diff --git a/Data/Distribution/Core.hs b/Data/Distribution/Core.hs
--- a/Data/Distribution/Core.hs
+++ b/Data/Distribution/Core.hs
@@ -35,6 +35,7 @@
       -- ** Transformation
     , select
     , assuming
+    , observing
       -- ** Combination
     , combineWith
       -- ** Sequences
@@ -271,6 +272,39 @@
     adjust x = x * (1 / total)
     total = sum $ Map.elems filtered
 
+
+-- | Returns a new distribution using the Bayesian update rule.
+--
+-- Using this example:
+-- https://en.wikipedia.org/wiki/Bayesian_inference#Probability_of_a_hypothesis
+--
+-- > data CookieBowl = Bowl1 | Bowl2 deriving (Eq,Ord)
+-- > data CookieType = Plain | ChocolateChip deriving (Eq,Ord)
+-- >
+-- > assumption :: Distribution CookieBowl
+-- > assumption = uniform [Bowl1,Bowl2]
+-- >
+-- > update :: Cookie -> Distribution CookieBowl -> Distribution CookieBowl
+-- > update c = observing f where
+-- >   f b = case b of
+-- >     -- Bowl #1 contains 10 chocolate chip cookies and 30 plain cookies
+-- >     Bowl1 -> fromList [(c == ChocolateChip,10),(c == Plain,30)]
+-- >     -- Bowl #2 contains 20 of each flavour of cookie
+-- >     Bowl2 -> fromList [(c == ChocolateChip,20),(c == Plain,20)]
+--
+-- The "update" function in this example can be used to update the probability
+-- distribution of which bowl you have based on observing a random cookie inside
+-- the bowl.
+observing :: (a -> Distribution Bool) -> Distribution a -> Distribution a
+observing f (Distribution xs) = Distribution $ fmap adjust filtered
+  where
+    filtered = Map.filter (/= 0) $ Map.mapWithKey tweak xs
+    tweak x p = let
+      Distribution px = f x
+      pt = fromMaybe 0 $ Map.lookup True px
+      in pt * p
+    adjust x = x * (1 / total)
+    total = sum $ Map.elems filtered
 
 -- Combination
 
diff --git a/distribution.cabal b/distribution.cabal
--- a/distribution.cabal
+++ b/distribution.cabal
@@ -8,7 +8,7 @@
 -- PVP summary:      +-+------- breaking API changes
 --                   | | +----- non-breaking API additions
 --                   | | | +--- code changes with no API change
-version:             1.1.0.0
+version:             1.1.1.0
 
 -- A short (one-line) description of the package.
 synopsis:             Finite discrete probability distributions.