mcmc 0.2.3 → 0.2.4

raw patch · 21 files changed

+147/−141 lines, 21 filesPVP: major bump suggested

API removals or changes: PVP suggests a major version bump

API changes (from Hackage documentation)

Files

• README.md +1/−2
• bench/Normal.hs +2/−2
• bench/Poisson.hs +4/−4
• mcmc.cabal +1/−1
• src/Mcmc.hs +4/−1
• src/Mcmc/Item.hs +11/−16
• src/Mcmc/Mcmc.hs +2/−0
• src/Mcmc/Metropolis.hs +3/−1
• src/Mcmc/Monitor.hs +0/−8
• src/Mcmc/Monitor/Parameter.hs +17/−1
• src/Mcmc/Monitor/ParameterBatch.hs +14/−0
• src/Mcmc/Prior.hs +3/−5
• src/Mcmc/Proposal.hs +15/−15
• src/Mcmc/Proposal/Bactrian.hs +18/−16
• src/Mcmc/Proposal/Generic.hs +2/−2
• src/Mcmc/Proposal/Scale.hs +14/−14
• src/Mcmc/Proposal/Slide.hs +16/−16
• src/Mcmc/Save.hs +4/−19
• src/Mcmc/Status.hs +10/−12
• test/Mcmc/ProposalSpec.hs +2/−2
• test/Mcmc/SaveSpec.hs +4/−4

@@ -6,8 +6,7 @@ Sample from a posterior using Markov chain Monte Carlo methods.  At the moment, the library is tailored to the Metropolis-Hastings algorithm-since it covers most use cases. However, implementation of more algorithms is-planned in the future.+since it covers most use cases. More algorithms will be implemented soon.   ## Documentation

@@ -37,7 +37,7 @@ proposals :: Cycle Double proposals =   fromList-    [slideSymmetric "medium" 1 1.0 True]+    [slideSymmetric 1.0 "medium" 1 True]  mons :: [MonitorParameter Double] mons = [monitorDouble "mu"]@@ -68,7 +68,7 @@ proposalsBactrian :: Cycle Double proposalsBactrian =   fromList-    [slideBactrian "bactrian" 1 0.5 1.0 True]+    [slideBactrian 0.5 1.0 "bactrian" 1 True]  normalBactrianBench :: GenIO -> IO () normalBactrianBench g = do

@@ -48,10 +48,10 @@   product [f ft yr x | (ft, yr) <- zip fatalities normalizedYears]  proposalAlpha :: Proposal I-proposalAlpha = _1 @~ slideSymmetric "alpha" 2 0.2 False+proposalAlpha = _1 @~ slideSymmetric 0.2 "alpha" 2 False  proposalBeta :: Proposal I-proposalBeta = _2 @~ slideSymmetric "beta" 1 0.2 False+proposalBeta = _2 @~ slideSymmetric 0.2 "beta" 1 False  proposals :: Cycle I proposals = fromList [proposalAlpha, proposalBeta]@@ -60,10 +60,10 @@ initial = (0, 0)  monAlpha :: MonitorParameter I-monAlpha = fst @. monitorDouble "alpha"+monAlpha = fst >$< monitorDouble "alpha"  monBeta :: MonitorParameter I-monBeta = snd @. monitorDouble "beta"+monBeta = snd >$< monitorDouble "beta"  monStd :: MonitorStdOut I monStd = monitorStdOut [monAlpha, monBeta] 150

@@ -1,6 +1,6 @@ cabal-version:  2.2 name:           mcmc-version:        0.2.3+version:        0.2.4 synopsis:       Sample from a posterior using Markov chain Monte Carlo description:    Please see the README on GitHub at <https://github.com/dschrempf/mcmc#readme> category:       Math, Statistics

@@ -86,10 +86,13 @@     (@~),     scale,     scaleUnbiased,+    scaleContrarily,+    scaleBactrian,     slide,-    slideBactrian,     slideSymmetric,     slideUniform,+    slideContrarily,+    slideBactrian,     Cycle,     fromList,     Order (..),

