NestedSampling (empty) → 0.1.1
raw patch · 6 files changed
+681/−0 lines, 6 filesdep +NestedSamplingdep +basedep +randomsetup-changed
Dependencies added: NestedSampling, base, random, vector
Files
- LICENSE +339/−0
- NestedSampling.cabal +43/−0
- README +25/−0
- Setup.hs +2/−0
- lib/Statistics/MiniNest.hs +115/−0
- lighthouse.hs +157/−0
+ LICENSE view
@@ -0,0 +1,339 @@+ GNU GENERAL PUBLIC LICENSE+ Version 2, June 1991++ Copyright (C) 1989, 1991 Free Software Foundation, Inc.,+ 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA+ Everyone is permitted to copy and distribute verbatim copies+ of this license document, but changing it is not allowed.++ Preamble++ The licenses for most software are designed to take away your+freedom to share and change it. By contrast, the GNU General Public+License is intended to guarantee your freedom to share and change free+software--to make sure the software is free for all its users. This+General Public License applies to most of the Free Software+Foundation's software and to any other program whose authors commit to+using it. (Some other Free Software Foundation software is covered by+the GNU Lesser General Public License instead.) You can apply it to+your programs, too.++ When we speak of free software, we are referring to freedom, not+price. Our General Public Licenses are designed to make sure that you+have the freedom to distribute copies of free software (and charge for+this service if you wish), that you receive source code or can get it+if you want it, that you can change the software or use pieces of it+in new free programs; and that you know you can do these things.++ To protect your rights, we need to make restrictions that forbid+anyone to deny you these rights or to ask you to surrender the rights.+These restrictions translate to certain responsibilities for you if you+distribute copies of the software, or if you modify it.++ For example, if you distribute copies of such a program, whether+gratis or for a fee, you must give the recipients all the rights that+you have. You must make sure that they, too, receive or can get the+source code. And you must show them these terms so they know their+rights.++ We protect your rights with two steps: (1) copyright the software, and+(2) offer you this license which gives you legal permission to copy,+distribute and/or modify the software.++ Also, for each author's protection and ours, we want to make certain+that everyone understands that there is no warranty for this free+software. If the software is modified by someone else and passed on, we+want its recipients to know that what they have is not the original, so+that any problems introduced by others will not reflect on the original+authors' reputations.++ Finally, any free program is threatened constantly by software+patents. We wish to avoid the danger that redistributors of a free+program will individually obtain patent licenses, in effect making the+program proprietary. To prevent this, we have made it clear that any+patent must be licensed for everyone's free use or not licensed at all.++ The precise terms and conditions for copying, distribution and+modification follow.++ GNU GENERAL PUBLIC LICENSE+ TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION++ 0. This License applies to any program or other work which contains+a notice placed by the copyright holder saying it may be distributed+under the terms of this General Public License. The "Program", below,+refers to any such program or work, and a "work based on the Program"+means either the Program or any derivative work under copyright law:+that is to say, a work containing the Program or a portion of it,+either verbatim or with modifications and/or translated into another+language. (Hereinafter, translation is included without limitation in+the term "modification".) Each licensee is addressed as "you".++Activities other than copying, distribution and modification are not+covered by this License; they are outside its scope. The act of+running the Program is not restricted, and the output from the Program+is covered only if its contents constitute a work based on the+Program (independent of having been made by running the Program).+Whether that is true depends on what the Program does.++ 1. You may copy and distribute verbatim copies of the Program's+source code as you receive it, in any medium, provided that you+conspicuously and appropriately publish on each copy an appropriate+copyright notice and disclaimer of warranty; keep intact all the+notices that refer to this License and to the absence of any warranty;+and give any other recipients of the Program a copy of this License+along with the Program.++You may charge a fee for the physical act of transferring a copy, and+you may at your option offer warranty protection in exchange for a fee.++ 2. You may modify your copy or copies of the Program or any portion+of it, thus forming a work based on the Program, and copy and+distribute such modifications or work under the terms of Section 1+above, provided that you also meet all of these conditions:++ a) You must cause the modified files to carry prominent notices+ stating that you changed the files and the date of any change.++ b) You must cause any work that you distribute or publish, that in+ whole or in part contains or is derived from the Program or any+ part thereof, to be licensed as a whole at no charge to all third+ parties under the terms of this License.++ c) If the modified program normally reads commands interactively+ when run, you must cause it, when started running for such+ interactive use in the most ordinary way, to print or display an+ announcement including an appropriate copyright notice and a+ notice that there is no warranty (or else, saying that you provide+ a warranty) and that users may redistribute the program under+ these conditions, and telling the user how to view a copy of this+ License. (Exception: if the Program itself is interactive but+ does not normally print such an announcement, your work based on+ the Program is not required to print an announcement.)