# The values to be attached to the probability tables,

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)