@@ -1,5 +1,4 @@ {-# LANGUAGE OverloadedStrings #-}-{-# OPTIONS_GHC -fno-warn-orphans #-}  -- | -- Module      :  Mcmc.Item@@ -18,15 +17,9 @@ where  import Data.Aeson+import Data.Aeson.Types import Numeric.Log -instance ToJSON a => ToJSON (Log a) where-  toJSON (Exp x) = toJSON x-  toEncoding (Exp x) = toEncoding x--instance FromJSON a => FromJSON (Log a) where-  parseJSON v = Exp <$> parseJSON v- -- | An 'Item', or link of the Markov chain. For reasons of computational -- efficiency, each state is associated with the corresponding prior and -- likelihood.@@ -41,13 +34,15 @@   deriving (Eq, Ord, Show, Read)  instance ToJSON a => ToJSON (Item a) where-  toJSON (Item x p l) = object ["s" .= x, "p" .= p, "l" .= l]-  toEncoding (Item x p l) = pairs ("s" .= x <> "p" .= p <> "l" .= l)+  toJSON (Item x (Exp p) (Exp l)) = object ["s" .= x, "p" .= p, "l" .= l]+  toEncoding (Item x (Exp p) (Exp l)) = pairs ("s" .= x <> "p" .= p <> "l" .= l) +item :: FromJSON a => Object -> Parser (Item a)+item v = do+  s <- v .: "s"+  p <- v .: "p"+  l <- v .: "l"+  return $ Item s (Exp p) (Exp l)+ instance FromJSON a => FromJSON (Item a) where-  parseJSON = withObject "Item" $-    \v ->-      Item-        <$> v .: "s"-        <*> v .: "p"-        <*> v .: "l"+  parseJSON = withObject "Item" item

@@ -11,6 +11,8 @@ -- Portability :  portable -- -- Creation date: Fri May 29 10:19:45 2020.+--+-- Functions to work with the 'Mcmc' state transformer. module Mcmc.Mcmc   ( Mcmc,     mcmcOutT,

@@ -12,6 +12,8 @@ -- Portability :  portable -- -- Creation date: Tue May  5 20:11:30 2020.+--+-- Metropolis-Hastings algorithm. module Mcmc.Metropolis   ( mh,     mhContinue,@@ -51,7 +53,7 @@  mhPropose :: Proposal a -> Mcmc a () mhPropose m = do-  let p = pSample $ pSimple m+  let p = pSimple m   s <- get   let (Item x pX lX) = item s       pF = priorF s

@@ -149,10 +149,6 @@     mfPeriod :: Int   } --- XXX: The file monitor also includes iteration, prior, likelihood, and--- posterior. What if I want to log trees; or other complex objects? In this--- case, we need a simpler monitor to a file.- -- | Monitor parameters to a file. monitorFile ::   -- | Name; used as part of the file name.@@ -246,10 +242,6 @@     mbParams :: [MonitorParameterBatch a],     mbSize :: Int   }---- XXX: The batch monitor also includes iteration, prior, likelihood, and--- posterior. What if I want to log trees; or other complex objects? In this--- case, we need a simpler monitor to a file.  -- | Monitor parameters to a file, see 'MonitorBatch'. monitorBatch ::

@@ -14,6 +14,7 @@ module Mcmc.Monitor.Parameter   ( -- * Parameter monitors     MonitorParameter (..),+    (>$<),     (@.),     monitorInt,     monitorDouble,@@ -24,8 +25,17 @@  import qualified Data.ByteString.Builder as BB import qualified Data.Double.Conversion.ByteString as BC+import Data.Functor.Contravariant  -- | Instruction about a parameter to monitor.+--+-- Convert a parameter monitor from one data type to another with '(>$<)'.+--+-- For example, monitor a 'Double' value being the first entry of a tuple:+--+-- @+-- mon = fst >$< monitorDouble+-- @ data MonitorParameter a = MonitorParameter   { -- | Name of parameter.     mpName :: String,@@ -33,15 +43,21 @@     mpFunc :: a -> BB.Builder   } +instance Contravariant (MonitorParameter) where+  contramap f (MonitorParameter n m) = MonitorParameter n (m . f)+ -- | Convert a parameter monitor from one data type to another. --+-- DEPRECATED.+-- -- For example, to monitor a 'Double' value being the first entry of a tuple: -- -- @ -- mon = fst @. monitorDouble -- @ (@.) :: (b -> a) -> MonitorParameter a -> MonitorParameter b-(@.) f (MonitorParameter n m) = MonitorParameter n (m . f)+(@.) = contramap+{-# DEPRECATED (@.) "Superseded by the contravariant instance, use '(>$<)'." #-}  -- | Monitor 'Int'. monitorInt ::

