Issue with Simpson's Paradox

[GregoryGelfond]

Consider the following representation of Simpson's Paradox:

% Probability Distribution

0.5::male.

0.6::recover :- male, drug.
0.7::recover :- male, not drug.
0.2::recover :- not male, drug.
0.3::recover :- not male, not drug.

0.75::drug :- male.
0.25::drug :- not male.

% Queries and Observations

do( drug ).

query(recover).

With this query I seem to get a probability of 0.45 (instead of my expected 0.4). Also, when I query with do(\+ drug) I seem to get the same result. If the file is in simpson.problog then the command I'm using is problog simpson.problog. Am I doing something wrong here?

[VincentDerk]

Hi, without adding any evidence on drug, my manual computation adds up to 0.45 so it seems correct to me.

male, drug, recover = 0.5 * 0.75 * 0.6 = 0.375 * 0.6 = 0.225
male, not(drug), recover = 0.5 * 0.25 * 0.7 = 0.125 * 0.7 = 0.0875
not(male), drug, recover = 0.5 * 0.25 * 0.2 = 0.125 * 0.2 = 0.025
not(male), not(drug), recover = 0.5 * 0.75 * 0.3 = 0.375 * 0.3 = 0.1125

prob(recover) = 0.1125 + 0.025 + 0.0875 + 0.225 = 0.45

Regarding do, I assume you mean evidence. Adding

evidence(drug).

yields 0.5 and

evidence(drug, false).

yields 0.4. I did not check those numbers but I assume they should be correct.

[GregoryGelfond]

Evidence seems to have the semantics of observations (i.e., non-destructive information), whereas do/1 conveys information that actually severs causal connections in the bayesian network.

I'm trying to go off of the examples posted here: https://dtai.cs.kuleuven.be/problog/tutorial/various/14_robot_key.html

Does problog only support evidence/2?

[rmanhaeve]

As you can see in the example you posted, the semantics of do/1 is explicitly encoded in the rules. You would have to do something similar in your example.