++These requirements apply to the modified work as a whole. If+identifiable sections of that work are not derived from the Program,+and can be reasonably considered independent and separate works in+themselves, then this License, and its terms, do not apply to those+sections when you distribute them as separate works. But when you+distribute the same sections as part of a whole which is a work based+on the Program, the distribution of the whole must be on the terms of+this License, whose permissions for other licensees extend to the+entire whole, and thus to each and every part regardless of who wrote it.++Thus, it is not the intent of this section to claim rights or contest+your rights to work written entirely by you; rather, the intent is to+exercise the right to control the distribution of derivative or+collective works based on the Program.++In addition, mere aggregation of another work not based on the Program+with the Program (or with a work based on the Program) on a volume of+a storage or distribution medium does not bring the other work under+the scope of this License.++ 3. You may copy and distribute the Program (or a work based on it,+under Section 2) in object code or executable form under the terms of+Sections 1 and 2 above provided that you also do one of the following:++ a) Accompany it with the complete corresponding machine-readable+ source code, which must be distributed under the terms of Sections+ 1 and 2 above on a medium customarily used for software interchange; or,++ b) Accompany it with a written offer, valid for at least three+ years, to give any third party, for a charge no more than your+ cost of physically performing source distribution, a complete+ machine-readable copy of the corresponding source code, to be+ distributed under the terms of Sections 1 and 2 above on a medium+ customarily used for software interchange; or,++ c) Accompany it with the information you received as to the offer+ to distribute corresponding source code. (This alternative is+ allowed only for noncommercial distribution and only if you+ received the program in object code or executable form with such+ an offer, in accord with Subsection b above.)++The source code for a work means the preferred form of the work for+making modifications to it. For an executable work, complete source+code means all the source code for all modules it contains, plus any+associated interface definition files, plus the scripts used to+control compilation and installation of the executable. However, as a+special exception, the source code distributed need not include+anything that is normally distributed (in either source or binary+form) with the major components (compiler, kernel, and so on) of the+operating system on which the executable runs, unless that component+itself accompanies the executable.++If distribution of executable or object code is made by offering+access to copy from a designated place, then offering equivalent+access to copy the source code from the same place counts as+distribution of the source code, even though third parties are not+compelled to copy the source along with the object code.++ 4. You may not copy, modify, sublicense, or distribute the Program+except as expressly provided under this License. Any attempt+otherwise to copy, modify, sublicense or distribute the Program is+void, and will automatically terminate your rights under this License.+However, parties who have received copies, or rights, from you under+this License will not have their licenses terminated so long as such+parties remain in full compliance.++ 5. You are not required to accept this License, since you have not+signed it. However, nothing else grants you permission to modify or+distribute the Program or its derivative works. These actions are+prohibited by law if you do not accept this License. Therefore, by+modifying or distributing the Program (or any work based on the+Program), you indicate your acceptance of this License to do so, and+all its terms and conditions for copying, distributing or modifying+the Program or works based on it.++ 6. Each time you redistribute the Program (or any work based on the+Program), the recipient automatically receives a license from the+original licensor to copy, distribute or modify the Program subject to+these terms and conditions. You may not impose any further+restrictions on the recipients' exercise of the rights granted herein.+You are not responsible for enforcing compliance by third parties to+this License.++ 7. If, as a consequence of a court judgment or allegation of patent+infringement or for any other reason (not limited to patent issues),+conditions are imposed on you (whether by court order, agreement or+otherwise) that contradict the conditions of this License, they do not+excuse you from the conditions of this License. If you cannot+distribute so as to satisfy simultaneously your obligations under this+License and any other pertinent obligations, then as a consequence you+may not distribute the Program at all. For example, if a patent+license would not permit royalty-free redistribution of the Program by+all those who receive copies directly or indirectly through you, then+the only way you could satisfy both it and this License would be to+refrain entirely from distribution of the Program.++If any portion of this section is held invalid or unenforceable under+any particular circumstance, the balance of the section is intended to+apply and the section as a whole is intended to apply in other+circumstances.