Tddc17 - Lab 2 Search

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  • Topic: Probability, Bayesian probability, Event
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TDDC17
 -­‐
 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(child|parent)
  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...
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