This document will cover two aspects:
This document will cover two aspects:
1. The values to be attached to the probability tables, and
2. The formulae to be used to compute the probabilities that are required.
Probability table specification In total there are 16 nodes for the Car diagnosis Bayesian network. This means that 16 probability tables are
required. These tables must be assigned values according to the specifications below.
1. Battery age table
ba _y 0.2 ba_n 0.8
2. Alternator broken table
ab_y 0.1 ab_n 0.9
3. Fanbelt broken table
fb_y 0.3 fb_n 0.7
4. Battery dead table
ba_y_bd_y 0.7 ba_y_bd_n 0.3 ba_n_bd_y 0.3 ba_n_bd_n 0.7
Note that this table represents conditional probabilities. Thus for example, the row ba_y_bd_y=0.2 should be
interpreted as the Pr(battery being dead|battery is aged) is 0.2. All other tables below which have more than two
rows also happen to represent conditional probabilities.
5. No charging table
ab_y_fb_y_nc_y 0.75
ab_y_fb_n_nc_y 0.4
ab_n_fb_y_nc_y 0.6 ab_n_fb_n_nc_y 0.1 ab_y_fb_y_nc=n 0.25 ab_y_fb_n_nc=n 0.6 ab_n_fb_y_nc=n 0.4 ab_n_fb_n_nc=n 0.9
6. Battery meter table
bd_y_bm_y 0.9 bd_y_bm_n 0.1 bd_n_bm_y 0.1 bd_n_bm_n 0.9
7. Battery flat table
bd_y_nc_y_bf_y 0.95
bd_y_nc_n_bf_y 0.85
bd_n_nc_y_bf_y 0.8 bd_n_nc_n_bf_y 0.1 bd_y_nc_y_bf_n 0.05 bd_y_nc_n_bf_n 0.15 bd_n_nc_y_bf_n 0.2 bd_n_nc_n_bf_n 0.9
8. No oil table
no _y 0.05 no_n 0.95
9. No gas table
ng _y 0.05 ng_n 0.95
10. Fuel line blocked table
fb _y 0.1 fb_n 0.9
11. Starter broken table
sb _y 0.1 sb_n 0.9
12. Lights table
l_y_bf_y 0.9 l_n_bf_y 0.3 l_y_bf_n 0.1 l_n_bf_n 0.7
13. Oil lights table
bf_y_no_y_ol_y 0.9
bf_y_no_n_ol_y 0.7
bf_n_no_y_ol_y 0.8 bf_n_no_n_ol_y 0.1 bf_y_no_y_ol_n 0.1 bf_y_no_n_ol_n 0.3 bf_n_no_y_ol_n 0.2 bf_n_no_n_ol_n 0.9
14. Gas gauge table
bf_y_ng_y_gg_y 0.95
bf_y_ng_n_gg_y 0.4
bf_n_ng_y_gg_y 0.7 bf_n_ng_n_gg_y 0.1 bf_y_ng_y_gg_n 0.05 bf_y_ng_n_gg_n 0.6 bf_n_ng_y_gg_n 0.3 bf_n_ng_n_gg_n 0.9
15. Car won’t start table
This table has 64 rows. There are 3 cases to consider:
1. For every combination of bf, no, ng, fb, sb with at least one of these variables taking the value y, the
probability is 0.9 for the cs_n outcome.
2. For the case when all 5 variables bf, no, ng, fb, sb take the value n with cs_n. In this case the probability is 0.1
3. The remaining case is when cs_N. The probabilities are now defined as the complement of the probabilities
of the first 32 rows. That is if the probability is p for the first row then it is (1-p) for the 33rd row, if it is q for
row 2 then it is (1-q) for row 34 and so on.
Note this table must be encoded in the graph with 64 rows and each row should have a probability as specified
above.
16. Dipstick low table
no_y_dl_y 0.95 no_n_dl_y 0.3 no_y_dl_n 0.05 no_n_d_n 0.7
Formulae for computation of probabilities In addition to the discussion below you are strongly advised to refer to the class notes on Bayesian learning.
Let us illustrate the computation of the probabilities by taking R2 as an example.
For R2 you are asked to compute P(-cs, +ab, +fb) – this is the joint probability that the car does not start whenever
both the alternator and fan belt are not functioning at the same time.
To understand how this is done, let us first look at a simpler situation.
P(+c, +a, +b) = P(+c|+a, +b)*P(+a)*P(+b)
Using this as a guide we can now work out P(-cs, +ab, +fb)