++It is not the purpose of this section to induce you to infringe any+patents or other property right claims or to contest validity of any+such claims; this section has the sole purpose of protecting the+integrity of the free software distribution system, which is+implemented by public license practices. Many people have made+generous contributions to the wide range of software distributed+through that system in reliance on consistent application of that+system; it is up to the author/donor to decide if he or she is willing+to distribute software through any other system and a licensee cannot+impose that choice.++This section is intended to make thoroughly clear what is believed to+be a consequence of the rest of this License.++ 8. If the distribution and/or use of the Program is restricted in+certain countries either by patents or by copyrighted interfaces, the+original copyright holder who places the Program under this License+may add an explicit geographical distribution limitation excluding+those countries, so that distribution is permitted only in or among+countries not thus excluded. In such case, this License incorporates+the limitation as if written in the body of this License.++ 9. The Free Software Foundation may publish revised and/or new versions+of the General Public License from time to time. Such new versions will+be similar in spirit to the present version, but may differ in detail to+address new problems or concerns.++Each version is given a distinguishing version number. If the Program+specifies a version number of this License which applies to it and "any+later version", you have the option of following the terms and conditions+either of that version or of any later version published by the Free+Software Foundation. If the Program does not specify a version number of+this License, you may choose any version ever published by the Free Software+Foundation.++ 10. If you wish to incorporate parts of the Program into other free+programs whose distribution conditions are different, write to the author+to ask for permission. For software which is copyrighted by the Free+Software Foundation, write to the Free Software Foundation; we sometimes+make exceptions for this. Our decision will be guided by the two goals+of preserving the free status of all derivatives of our free software and+of promoting the sharing and reuse of software generally.++ NO WARRANTY++ 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY+FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN+OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES+PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED+OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF+MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS+TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE+PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,+REPAIR OR CORRECTION.++ 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR+REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,+INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING+OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED+TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY+YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER+PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE+POSSIBILITY OF SUCH DAMAGES.++ END OF TERMS AND CONDITIONS++ How to Apply These Terms to Your New Programs++ If you develop a new program, and you want it to be of the greatest+possible use to the public, the best way to achieve this is to make it+free software which everyone can redistribute and change under these terms.++ To do so, attach the following notices to the program. It is safest+to attach them to the start of each source file to most effectively+convey the exclusion of warranty; and each file should have at least+the "copyright" line and a pointer to where the full notice is found.++ <one line to give the program's name and a brief idea of what it does.>+ Copyright (C) <year> <name of author>++ This program is free software; you can redistribute it and/or modify+ it under the terms of the GNU General Public License as published by+ the Free Software Foundation; either version 2 of the License, or+ (at your option) any later version.++ This program is distributed in the hope that it will be useful,+ but WITHOUT ANY WARRANTY; without even the implied warranty of+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the+ GNU General Public License for more details.++ You should have received a copy of the GNU General Public License along+ with this program; if not, write to the Free Software Foundation, Inc.,+ 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.++Also add information on how to contact you by electronic and paper mail.++If the program is interactive, make it output a short notice like this+when it starts in an interactive mode:++ Gnomovision version 69, Copyright (C) year name of author+ Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.+ This is free software, and you are welcome to redistribute it+ under certain conditions; type `show c' for details.++The hypothetical commands `show w' and `show c' should show the appropriate+parts of the General Public License. Of course, the commands you use may+be called something other than `show w' and `show c'; they could even be+mouse-clicks or menu items--whatever suits your program.++You should also get your employer (if you work as a programmer) or your+school, if any, to sign a "copyright disclaimer" for the program, if+necessary. Here is a sample; alter the names:++ Yoyodyne, Inc., hereby disclaims all copyright interest in the program+ `Gnomovision' (which makes passes at compilers) written by James Hacker.++ <signature of Ty Coon>, 1 April 1989+ Ty Coon, President of Vice++This General Public License does not permit incorporating your program into+proprietary programs. If your program is a subroutine library, you may+consider it more useful to permit linking proprietary applications with the+library. If this is what you want to do, use the GNU Lesser General+Public License instead of this License.
