Bayes Rule Using SQL

Question

Wanted to confirm the technique i am using to calculate the a-posterior probabilities of the following disease is correct for the following Bayes Network http://spark-public.s3.amazonaws.com/bigdata/documents/HW6.pdf

SELECT Dyspnoea.d, SUM(Dyspnoea.p*Either.p*Tuberculosis.p*Asia.p*p*Smoking.p*Bronchitis.p)
    FROM Dyspnoea
    INNER JOIN Either ON Dyspnoea.e = Either.e
    INNER JOIN Tuberculosis ON Either.t = Tuberculosis.t
    INNER JOIN Asia ON Tuberculosis.a = Asia.a
    INNER JOIN LungCancer ON Either.l = LungCancer.l
    INNER JOIN Bronchitis ON Dyspnoea.b = Bronchitis.b
    INNER JOIN Smoking ON LungCancer.s = Smoking.s AND Bronchitis.s = Smoking.s
    WHERE Asia.a = 1 AND Smoking.s = 0
    GROUP BY Dyspnoea.d

Or should it be calculated like this since some events are independent of each other

SELECT Dyspnoea.d, SUM(((Dyspnoea.p*Either.p*Tuberculosis.p*Asia.p)+(Dyspnoea.p*Either.p*LungCancer.p*Smoking.p)) + (Dyspnoea.p*Bronchitis.b*Smoking.p))
    FROM Dyspnoea
    INNER JOIN Either ON Dyspnoea.e = Either.e
    INNER JOIN Tuberculosis ON Either.t = Tuberculosis.t
    INNER JOIN Asia ON Tuberculosis.a = Asia.a
    INNER JOIN LungCancer ON Either.l = LungCancer.l
    INNER JOIN Bronchitis ON Dyspnoea.b = Bronchitis.b
    INNER JOIN Smoking ON LungCancer.s = Smoking.s AND Bronchitis.s = Smoking.s
    WHERE Asia.a = 1 AND Smoking.s = 0
    GROUP BY Dyspnoea.d

Answer 1

It works on the base of complete query.

The tables I used are:

CREATE TABLE `taba` (
  `A` char(1) DEFAULT NULL,
  `P` decimal(4,2) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1;

insert  into `taba`(`A`,`P`) values ('Y','0.01'),('N','0.99');

CREATE TABLE `tabbs` (
  `B` char(1) DEFAULT NULL,
  `S` char(1) DEFAULT NULL,
  `P` decimal(4,2) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1;

insert  into `tabbs`(`B`,`S`,`P`) 
values ('Y','Y','0.60'),('Y','N','0.30'),('N','Y','0.40'),('N','N','0.70');

CREATE TABLE `tabdeb` (
  `D` char(1) DEFAULT NULL,
  `E` char(1) DEFAULT NULL,
  `B` char(1) DEFAULT NULL,
  `P` decimal(4,2) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1;

insert  into `tabdeb`(`D`,`E`,`B`,`P`) 
values ('Y','Y','Y','0.90'), ('Y','Y','N','0.70'), ('Y','N','Y','0.80')
     , ('Y','N','N','0.10'), ('N','Y','Y','0.10'), ('N','Y','N','0.30')
     , ('N','N','Y','0.20'), ('N','N','N','0.90');

CREATE TABLE `tabelt` (
  `E` char(1) DEFAULT NULL,
  `L` char(1) DEFAULT NULL,
  `T` char(1) DEFAULT NULL,
  `P` decimal(4,2) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1;


insert into `tabelt`(`E`,`L`,`T`,`P`) 
values ('Y','Y','Y','1.00'), ('Y','Y','N','1.00'), ('Y','N','Y','1.00')
     , ('Y','N','N','0.00'), ('N','Y','Y','0.00'), ('N','Y','N','0.00')
     , ('N','N','Y','0.00'), ('N','N','N','1.00');

CREATE TABLE `tabls` (
  `L` char(1) DEFAULT NULL,
  `S` char(1) DEFAULT NULL,
  `P` decimal(4,2) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1;


insert into `tabls` (`L`,`S`,`P`) 
values ('Y','Y','0.10'), ('Y','N','0.01'), ('N','Y','0.90')
     , ('N','N','0.99');

CREATE TABLE `tabs` (
  `S` char(1) DEFAULT NULL,
  `P` decimal(4,2) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1;

insert  into `tabs`(`S`,`P`) values ('Y','0.50'), ('N','0.50');


CREATE TABLE `tabta` (
  `T` char(1) DEFAULT NULL,
  `A` char(1) DEFAULT NULL,
  `P` decimal(4,2) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1;


insert into `tabta`(`T`,`A`,`P`) 
values ('Y','Y','0.05'), ('Y','N','0.01')
     , ('N','Y','0.95'), ('N','N','0.99');

