Thanks Peter and Kevin for their detailed answers to my question. It is
fun to play with HUGIN.
Two more questions:
(1) If there must be a node for each observation, what should I do if
I cannot determine the number of observations in advance? Can
nodes/links be added and/or removed after some observation? For
example, can I carry out 10 more abservations in Peter's network
without redo the first group of 10 observations?
(2) In this example, if we assume a total ignorance before any
observation (except that each outcome will either be an H or a T), the
probability of "The next outcome is an H" (call it p) should be
completely determined by the number of H observed so far (call it h)
and the number of T observed so far (call it t), right? In ideal
situation (such as to allow infinite discrete states), what is the
function to get p from h and t in a BN?
Pei
> From: "Hansen, Peter Friis" <[EMAIL PROTECTED]>
>
> Hello Pei
>
> I have enclosed a small BN (ASCII file) that shows you how this works - at
> least if I understand your concerns correctly. It is modelled using HUGIN,
> and you may need to download a demo of HUGIN from www.hugin.dk
> <http://www.hugin.dk> to run this example.
>
> The enclosed network is as follows: The main node is our belief in the
> probability of getting an H reading. Our problem is, of course, that we do
> not know much about the machine David gave us, only that it is (after having
> pressed the button) able to give us an H or a T, and that the individual
> outcomes are independent. Since "I don't know" what P[H] is I have assigned
> a uniform distribution (discrete, though) to the node "Belief in H", that
> is, P[H] can be anything in the interval [0;1]. In the discrete world I
> have chosen the probability levels [0, 0.1, 0.2, ..., 0.9, 1.0]. Since I am
> indifferent to any of these probability levels I guess this describes well
> that "I don't know" - whatever that may mean. Moreover, I have added 11
> observation nodes, that allows me to gain more knowledge of my belief in
> P[H] while I play with the machine. The observation nodes are, of course,
> children of the node "Belief in H". Since I have assigned a uniform
> distribution to my "Belief in H" the marginal probability of the outcome is
> P[H] = P[T] = 0.5.
>
> If you have installed the demo version of HUGIN, saved the button.net file
> to a directory and double clicked on the file you are now running the HUGIN
> program. You see the assigned probability distributions. If you click on
> the lightning icon (Run), we may check how our belief in H changes when more
> results become available.
>
> First press the third lower icon (Expand node list) so that we easily can
> see all the marginal probabilities. To make things somewhat easier, we just
> want to turn Auto Propagation on: Press Alt+Enter select "Use Auto
> Propagation".
>
> Now we may run the game. Double click on the observation result you get