@@ -16,6 +16,7 @@ module Mcmc.Monitor.ParameterBatch   ( -- * Batch parameter monitors     MonitorParameterBatch (..),+    (>$<),     (@#),     monitorBatchMean,     monitorBatchMeanF,@@ -26,12 +27,21 @@  import qualified Data.ByteString.Builder as BB import qualified Data.Double.Conversion.ByteString as BC+import Data.Functor.Contravariant  -- | Instruction about a parameter to monitor via batch means. Usually, the -- monitored parameter is average over the batch size. However, arbitrary -- functions performing more complicated analyses on the states in the batch can -- be provided. --+-- Convert a batch monitor from one data type to another with '(>$<)'.+--+-- For example, batch monitor the mean of the first entry of a tuple:+--+-- @+-- mon = fst >$< monitorBatchMean+-- @+-- -- XXX: Batch monitors are slow at the moment because the monitored parameter -- has to be extracted from the state for each iteration. data MonitorParameterBatch a = MonitorParameterBatch@@ -41,6 +51,9 @@     mbpFunc :: [a] -> BB.Builder   } +instance Contravariant (MonitorParameterBatch) where+  contramap f (MonitorParameterBatch n m) = MonitorParameterBatch n (m . map f)+ -- | Convert a batch parameter monitor from one data type to another. -- -- For example, to batch monitor the mean of the first entry of a tuple:@@ -50,6 +63,7 @@ -- @ (@#) :: (b -> a) -> MonitorParameterBatch a -> MonitorParameterBatch b (@#) f (MonitorParameterBatch n m) = MonitorParameterBatch n (m . map f)+{-# DEPRECATED (@#) "Superseded by the contravariant instance, use '(>$<)'." #-}  mean :: Real a => [a] -> Double mean xs = realToFrac (sum xs) / fromIntegral (length xs)

@@ -19,9 +19,7 @@     normal,     exponential,     gamma,--    -- * Discrete priors-+    -- -- * Discrete priors     -- No discrete priors are available yet.      -- * Auxiliary functions@@ -98,8 +96,8 @@  -- | Intelligent product that stops when encountering a zero. ----- Use with care because the elements have to be checked for positiveness, and--- this can take some time if the list is long and does not contain any zeroes.+-- Use with care because the elements are checked for positiveness, and this can+-- take some time if the list is long and does not contain any zeroes. product' :: [Log Double] -> Log Double product' = fromMaybe 0 . prodM 

@@ -19,7 +19,7 @@   ( -- * Proposal     Proposal (..),     (@~),-    ProposalSimple (..),+    ProposalSimple,     Tuner (tParam, tFunc),     createProposal,     tune,@@ -45,6 +45,7 @@ where  import Data.Aeson+import Data.Bifunctor import qualified Data.ByteString.Builder as BB import qualified Data.ByteString.Lazy.Char8 as BL import Data.Default@@ -92,7 +93,7 @@ -- For example: -- -- @--- scaleFirstEntryOfTuple = scale >>> _1+-- scaleFirstEntryOfTuple = _1 @~ scale -- @ (@~) :: Lens' b a -> Proposal a -> Proposal b (@~) l (Proposal n w s t) = Proposal n w (convertS l s) (convertT l <$> t)@@ -104,13 +105,12 @@ -- -- In order to calculate the Metropolis-Hastings ratio, we need to know the -- ratio of the backward to forward kernels (i.e., the probability masses or--- probability densities). For unbiased proposals, this ratio is 1.0.-newtype ProposalSimple a = ProposalSimple-  { pSample :: a -> GenIO -> IO (a, Log Double)-  }+-- probability densities). For unbiased proposals, this ratio is 1.0. For biased+-- proposals, the ratio is ?.+type ProposalSimple a = a -> GenIO -> IO (a, Log Double)  convertS :: Lens' b a -> ProposalSimple a -> ProposalSimple b-convertS l (ProposalSimple s) = ProposalSimple s'+convertS l s = s'   where     s' v g = do       (x', r) <- s (v ^. l) g@@ -129,19 +129,19 @@  -- | Create a possibly tuneable proposal. createProposal ::-  -- | Name.-  String ->-  -- | Weight.-  Int ->   -- | Function creating a simple proposal for a given tuning parameter. The   -- larger the tuning parameter, the larger the proposal (and the lower the   -- expected acceptance ratio), and vice versa.   (Double -> ProposalSimple a) ->+  -- | Name.+  String ->+  -- | Weight.+  Int ->   -- | Activate tuning?   Bool ->   Proposal a-createProposal n w f True = Proposal n w (f 1.0) (Just $ Tuner 1.0 f)-createProposal n w f False = Proposal n w (f 1.0) Nothing+createProposal f n w True = Proposal n w (f 1.0) (Just $ Tuner 1.0 f)+createProposal f n w False = Proposal n w (f 1.0) Nothing  -- Minimal tuning parameter; subject to change. tuningParamMin :: Double@@ -345,8 +345,8 @@  -- | For key @k@, prepend an accepted (True) or rejected (False) proposal. pushA :: (Ord k, Show k) => k -> Bool -> Acceptance k -> Acceptance k-pushA k True = Acceptance . M.adjust (\(a, r) -> (succ a, r)) k . fromAcceptance-pushA k False = Acceptance . M.adjust (\(a, r) -> (a, succ r)) k . fromAcceptance+pushA k True = Acceptance . M.adjust (first succ) k . fromAcceptance+pushA k False = Acceptance . M.adjust (second succ) k . fromAcceptance {-# INLINEABLE pushA #-}  -- | Reset acceptance storage.

