Causal models

Patterns of inference

Name of the game in these examples is to understand what effect manipulating b will have on a.

That is, if we change b, how will a change?

Statistical dependence

var model = function(observation){
  var c = flip(0.5)
  var b = flip(0.5)
  var a = b ? flip(0.9) : flip(0.2)
  condition(b == observation)
  return {"a": a}
}
var b_is_true = Infer({method: "rejection", samples:1000},
     function(){ model(true) })

print("We observe b is true")
viz.auto(b_is_true)

var b_is_false = Infer({method: "rejection", samples:1000},
     function(){ model(false) })

print("We observe b is not true")
viz.auto(b_is_false)

var model = function(observation){
  var c = flip(0.5)
  var b = c ? flip(0.1) : flip(0.9)
  var a = c ? flip(0.1) : flip(0.9)
  condition(b == observation)
  return {"a": a}
}
var b_is_true = Infer({method: "rejection", samples:1000},
     function(){ model(true) })

print("We observe b is true")
viz.auto(b_is_true)

var b_is_false = Infer({method: "rejection", samples:1000},
     function(){ model(false) })

print("We observe b is not true")
viz.auto(b_is_false)

Screening off

var model = function(observation){
  var c = flip(0.5)
  var b = c ? flip(0.1) : flip(0.9)
  var a = c ? flip(0.1) : flip(0.9)
  condition(b == observation)
  return {"a": a}
}

var b_is_true = Infer({method: "rejection", samples:10000},
     function(){ model(true) })

print("We observe b is true")
viz.auto(b_is_true)

var b_is_false = Infer({method: "rejection", samples:10000},
     function(){ model(false) })

print("We observe b is not true")
viz.auto(b_is_false)

Now, what happens if we know c to be true ?

var model = function(observation){
  var c = flip(0.5)
  var b = c ? flip(0.1) : flip(0.9)
  var a = c ? flip(0.1) : flip(0.9)
  condition(c & (b == observation))
  return {"a": a}
}

var b_is_true = Infer({method: "rejection", samples:10000},
     function(){ model(true) })

print("We observe c and that b is true")
viz.auto(b_is_true)

var b_is_false = Infer({method: "rejection", samples:10000},
     function(){ model(false) })

print("We observe c and that b is not true")
viz.auto(b_is_false)

Explaining away

var model = function(observation){
  var a = flip(0.5)
  var b = flip(0.5)
  var c = (a || b) ? flip(0.9) : flip(0.2)
  condition(b == observation)
  return {"a": a}
}

var b_is_true = Infer({method: "rejection", samples:10000},
     function(){ model(true) })

print("We observe b is true")
viz.auto(b_is_true)

var b_is_false = Infer({method: "rejection", samples:10000},
     function(){ model(false) })

print("We observe b is not true")
viz.auto(b_is_false)

var model = function(observation){
  var a = flip(0.5)
  var b = flip(0.5)
  var c = (a || b) ? flip(0.9) : flip(0.2)
  condition(c & (b == observation))
  return {"a": a}
}

var b_is_true = Infer({method: "rejection", samples:1000},
     function(){ model(true) })

print("We observe c and that b is true")
viz.auto(b_is_true)

var b_is_false = Infer({method: "rejection", samples:1000},
     function(){ model(false) })

print("We observe c and that b is not true")
viz.auto(b_is_false)

In the next chapter, we’ll show how you can elaborate your models to better represent your data (under development).

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