> from David's button machine, and notice how your "Belief in H" changes when
> you have the (0:0), (2:2), and (5:5) observation. Isn't this great fun?
>
> Peter
>
> <<button.net>>
>
>
>
>
> Peter Friis Hansen
> Associate Professor, Ph.D.
> Department of Naval Architecture and Offshore Engineering,
> Build. 101E, Technical University of Denmark,
> DK-2800 Lyngby, Denmark
> Tel: + 45 45 25 13 88
> Fax: +45 45 88 43 25
> Email: [EMAIL PROTECTED]
> Web: http://www.ish.dtu.dk/pfh/
>
>
> ------_=_NextPart_000_01BEB1A8.F7EAE890
> Content-Type: application/octet-stream;
> name="button.net"
> Content-Transfer-Encoding: quoted-printable
> Content-Disposition: attachment;
> filename="button.net"
>
> net
> {
> node_size =3D (80 40);
> HR_Grid_X =3D "10";
> HR_Grid_Y =3D "10";
> HR_Grid_GridSnap =3D "1";
> HR_Grid_GridShow =3D "0";
> HR_Font_Name =3D "Arial";
> HR_Font_Size =3D "-12";
> HR_Font_Weight =3D "400";
> HR_Font_Italic =3D "0";
> HR_Propagate_Auto =3D "0";
> HR_Propagate_AutoSum =3D "1";
> HR_Propagate_AutoNormal =3D "1";
> HR_Compile_TriangMethod =3D "0";
> HR_Compile_Compress =3D "0";
> HR_Compile_Approximate =3D "0";
> HR_Compile_ApproxEpsilon =3D "0.00001";
> HR_Monitor_AutoUpdGraph =3D "0";
> HR_Monitor_GraphPrecision =3D "100";
> HR_Monitor_OpenGraph =3D "0";
> HR_Monitor_InitStates =3D "5";
> HR_Monitor_InitSD =3D "2";
> HR_Color_DiscreteChance =3D "16";
> HR_Color_ContinuosChance =3D "48";
> HR_Color_Utility =3D "36";
> HR_Color_Decision =3D "17";
> HR_Groups_UserGroupsNo =3D "0";
> HR_Groups_GroupNames =3D "";
> HR_Groups_GroupColors =3D "";
> }
>
> node Obs_11
> {
> label =3D "Obs 11";
> position =3D (550 240);
> states =3D ("Head" "Tail");
> }
>
> node Obs_10
> {
> label =3D "Obs 10";
> position =3D (540 180);
> states =3D ("Head" "Tail");
> }
>
> node Obs_9
> {
> label =3D "Obs 9";
> position =3D (510 130);
> states =3D ("Head" "Tail");
> }
>
> node Obs_8
> {
> label =3D "Obs 8";
> position =3D (470 80);
> states =3D ("Head" "Tail");
> }
>
> node Obs_7
> {
> label =3D "Obs 7";
> position =3D (410 30);
> states =3D ("Head" "Tail");
> }
>
> node Obs_6
> {
> label =3D "Obs 6";
> position =3D (330 0);
> states =3D ("Head" "Tail");
> }
>
> node Obs_5
> {
> label =3D "Obs 5";
> position =3D (240 0);
> states =3D ("Head" "Tail");
> }
>
> node Obs_4
> {
> label =3D "Obs 4";
> position =3D (150 10);
> states =3D ("Head" "Tail");
> }
>
> node Obs_3
> {
> label =3D "Obs 3";
> position =3D (70 40);
> states =3D ("Head" "Tail");
> }
>
> node Obs_2
> {
> label =3D "Obs 2";
> position =3D (20 90);
> states =3D ("Head" "Tail");
> }
>
> node Obs_1
> {
> label =3D "Obs 1";
> position =3D (0 160);
> states =3D ("Head" "Tail");
> }
>
> node Belief
> {
> label =3D "Belief in H";
> position =3D (270 270);
> states =3D ("0" "0.1" "0.2" "0.3" "0.4" "0.5" "0.6" "0.7" "0.8" =
> "0.9" "1");
> }
>
> potential (Obs_11 | Belief)
> {
> data =3D (( 0 1 ) % 0
> ( 0.1 0.9 ) % 0.1