@@ -67,30 +67,32 @@   | m < 0 = error "bactrianAdditiveSimple: Spike parameter negative."   | m >= 1 = error "bactrianAdditiveSimple: Spike parameter 1.0 or larger."   | s <= 0 = error "bactrianAdditiveSimple: Standard deviation 0.0 or smaller."-  | otherwise = ProposalSimple $ bactrianAdditive m (t * s)+  | otherwise = bactrianAdditive m (t * s)  -- | Additive symmetric proposal with kernel similar to the silhouette of a--- Bactrian camel. The [Bactrian--- kernel](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3845170/figure/fig01)--- is a mixture of two symmetrically arranged normal distributions. The spike+-- Bactrian camel.+--+-- The [Bactrian+-- kernel](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3845170/figure/fig01) is+-- a mixture of two symmetrically arranged normal distributions. The spike -- parameter loosely determines the standard deviations of the individual humps--- while the other parameter refers to the standard deviation of the complete+-- while the second parameter refers to the standard deviation of the complete -- Bactrian kernel. -- -- See https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3845170/. slideBactrian ::-  -- | Name.-  String ->-  -- | Weight.-  Int ->   -- | Spike parameter.   Double ->   -- | Standard deviation.   Double ->+  -- | Name.+  String ->+  -- | Weight.+  Int ->   -- | Enable tuning.   Bool ->   Proposal Double-slideBactrian n w m s = createProposal n w (bactrianAdditiveSimple m s)+slideBactrian m s = createProposal (bactrianAdditiveSimple m s)  -- We have: -- x  (1+dx ) = x'@@ -118,20 +120,20 @@   | m < 0 = error "bactrianMultSimple: Spike parameter negative."   | m >= 1 = error "bactrianMultSimple: Spike parameter 1.0 or larger."   | s <= 0 = error "bactrianMultSimple: Standard deviation 0.0 or smaller."-  | otherwise = ProposalSimple $ bactrianMult m (t * s)+  | otherwise = bactrianMult m (t * s)  -- | Multiplicative proposal with kernel similar to the silhouette of a Bactrian -- camel. See 'slideBactrian'. scaleBactrian ::-  -- | Name.-  String ->-  -- | Weight.-  Int ->   -- | Spike parameter.   Double ->   -- | Standard deviation.   Double ->+  -- | Name.+  String ->+  -- | Weight.+  Int ->   -- | Enable tuning.   Bool ->   Proposal Double-scaleBactrian n w m s = createProposal n w (bactrianMultSimple m s)+scaleBactrian m s = createProposal (bactrianMultSimple m s)

