Factor variables: ['FH']
Factor values:
[ 0.92692982  0.07307018]

=============================

==> Final answer:

['FH']
[F T] = [ 0.92692982  0.07307018]

Thus, Pr(FH) = 0.073