+ NestedSampling.cabal view
@@ -0,0 +1,43 @@+Name: NestedSampling+Version: 0.1.1+Synopsis: A port of John Skilling's nested sampling C code to Haskell.++Description: Nested Sampling is a numerical algorithm for approximate Bayesian+ inference. It generates samples from the posterior+ distribution but its main purpose is to estimate the+ evidence P(M|D) of the model conditioned on the observed+ data. More information on Nested Sampling is available+ at http://en.wikipedia.org/wiki/Nested_sampling_algorithm.++ The original code can be found at+ http://www.inference.phy.cam.ac.uk/bayesys/sivia/+ along with documentation at+ http://www.inference.phy.cam.ac.uk/bayesys/.+ An example program called lighthouse.hs is included.++ So far, only the simple demonstration file called mininest.c+ has been ported. There is a more sophisticated C library+ available at+ http://www.inference.phy.cam.ac.uk/bayesys/nest/nest.tar.gz+ but it has not been ported to Haskell yet.++Homepage: https://github.com/ijt/haskell_nested_sampling+License: GPL-2+License-file: LICENSE+Author: Issac Trotts+Maintainer: issac.trotts@gmail.com+Copyright: (C) Sivia, Skilling 2006, Trotts 2011+Category: Statistics+Build-type: Simple+Extra-source-files: lighthouse.hs README+Cabal-version: >=1.8++Library+ Exposed-modules: Statistics.MiniNest+ Build-depends: base >= 4 && < 5, random+ hs-source-dirs: lib++Executable lighthouse+ Main-Is: lighthouse.hs+ Build-depends: base >= 4 && < 5, random, vector, NestedSampling+
+ README view
@@ -0,0 +1,25 @@+The code here is a fairly straightforward translation of the tutorial+nested sampling code from Skilling and Sivia. The translation was+done by Issac Trotts starting in June 2011.++What follows is an adaptation of the original README:++This directory holds little toy nested-sampling programs+in Haskell, adapted from the C code in the update of Devinder's book "Data+Analysis: a Bayesian Tutorial" (2nd edition) OUP 2006.++To get started, install Haskell (GHC), then run+$ cabal install++Try out the example program like this:++$ lighthouse +logZ: -160.48 +- 0.17+information: 2.90 nats+1000 samples++x = 1.25 +- 0.18+y = 1.00 +- 0.20++Details can be found at the top of lighthouse.hs.+
+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ lib/Statistics/MiniNest.hs view
@@ -0,0 +1,115 @@+module Statistics.MiniNest where++import Control.Monad (forM)+import Data.IORef+import Data.List (sort)+import System.Random (randomRIO)+import Text.Printf++-- logarithmic addition log(exp(x)+exp(y))+plus :: Double -> Double -> Double+plus x y+ | x > y = x + log (1 + exp (y-x))+ | otherwise = y + log (1 + exp (x-y))++data NestedSamplingResult a = NestedSamplingResult {+ nsLogZ :: Double,+ nsLogZdelta :: Double, -- evidence +- deviation+ nsInfoNats :: Double, -- information in nats+ nsSamples :: [a] }++instance Show (NestedSamplingResult a) where+ show result =+ (printf "logZ: %.2f +- %.2f\n" (nsLogZ result) (nsLogZdelta result) ++ + printf "information: %.2f nats\n" (nsInfoNats result) +++ printf "%i samples\n" (length $ nsSamples result))++class SamplingObject a where+ setLogWt :: a -> Double -> a+ getLogWt :: a -> Double+ getLogL :: a -> Double++-- |nestedSampling computes the evidence Z and samples from the posterior.+-- Args:+-- priorSamples: a list of samples from the prior.+-- explore: a function that evolves an object within a likelihood constraint.+-- iterations: number of iterations to run.