@@ -50,7 +50,7 @@   -- required for biased proposals.   Maybe (Double -> Double) ->   ProposalSimple a-genericContinuous d f fInv = ProposalSimple $ sampleCont d f fInv+genericContinuous d f fInv = sampleCont d f fInv  sampleDiscrete ::   (DiscreteDistr d, DiscreteGen d) =>@@ -82,4 +82,4 @@   -- required for biased proposals.   Maybe (Int -> Int) ->   ProposalSimple a-genericDiscrete fd f fInv = ProposalSimple $ sampleDiscrete fd f fInv+genericDiscrete fd f fInv = sampleDiscrete fd f fInv

@@ -29,37 +29,37 @@  -- | Multiplicative proposal with Gamma distributed kernel. scale ::-  -- | Name.-  String ->-  -- | Weight.-  Int ->   -- | Shape.   Double ->   -- | Scale.   Double ->+  -- | Name.+  String ->+  -- | Weight.+  Int ->   -- | Enable tuning.   Bool ->   Proposal Double-scale n w k th = createProposal n w (scaleSimple k th)+scale k th = createProposal (scaleSimple k th)  -- | Multiplicative proposal with Gamma distributed kernel. -- -- The scale of the Gamma distributions is set to (shape)^{-1}, so that the mean -- of the Gamma distribution is 1.0. scaleUnbiased ::+  -- | Shape.+  Double ->   -- | Name.   String ->   -- | Weight.   Int ->-  -- | Shape.-  Double ->   -- | Enable tuning.   Bool ->   Proposal Double-scaleUnbiased n w k = createProposal n w (scaleSimple k (1 / k))+scaleUnbiased k = createProposal (scaleSimple k (1 / k))  contra :: (Double, Double) -> Double -> (Double, Double)-contra (x, y) z = (x*z, y/z)+contra (x, y) z = (x * z, y / z)  scaleContrarilySimple :: Double -> Double -> Double -> ProposalSimple (Double, Double) scaleContrarilySimple k th t = genericContinuous (gammaDistr (k / t) (th * t)) contra (Just recip)@@ -69,15 +69,15 @@ -- The two values are scaled contrarily so that their product stays constant. -- Contrary proposals are useful when parameters are confounded. scaleContrarily ::-  -- | Name.-  String ->-  -- | Weight.-  Int ->   -- | Shape.   Double ->   -- | Scale.   Double ->+  -- | Name.+  String ->+  -- | Weight.+  Int ->   -- | Enable tuning.   Bool ->   Proposal (Double, Double)-scaleContrarily n w k th = createProposal n w (scaleContrarilySimple k th)+scaleContrarily k th = createProposal (scaleContrarilySimple k th)

@@ -30,18 +30,18 @@  -- | Additive proposal with normally distributed kernel. slide ::-  -- | Name.-  String ->-  -- | Weight.-  Int ->   -- | Mean.   Double ->   -- | Standard deviation.   Double ->+  -- | Name.+  String ->+  -- | Weight.+  Int ->   -- | Enable tuning.   Bool ->   Proposal Double-slide n w m s = createProposal n w (slideSimple m s)+slide m s = createProposal (slideSimple m s)  -- The actual proposal with tuning parameter. slideSymmetricSimple :: Double -> Double -> ProposalSimple Double@@ -51,16 +51,16 @@ -- proposal is very fast, because the Metropolis-Hastings ratio does not include -- calculation of the forwards and backwards kernels. slideSymmetric ::+  -- | Standard deviation.+  Double ->   -- | Name.   String ->   -- | Weight.   Int ->-  -- | Standard deviation.-  Double ->   -- | Enable tuning.   Bool ->   Proposal Double-slideSymmetric n w s = createProposal n w (slideSymmetricSimple s)+slideSymmetric s = createProposal (slideSymmetricSimple s)  -- The actual proposal with tuning parameter. slideUniformSimple :: Double -> Double -> ProposalSimple Double@@ -71,16 +71,16 @@ -- because the Metropolis-Hastings ratio does not include calculation of the -- forwards and backwards kernels. slideUniform ::+  -- | Delta.+  Double ->   -- | Name.   String ->   -- | Weight.   Int ->-  -- | Delta.-  Double ->   -- | Enable tuning.   Bool ->   Proposal Double-slideUniform n w d = createProposal n w (slideUniformSimple d)+slideUniform d = createProposal (slideUniformSimple d)  contra :: (Double, Double) -> Double -> (Double, Double) contra (x, y) d = (x + d, y - d)@@ -93,15 +93,15 @@ -- The two values are slid contrarily so that their sum stays constant. Contrary -- proposals are useful when parameters are confounded. slideContrarily ::-  -- | Name.-  String ->-  -- | Weight.-  Int ->   -- | Mean.   Double ->   -- | Standard deviation.   Double ->+  -- | Name.+  String ->+  -- | Weight.+  Int ->   -- | Enable tuning.   Bool ->   Proposal (Double, Double)-slideContrarily n w m s = createProposal n w (slideContrarilySimple m s)+slideContrarily m s = createProposal (slideContrarilySimple m s)