> ( 0.2 0.8 ) % 0.2
> ( 0.3 0.7 ) % 0.3
> ( 0.4 0.6 ) % 0.4
> ( 0.5 0.5 ) % 0.5
> ( 0.6 0.4 ) % 0.6
> ( 0.7 0.3 ) % 0.7
> ( 0.8 0.2 ) % 0.8
> ( 0.9 0.1 ) % 0.9
> ( 1 0 )); % 1
> }
>
> potential (Obs_10 | Belief)
> {
> data =3D (( 0 1 ) % 0
> ( 0.1 0.9 ) % 0.1
> ( 0.2 0.8 ) % 0.2
> ( 0.3 0.7 ) % 0.3
> ( 0.4 0.6 ) % 0.4
> ( 0.5 0.5 ) % 0.5
> ( 0.6 0.4 ) % 0.6
> ( 0.7 0.3 ) % 0.7
> ( 0.8 0.2 ) % 0.8
> ( 0.9 0.1 ) % 0.9
> ( 1 0 )); % 1
> }
>
> potential (Obs_9 | Belief)
> {
> data =3D (( 0 1 ) % 0
> ( 0.1 0.9 ) % 0.1
> ( 0.2 0.8 ) % 0.2
> ( 0.3 0.7 ) % 0.3
> ( 0.4 0.6 ) % 0.4
> ( 0.5 0.5 ) % 0.5
> ( 0.6 0.4 ) % 0.6
> ( 0.7 0.3 ) % 0.7
> ( 0.8 0.2 ) % 0.8
> ( 0.9 0.1 ) % 0.9
> ( 1 0 )); % 1
> }
>
> potential (Obs_8 | Belief)
> {
> data =3D (( 0 1 ) % 0
> ( 0.1 0.9 ) % 0.1
> ( 0.2 0.8 ) % 0.2
> ( 0.3 0.7 ) % 0.3
> ( 0.4 0.6 ) % 0.4
> ( 0.5 0.5 ) % 0.5
> ( 0.6 0.4 ) % 0.6
> ( 0.7 0.3 ) % 0.7
> ( 0.8 0.2 ) % 0.8
> ( 0.9 0.1 ) % 0.9
> ( 1 0 )); % 1
> }
>
> potential (Obs_7 | Belief)
> {
> data =3D (( 0 1 ) % 0
> ( 0.1 0.9 ) % 0.1
> ( 0.2 0.8 ) % 0.2
> ( 0.3 0.7 ) % 0.3
> ( 0.4 0.6 ) % 0.4
> ( 0.5 0.5 ) % 0.5
> ( 0.6 0.4 ) % 0.6
> ( 0.7 0.3 ) % 0.7
> ( 0.8 0.2 ) % 0.8
> ( 0.9 0.1 ) % 0.9
> ( 1 0 )); % 1
> }
>
> potential (Obs_6 | Belief)
> {
> data =3D (( 0 1 ) % 0
> ( 0.1 0.9 ) % 0.1
> ( 0.2 0.8 ) % 0.2
> ( 0.3 0.7 ) % 0.3
> ( 0.4 0.6 ) % 0.4
> ( 0.5 0.5 ) % 0.5
> ( 0.6 0.4 ) % 0.6
> ( 0.7 0.3 ) % 0.7
> ( 0.8 0.2 ) % 0.8
> ( 0.9 0.1 ) % 0.9
> ( 1 0 )); % 1
> }
>
> potential (Obs_5 | Belief)
> {
> data =3D (( 0 1 ) % 0
> ( 0.1 0.9 ) % 0.1
> ( 0.2 0.8 ) % 0.2
> ( 0.3 0.7 ) % 0.3
> ( 0.4 0.6 ) % 0.4
> ( 0.5 0.5 ) % 0.5
> ( 0.6 0.4 ) % 0.6
> ( 0.7 0.3 ) % 0.7
> ( 0.8 0.2 ) % 0.8
> ( 0.9 0.1 ) % 0.9
> ( 1 0 )); % 1
> }
>
> potential (Obs_4 | Belief)
> {
> data =3D (( 0 1 ) % 0
> ( 0.1 0.9 ) % 0.1
> ( 0.2 0.8 ) % 0.2
> ( 0.3 0.7 ) % 0.3
> ( 0.4 0.6 ) % 0.4
> ( 0.5 0.5 ) % 0.5
> ( 0.6 0.4 ) % 0.6
> ( 0.7 0.3 ) % 0.7
> ( 0.8 0.2 ) % 0.8
> ( 0.9 0.1 ) % 0.9
> ( 1 0 )); % 1
> }
>
> potential (Obs_3 | Belief)
> {
> data =3D (( 0 1 ) % 0
> ( 0.1 0.9 ) % 0.1
> ( 0.2 0.8 ) % 0.2
> ( 0.3 0.7 ) % 0.3
> ( 0.4 0.6 ) % 0.4
> ( 0.5 0.5 ) % 0.5
> ( 0.6 0.4 ) % 0.6
> ( 0.7 0.3 ) % 0.7
> ( 0.8 0.2 ) % 0.8
> ( 0.9 0.1 ) % 0.9
> ( 1 0 )); % 1
> }
>
> potential (Obs_2 | Belief)
> {
> data =3D (( 0 1 ) % 0
> ( 0.1 0.9 ) % 0.1
> ( 0.2 0.8 ) % 0.2
> ( 0.3 0.7 ) % 0.3
> ( 0.4 0.6 ) % 0.4
> ( 0.5 0.5 ) % 0.5
> ( 0.6 0.4 ) % 0.6
> ( 0.7 0.3 ) % 0.7
> ( 0.8 0.2 ) % 0.8
> ( 0.9 0.1 ) % 0.9
> ( 1 0 )); % 1
> }
>
> potential (Obs_1 | Belief)
> {
> data =3D (( 0 1 ) % 0
> ( 0.1 0.9 ) % 0.1
> ( 0.2 0.8 ) % 0.2
> ( 0.3 0.7 ) % 0.3
> ( 0.4 0.6 ) % 0.4
> ( 0.5 0.5 ) % 0.5
> ( 0.6 0.4 ) % 0.6
> ( 0.7 0.3 ) % 0.7
> ( 0.8 0.2 ) % 0.8
> ( 0.9 0.1 ) % 0.9
> ( 1 0 )); % 1
> }
>
> potential (Belief)
> {
> data =3D ( 0.05 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.05 );
> }
>
> ------_=_NextPart_000_01BEB1A8.F7EAE890--
>