+nestedSampling :: (Ord a, SamplingObject a) => [a] -> (a -> Double -> IO a) -> Int -> IO (NestedSamplingResult a)+nestedSampling priorSamples explore iterations = do+ let n = length priorSamples++ -- Collection of n objects+ objsRef <- newIORef priorSamples+ samplesRef <- newIORef [] -- Posterior samples+ hRef <- newIORef 0 -- Information, initially 0+ logZRef <- newIORef (-10**37) -- ln(Evidence Z, initially 0)++ -- Outermost interval of prior mass+ -- ln(width in prior mass)+ logWidthRef <- newIORef $ getLogWidth n++ -- NESTED SAMPLING LOOP ______________________________________________+ forM [1..iterations] (\nest -> do+ -- Worst object in collection, with Weight = width * Likelihood+ objs <- readIORef objsRef+ let worst = head $ sort objs+ logwidth <- readIORef logWidthRef+ let worst' = setLogWt worst (logwidth + (getLogL worst))++ -- Update Evidence Z and Information H+ logZ <- readIORef logZRef+ h <- readIORef hRef+ let logZnew = plus logZ (getLogWt worst')+ writeIORef hRef $ (exp $ getLogWt worst' - logZnew) * (getLogL worst')+ + (exp $ logZ - logZnew) * (h + logZ) - logZnew+ writeIORef logZRef logZnew++ -- Posterior Samples (optional)+ oldSamples <- readIORef samplesRef+ writeIORef samplesRef (worst' : oldSamples)++ -- Kill worst object.+ let objs' = drop 1 $ sort objs+ writeIORef objsRef objs'++ -- Copy another object at random.+ objToCopy <- choice objs'++ -- new likelihood constraint+ let logLstar = getLogL worst'++ -- Evolve copied object within constraint+ mutatedCopy <- explore objToCopy logLstar++ -- Save copied and mutated object.+ writeIORef objsRef (mutatedCopy : objs')++ -- Shrink interval+ writeIORef logWidthRef (logwidth - 1.0 / fromIntegral n))++ -- Exit with evidence Z, information H, and optional posterior Samples+ logZ <- readIORef logZRef+ h <- readIORef hRef+ samples <- readIORef samplesRef+ return $ NestedSamplingResult {+ nsLogZ=logZ,+ nsLogZdelta=sqrt (h / fromIntegral n), -- evidence +- deviation+ nsInfoNats=h, -- information in nats+ nsSamples=samples+ }++-- |choice chooses uniformly at random from a list.+choice :: [a] -> IO a+choice [] = error "No items specified for choice."+choice [x] = return x+choice xs = do+ let n = length xs+ k <- randomRIO (0, n-1)+ return $ xs !! k++floatRatio :: Int -> Int -> Float+floatRatio n1 n2 = fromIntegral n1 / fromIntegral n2++getLogWidth :: Int -> Double+getLogWidth n = log $ 1.0 - exp(-1.0 / fromIntegral n)+
+ lighthouse.hs view
@@ -0,0 +1,157 @@+-- lighthouse.hs "LIGHTHOUSE" NESTED SAMPLING APPLICATION+-- (GNU General Public License software, (C) Sivia and Skilling 2006)+-- u=0 u=1+-- -------------------------------------+-- y=2 |:::::::::::::::::::::::::::::::::::::| v=1+-- |::::::::::::::::::::::LIGHT::::::::::|+-- north|::::::::::::::::::::::HOUSE::::::::::|+-- |:::::::::::::::::::::::::::::::::::::|+-- |:::::::::::::::::::::::::::::::::::::|+-- y=0 |:::::::::::::::::::::::::::::::::::::| v=0+-- --*--------------*----*--------*-**--**--*-*-------------*--------+-- x=-2 coastline -->east x=2+-- Problem:+-- Lighthouse at (x,y) emitted n flashes observed at D[.] on coast.