iCAUSALBAYES USER MANUAL
Contents
1. A real world analogy would be an experiment or a law that enforced Sunscreen use regardless of skin pigmentation so that Melanin Index Is eliminated as a confound Some people will find the idea of a sunscreen law objectionable and anyone who enacted such a law would have to contend with problems related 9 to compliance and enforcement But never mind all that This is just a what if scenario What if we enforced sunscreen usage What if sunscreen use had nothing to do with skin pigmentation Tap with two fingers a second time to put Sunscreen into Doing mode indicated by a wrench Doing means we intervene to fix the value of Sunscreen in such a way that Melanin Index has no effect on it you will notice that the arrow from Melanin Index to Sunscreen disappears Now drag the observed value line around AS Sunscreen use goes down Melanoma increases aS Sunscreen use increases Melanoma rates go down Melanin Index is unaffected because we are manipulating Sunscreen use directly there is no relationship between Sunscreen use and Melanin Index or skin pigmentation Sunscreen MLs per Person s lf you perform these manipulations of Sunscreen while Observing different values for Melanin Index you will notice that while increased Sunscreen use always lowers melanoma rates the mean for Melanoma Is higher for people with lighter skin and lower for people with darker skin Melanin Index in this scenario has no effect on Sunscreen but2. coefficient for Sunscreen We ll use the Error Term Mean and Standard Deviation defaults here too Tap Edit Variable to return to the previous view Remember to tap Done on the keyboard first Tap Done in Edit Variable lt Edit Variable Explanatory Variables EXISTING EXPLANATORY VARIABLES Melanin Index Index 0 823 Sunscreen MIs per Person 0 415 ERROR TERM Mean 0 Standard Deviation POTENTIAL EXPLANATORY VARIABLES Now we have arrows from Sunscreen and Melanin Index to Melanoma This is something that might be learned by an ordinary regression analysis and it says that the incidence of melanoma varies with both Melanin Index and Sunscreen use Arrange and resize the variables so you can see everything Save the network if you like and then tap to return to the network view You might also like to set the Display Options You can set Display Options for the network as a whole or for each node individually Our small network is complete Melanoma Incidence per 100 Scale 2 Sunscreen Mls per Person Melanin Index Index Scale 2 OBSERVING AND DOING There is a long standing controversy over sunscreen There are those who say that people who use sunscreen end up spending more time in the sun and that the increased sun exposure negates and even outweighs any protection sunscreen might provide Some argue that sunscreen users have lower levels of vitamin D which protects aga
3. it is still a factor when it comes to the observed incidence of Melanoma The lighter the skin the greater the susceptibility to Melanoma However Sunscreen use always reduces the incidence of Melanoma 10 Again we can conclude that Melanin Index is aconfound and that Sunscreen use reduces the incidence of Melanoma But this time we were able to reach that conclusion much more quickly and directly 11 How would we calculate p MIS in this case The calculation above where we are Observing is not correct here In this scenario where we manipulate Sunscreen in such a way that it does not depend on skin pigmentation it would an error to multiply p MIDS by p DIS There isa relationship between Melanin Index or in binary terms D and D and Melanoma rate but Sunscreen use is independent of skin pigmentation So in the Doing case p MIDS should be multiplied by the proportion of persons who are dark skinned and p MI DS by the proportion that are light skinned which gives us this P M S P M DS P D P M ADS P D In graphical terms the difference between the Observing calculation and the Doing calculation is the presence Observing or absence Doing of an arrow between Melanin Index and sunscreen MENU ITEMS COLOR AND GRAPHICS To change the display options for a variable tap and hold then tap Color and Graphics Cancel Edit Variable Done GENERAL Name Melanin Index Unit Index GRAPH Lower Boun
4. variable This one is will be an Explanatory Variable for Sunscreen We ll call it Melanin Index This variable is a measure of skin pigmentation as determined by a reflectometer For the Unit we ll use Index Again we ll leave the Upper and Lower Bounds on Auto Again we ll use the defaults for the Prior Distribution Position the variables as you like Use the familiar two finger pinch inside a node to make it bigger or smaller or outside to expand or contract the network as a whole Now we ll make Melanin Index an explanatory variable for Sunscreen Touch and hold inside Sunscreen to edit the variable Sunscreen Mis per Person Scale 1 In the Edit Variable view tap Explanatory Variables Cancel Edit Variable Done GENERAL Name Sunscreen Unit Mis per Person GRAPH Lower Bound 4 Auto C Upper Bound 4 Auto C PRIOR DISTRIBUTION Standard Deviation Explanatory Variables Color and Graphics By Me lat le lt Edit Variable Explanatory Variables EXISTING EXPLANATORY VARIABLES POTENTIAL EXPLANATORY VARIABLES Melanin Index Index In the Explanatory Variables view swipe left to make Melanin Index an Explanatory Variable lt Edit Variable Explanatory Variables EXISTING EXPLANATORY VARIABLES POTENTIAL EXPLANATORY VARIABLES Make Explanatory Melanin Index will move from the Potential Explanatory Variables to Existing Explanatory Variables and an Er