@@ -93,19 +93,8 @@  -- | Save a 'Status' to file. ----- Saved information:--- - state--- - iteration--- - trace--- - acceptance ratios--- - generator------ Important information that cannot be saved and has to be provided again when--- a chain is restored:--- - prior function--- - likelihood function--- - cycle--- - monitor+-- Some important values have to be provided upon restoring the status. See+-- 'loadStatus'. saveStatus :: ToJSON a => FilePath -> Status a -> IO () saveStatus fn s = BL.writeFile fn $ compress $ encode (toSave s) @@ -175,13 +164,9 @@   -- already a good indicator.   when     (p x /= svp)-    ( error-        "loadStatus: Provided prior function does not match the saved prior."-    )+    (error "loadStatus: Provided prior function does not match the saved prior.")   when     (l x /= svl)-    ( error-        "loadStatus: Provided likelihood function does not match the saved likelihood."-    )+    (error "loadStatus: Provided likelihood function does not match the saved likelihood.")   removeFile fn   return s

@@ -1,18 +1,13 @@--- XXX: Add possibility to store supplementary information about the chain.------ Maybe something like Trace b; and give a function a -> b to extract--- supplementary info.+-- Note: It is not necessary to add another type @b@ to store supplementary+-- information about the chain. The information can just be stored in @a@+-- equally well. --- XXX: Status tuned exclusively to the Metropolis-Hastings algorithm. We--- should abstract the algorithm from the chain. For example,+-- XXX: Status tuned exclusively to the Metropolis-Hastings algorithm. We should+-- abstract the algorithm from the chain. Maybe something like: -- -- @--- data Status a b = Status { Chain a; Algorithm a b}+-- data Status a = Status { Chain a; Algorithm a} -- @------ where a described the state space and b the auxiliary information of the--- algorithm. This would also solve the above problem, for example in terms of--- the Hamiltonian algorithm  -- | -- Module      :  Mcmc.Status@@ -49,6 +44,9 @@  -- | The 'Status' contains all information to run an MCMC chain. It is -- constructed using the function 'status'.+--+-- The polymorphic type @a@ stores the state of the chain. It can also be used+-- to store auxiliary information. data Status a = Status   { -- MCMC related variables; saved. @@ -136,7 +134,7 @@   -- that auto tuning only happens during burn in.   Int ->   -- | A source of randomness. For reproducible runs, make-  -- sure to use a generator with the same seed.+  -- sure to use generators with the same, fixed seed.   GenIO ->   Status a status n p l c m x mB mT nI g

@@ -20,10 +20,10 @@ import Test.Hspec  p1 :: Proposal Double-p1 = slideSymmetric "test1" 1 1.0 True+p1 = slideSymmetric 1.0 "test1" 1 True  p2 :: Proposal Double-p2 = slideSymmetric "test2" 3 1.0 True+p2 = slideSymmetric 1.0 "test2" 3 True  c :: Cycle Double c = fromList [p1, p2]

@@ -38,10 +38,10 @@ proposals :: Cycle Double proposals =   fromList-    [ slideSymmetric "small" 5 0.1 True,-      slideSymmetric "medium" 2 1.0 True,-      slideSymmetric "large" 2 5.0 True,-      slide "skewed" 1 1.0 4.0 True+    [ slideSymmetric 0.1 "small" 5 True,+      slideSymmetric 1.0 "medium" 2 True,+      slideSymmetric 5.0 "large" 2 True,+      slide 1.0 4.0 "skewed" 1 True     ]  monStd :: MonitorStdOut Double