CREATE TABLE `tabxe` (
  `X` char(1) DEFAULT NULL,
  `E` char(1) DEFAULT NULL,
  `P` decimal(4,2) DEFAULT NULL
) ENGINE=MyISAM DEFAULT CHARSET=latin1;

insert into `tabxe`(`X`,`E`,`P`) 
values ('Y','Y','0.98'), ('Y','N','0.05')
     , ('N','Y','0.02'), ('N','N','0.95');

and the query:

SELECT tabdeb.e 
     , SUM(tabdeb.p * tabeLT.p * TaBTA.p * taba.p 
          * tabls.p * |tabbs.p * tabs.P * tabxe.P ) prob
  FROM tabdeb
 INNER JOIN tabelt ON tabdeb.e = tabelt.e
 INNER JOIN tabta ON tabelt.t = tabta.t
 INNER JOIN taba ON tabta.a = taba.a
 INNER JOIN tabls ON tabelt.l = tabls.l
 INNER JOIN tabbs ON tabdeb.b = tabbs.b
 INNER JOIN tabs ON tabls.s = tabs.s AND tabbs.s = tabs.s
 INNER JOIN tabxe ON tabxe.E=tabelt.E
 WHERE tabta.A = 'N' 
   AND tabxe.x='Y' -- AND tabdeb.D='Y'
 GROUP BY tabdeb.e

SELECT tabelt.t, SUM(tabdeb.p*
tabeLT.p*
TaBTA.p*
taba.p*
tabls.p*
tabbs.p*
tabs.P*tabxe.P
) AS prob
          FROM tabdeb
    INNER JOIN tabelt ON tabdeb.e = tabelt.e
    INNER JOIN tabta ON tabelt.t = tabta.t
    INNER JOIN taba ON tabta.a = taba.a
    INNER JOIN tabls ON tabelt.l = tabls.l
    INNER JOIN tabbs ON tabdeb.b = tabbs.b
    INNER JOIN tabs ON tabls.s = tabs.s AND tabbs.s = tabs.s
    INNER JOIN tabxe ON tabxe.E=tabelt.E
    WHERE tabta.A='N' AND tabxe.x='Y' -- AND tabdeb.D='Y'
    GROUP BY tabelt.t

=====================================================
=====================================================
-- lungcancer
SELECT tabelt.l, SUM(tabdeb.p*
tabeLT.p*
TaBTA.p*
taba.p*
tabls.p*
tabbs.p*
tabs.P*tabxe.P
) AS prob
          FROM tabdeb
    INNER JOIN tabelt ON tabdeb.e = tabelt.e
    INNER JOIN tabta ON tabelt.t = tabta.t
    INNER JOIN taba ON tabta.a = taba.a
    INNER JOIN tabls ON tabelt.l = tabls.l
    INNER JOIN tabbs ON tabdeb.b = tabbs.b
    INNER JOIN tabs ON tabls.s = tabs.s AND tabbs.s = tabs.s
    INNER JOIN tabxe ON tabxe.E=tabelt.E
    WHERE tabta.A='N' AND tabxe.x='Y' -- AND tabdeb.D='Y'
    GROUP BY tabelt.l
=====================================================
=====================================================
-- Bronchitis
SELECT tabdeb.b, SUM(tabdeb.p*
tabeLT.p*
TaBTA.p*
taba.p*
tabls.p*
tabbs.p*
tabs.P*tabxe.P
) AS prob
          FROM tabdeb
    INNER JOIN tabelt ON tabdeb.e = tabelt.e
    INNER JOIN tabta ON tabelt.t = tabta.t
    INNER JOIN taba ON tabta.a = taba.a
    INNER JOIN tabls ON tabelt.l = tabls.l
    INNER JOIN tabbs ON tabdeb.b = tabbs.b
    INNER JOIN tabs ON tabls.s = tabs.s AND tabbs.s = tabs.s
    INNER JOIN tabxe ON tabxe.E=tabelt.E
    WHERE tabta.A='N' AND tabxe.x='Y' -- AND tabdeb.D='Y'
    GROUP BY tabdeb.B

=======================================================
=======================================================
-- dysomnia
SELECT tabdeb.d, SUM(tabdeb.p*
tabeLT.p*
TaBTA.p*
taba.p*
tabls.p*
tabbs.p*
tabs.P*tabxe.P
) prob
          FROM tabdeb
    INNER JOIN tabelt ON tabdeb.e = tabelt.e
    INNER JOIN tabta ON tabelt.t = tabta.t
    INNER JOIN taba ON tabta.a = taba.a
    INNER JOIN tabls ON tabelt.l = tabls.l
    INNER JOIN tabbs ON tabdeb.b = tabbs.b
    INNER JOIN tabs ON tabls.s = tabs.s AND tabbs.s = tabs.s
    INNER JOIN tabxe ON tabxe.E=tabelt.E
    WHERE tabta.A='N' AND tabxe.x='Y' -- AND tabdeb.D='Y'
    GROUP BY tabdeb.d