5. ICAUSALBAYES USER MANUAL INTRODUCTION You can use this app to build a causal Bayesian network and experiment with inferences We hope you ll find it interesting and helpful We expect most of our users will be Al students with a basic knowledge of probability and Statistics You don t need a deep understanding of regression to use the app but you do need to be aware of some terminology and the basic regression equation a response variable RV depends on one or more explanatory variables EV plus an error term ET The basic regression equation then is RV C EV Ci EV C EV ET CREATING A NETWORK A TUTORIAL There are two ways to create a network 1 Build a network in the app 2 Create and import an xml file that describes a network To see the required format use the app to e mail a network either one you build yourself or one of the networks bundled with the app and open the attached xml file in a text editor We recommend you use the app to build your networks aS we use a canned XML parser that may not handle typos well but if you want to import an xml file e mail the file and use Open in in iPad Mail to open it in the Bayesian app BUILDING A NETWORK IN THE APP We ll use the same 3 node throughout this manual This network comes bundled with the app but here we ll build it from scratch Tap the button at the top right of the home Your Networks screen to create a new netwo
6. d 4 Auto C Upper Bound 4 Auto PRIOR DISTRIBUTION Mean 0 Standard Deviation Explanatory Variables Color and Graphics ao 12 lt Edit Variable Variable Display Options GENERAL Use Network Settings Header Color GRAPH Display Mode Area Background Color Area Color Ghosting Turn Use Network Settings off to over ride the network settings for this variable For network settings see DISPLAY OPTIONS below If you over ride the network settings you can Set the Header Color for the variable Turn ghosting on or off When Ghosting is on the prior distribution for a variable appears as a ghost behind any posterior distribution Set the Display Mode You can choose to display the distribution as a line a curve an area or both Select a Background Color Select a Line Color if the Display Mode is Line or Both Select an Area Color if the Display Mode is Area or Both DISPLAY OPTIONS To change the display options for a network tap Display Options in the upper right of the main window Carrier gt 11 47 AM 100 mmm Back Save SaveAs Email Sunscreen Example Display Options G 13 You can Set the Arrow Display Mode to Simple or Color Coded If you choose Color Coded the intensity of the color of an arrow will reflect the strength of the relationship between two variables Select a Header Color for the variables Turn ghost
7. ing on or off When Ghosting is on the prior distribution for a variable appears as a ghost behind any posterior distribution Choose to display distributions as lines curves areas or both Select a Background Color for the nodes Select a Line Color if the Display Mode is Line or Both Select an Area Color if the Display Mode is Area or Both Cancel Network Display Options Done GENERAL Arrow Display Mode Simple Color Coded Header Color GRAPH Ghosting q Display Mode Both Background Color _ Line Color Area Color 14 SAVE SAVE AS and E MAIL Tap Save or Save As in the upper left of the main window to save a network as an xml file Tap E mail to e mail the xml file for a network Carrier F i 11 47 AM i 100 mmm Back Save SaveAs Email Sunscreen Example Display Options i HELP Tap the 1 icon in the upper right corner of the main window to review the gestures described above iPad 1 34 PM 3 C Back Save SaveAss Email Sunscreen Example Display Options 15
