‐
Lab
3
Part
2
Q5
P (Meltdown) = 0,02578 P(Meltdown  Ica weather) = 0.03472 b) Suppose
that
both
warning
sensors
indicate
failure.
What
is
the
risk
of
a
meltdown
in
that
case?
Compare
this
result
with
the
risk
of
a
melt‐down
when
there
is
an
actual
pump
failure
and
water
leak.
What
is
the
difference?
The
answers
must
be
expressed
as
conditional
probabilities
of
the
observed
variables,
P(Meltdown...).
P(Meltdown  PumpFailureWarning, WaterLeakWarning) = 0,14535 P (Meltdown  PumpFailure, WaterLeak) = 0,2 c) The
conditional
probabilities
for
the
stochastic
variables
are
often
estimated
by
repeated
experiments
or
observations.
Why
is
it
sometimes
very
difficult
to
get
accurate
numbers
for
these?
What
conditional
probabilites
in
the
model
of
the
plant
do
you
think
are
difficult
or
impossible
to
estimate?
a)
What
is
the
risk
of
melt‐down
in
the
power
plant
during
a
day
if
no
observations
have
been
made?
What
if
there
is
icy
weather?
It is hard to fully understand all possible factors that can effect or trigger an event and how they interact with each other. Observations are always a description of the past and is not always accurate in forecasting the future. E.g. Icy weather is not a thing you can measure and span over a wide range of weather conditions including combinations of precipitation, wind and temperature. d) Assume
that
the
"IcyWeather"
variable
is
changed
to
a
more
accurate
"Temperature"
variable
instead
(don't
change
your
model).
What
are
the
different
alternatives
for
the
domain
of
this
variable?
What
will
happen
with
the
probability
distribution
of
P(WaterLeak

Temperature)
in
each
alternative?
The domain decreases in size of possible states as for example precipitation and wind is no longer a part of the estimations. The temperature will be represented as an absolute number or intervals, instead of just true or false. Resulting in a lot more defining of the probabilities of the child nodes with aspect to each value/interval of temperature.
Q6
a)
What
does
a
probability
table
in
a
Bayesian
network
represent?
The probability table shows the probability for all states of the node given the states of the parent nodes. b) What
is
a
joint
probability
distribution?
Using
the
chain
rule
on
the
structure
of
the
Bayesian
network
to
rewrite
the
joint
distribution
as
a
product
of
P(childparent)
expressions,
calculate
manually
the
particular
entry
in
the
joint
distribution
of
P(Meltdown=F,
PumpFailureWarning=F,
PumpFailure=F,
WaterLeakWaring=F,
WaterLeak=F,
IcyWeather=F).
Is
this
a
common
state
for
the
nuclear
plant
to
be
in?
Kedjeregeln ger följanade:
P(alla är falska) = P(ICYWEATHER) * P(PUMPFAILURE) * P(PW  PUMPFAILURE) * P(MELTDOWN PUMPFAILURE, WL) * P(WL  ICYWEATHER) * P(WATERLEAKW  WL) = 0,95 * 0,9 * 0,95 * 1 * 0,9 * 0,95 = 0,69 Ja, detta är ett vanligt tillstånd. c) What
is
the
probability
of
a
meltdown
if
you
know...