8. inst skin cancer as well as other cancers Others maintain that some sunscreen ingredients increase the risk of melanoma and other cancers On the other hand most dermatologists and cancer organizations say that if you want to reduce your risk of melanoma you should use sunscreen consistently Suppose the observational data suggests that sunscreen use doesn t much affect the probability that you will develop melanoma Now let s investigate OBSERVING Tap the Sunscreen variable with two fingers to put it into Observing mode you know you are in Observing mode when you see an eye icon in the upper right of the window Sunscreen MLs per Person s A line representing an observed value will appear in place of the distribution curve Leave the other two variables in Graph mode indicated by a sparkline Now drag the line around to see the values of the other two variables for a given value of the Sunscreen variable You will see that the distribution for Melanoma doesn t move very much It would seem that Sunscreen use doesn t much affect the incidence of Melanoma u 0 05332 However you might also observe something we mentioned earlier when we set up Melanin Index as an explanatory variable for Sunscreen when Sunscreen goes up Melanin Index goes down when Sunscreen goes down Melanin Index goes up It appears that people with darker skin use less Sunscreen overall while people with lighter skin use more intuitivel
9. rk iPad Sunscreen Success Example 12 05 PM Your Networks 98 M 4 Edit Last Modified May 29 2014 11 00 AM Last Modified May 27 2014 7 42 PM Touch and hold anywhere on the screen to create a new variable at that location Use the New Variable view to configure the variable Cancel GENERAL Name Unit GRAPH New Variable Sunscreen Mis per Person Lower Bound 4 Auto q Upper Bound 4 Auto O PRIOR DISTRIBUTION Mean Standard Deviation Explanatory Variables Color and Graphics Give your variable a name Sunscreen For the Unit enter Mls per Person Done You can enter a Lower and Upper Bound for the graph or leave these one or both on Auto This determines how many Standard Deviations will be displayed for the variable We ll leave these on Auto You can always come back and change this In fact you can always come back and change anything For the Prior Distribution leave the Mean and Standard Deviation at 0 and 1 respectively Tap Done on the keyboard and then Done in the top right of the New Variable view You should see the Sunscreen variable on your screen The Sunscreen node shows that MIs per Person is approximately normally distributed with a mean of O At this point this node says on average people use x mls of Sunscreen Sunscreen Mls per Person Scale 1 Now let s add another
10. ror Term will appear Explanatory Variables EXISTING EXPLANATORY VARIABLES Melanin Index Index ERROR TERM Standard Deviation POTENTIAL EXPLANATORY VARIABLES 1 2 3 4 5 6 T 8 9 0 amp a SS Enter 0 8 as the coefficient for Melanin Index Leave the Error Term Mean and Standard Deviation at their default values Tap Edit Variable in the upper left corner to return to the previous screen If you don t see Edit Variable tap Done on the keyboard Back in the Edit Variable view you will notice that the Prior Distribution is gone Tap Done Sunscreen MIs per Person s Melanin Index Index af Scale 2 Scale 1 Now there is an arrow from Melanin Index to Sunscreen We have changed the meaning of both variables The arrow indicates that Melanin Index affects Sunscreen use The coefficient of Melanin Index tells us how people with a lower Melanin Index use more Sunscreen This is something a Bayes Net learning algorithm might discover Our third and last variable will be called Melanoma For Units we ll use Incidence per 100 Once again we ll leave Upper and Lower Bounds on Auto Since we have already created the Explanatory Variables for Melanoma we can ignore the Prior Distribution and set these up right away Tap Explanatory Variables swipe to make both Sunscreen and Melanin Index explanatory variables and enter 823 as the coefficient for Melanin Index and 415 as the
11. y this makes sense So what happens if we observe the effect of different values for Melanin Index Tap to Observe the Melanin Index variable and drag the observed value line to the left We are observing values for people with little skin pigmentation Now drag the line for Sunscreen to the right It appears that for people with little skin pigmentation as Sunscreen usage increases the incidence of Melanoma goes down Conversely as Sunscreen usage decreases the incidence of Melanoma goes up Let s see what happens when Melanin Index has a higher value Drag the line to the right and then observe the effect of different values for Sunscreen ON Melanoma Again more Sunscreen means less Melanoma and less Sunscreen means more Melanoma though the mean has moved to the left It would seem that Melanin Index is a confound and that Sunscreen use reduces Melanoma rates It will be useful to consider how the probability of Melanoma M given a particular observed value of Sunscreen S is calculated For the sake of simplicity we ll pretend we re dealing with discrete binary variables D and D represent dark skin and light skin respectively The calculation is as follows P M S P M DS P D S P M ADS P D S DOING We can approach this in another way instead of Observing what happens with different distributions of Sunscreen and Melanin Index we can try Doing something so that Sunscreen Is not affected by Melanin Index
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