+-- Inputs:+-- Prior(u) is uniform (=1) over (0,1), mapped to x = 4*u - 2; and+-- Prior(v) is uniform (=1) over (0,1), mapped to y = 2*v; so that+-- Position is 2-dimensional -2 < x < 2, 0 < y < 2 with flat prior+-- Likelihood is L(x,y) = PRODUCT[k] (y/pi) / ((D[k] - x)^2 + y^2)+-- Outputs:+-- Evidence is Z = INTEGRAL L(x,y) Prior(x,y) dxdy+-- Posterior is P(x,y) = L(x,y) / Z estimating lighthouse position+-- Information is H = INTEGRAL P(x,y) log(P(x,y)/Prior(x,y)) dxdy++import qualified Data.Vector.Unboxed as UV+import Control.Monad (mapM)+import Statistics.MiniNest+import System.Random (randomIO)+import Text.Printf++data Lighthouse = Lighthouse {+ lhU :: Double,+ lhV :: Double,+ lhX :: Double,+ lhY :: Double,+ lhLogL :: Double,+ lhLogWt :: Double +} deriving (Eq, Show)++instance Ord Lighthouse where+ a <= b = lhLogL a <= lhLogL b++instance SamplingObject Lighthouse where+ setLogWt lh newLogWt = lh { lhLogWt = newLogWt }+ getLogWt lh = lhLogWt lh+ getLogL lh = lhLogL lh++logLhoodOfData :: UV.Vector Double -> Double -> Double -> Double+logLhoodOfData observations x y = UV.sum $ UV.map term observations+ where term dk = log (y / pi) - log ((dk - x)*(dk - x) + y*y)++-- logLikelihood function+-- x: Easterly position+-- y: Northerly position+logLhood :: Double -> Double -> Double+logLhood x y = logLhoodOfData lhData x y++lhData = UV.fromList [4.73, 0.45, -1.73, 1.09, 2.19, 0.12, 1.31,+ 1.00, 1.32, 1.07, 0.86, -0.49, -2.59, 1.73, 2.11,+ 1.61, 4.98, 1.71, 2.23,-57.20, 0.96, 1.25, -1.56,+ 2.45, 1.19, 2.17,-10.66, 1.91, -4.16, 1.92, 0.10, 1.98,+ -2.51, 5.55, -0.47, 1.91, 0.95, -0.78, -0.84, 1.72,+ -0.01, 1.48, 2.70, 1.21, 4.41, -4.79, 1.33, 0.81,+ 0.20, 1.58, 1.29, 16.19, 2.75, -2.38, -1.79,+ 6.50,-18.53, 0.72, 0.94, 3.64, 1.94, -0.11, 1.57, 0.57]++-- |Sample from U[0,1]+uniform :: IO Double+uniform = randomIO++sampleFromPrior :: IO Lighthouse+sampleFromPrior = do+ u <- uniform+ v <- uniform+ let x=4*u - 2+ y=2*v+ return $ Lighthouse u v x y (logLhood x y) 0++-- |Evolve Lighthouse within likelihood constraint+-- obj: Lighthouse being evolved+-- logLstar: Likelihood constraint L > Lstar+explore :: Lighthouse -> Double -> IO Lighthouse+explore obj logLstar =+ explore' step m accept reject (lhU obj) (lhV obj) (lhX obj) (lhY obj)+ (lhLogL obj)+ where step = 0.1 -- Initial guess suitable step-size in (0,1)+ m = 20 -- MCMC counter (pre-judged # steps)+ accept = 0 -- # MCMC acceptances+ reject = 0 -- # MCMC rejections+ explore' step m accept reject u v x y logL = do+ -- Trial Lighthouse+ unif1 <- uniform+ unif2 <- uniform+ let u' = wrapAround $ u + step * (2*unif1 - 1) -- |move| < step+ v' = wrapAround $ v + step * (2*unif2 - 1) -- |move| < step+ x' = 4*u' - 2 -- map to x+ y' = 2*v' -- map to y+ logL' = logLhood x' y'++ -- Accept if and only if within hard likelihood constraint+ obj' <- + if logL' > logLstar+ then return $ Lighthouse u' v' x' y' logL' (lhLogWt obj)+ else return $ Lighthouse u v x y logL (lhLogWt obj)+ (accept, reject) <- if logL' > logLstar+ then return (accept + 1, reject)+ else return (accept, reject + 1)+ + -- Refine step-size to let acceptance ratio converge around 50%+ step <- if accept > reject+ then return $ step * exp(1.0 / accept)+ else return step+ step <- if accept < reject+ then return $ step / exp(1.0 / reject)+ else return step+ if m == 0+ then return obj'+ else explore' step (m-1) accept reject (lhU obj') (lhV obj')+ (lhX obj') (lhY obj') (lhLogL obj')++wrapAround :: Double -> Double+wrapAround x = x - (fromIntegral $ floor x)++data Stats = Stats { meanX :: Double,+ meanY :: Double,+ stddevX :: Double,+ stddevY :: Double }++instance Show Stats where+ show s = (printf "x = %.2f +- %.2f\n" (meanX s) (stddevX s) +++ printf "y = %.2f +- %.2f\n" (meanY s) (stddevY s))++-- Posterior properties, here mean and stddev of x,y+-- Args:+-- samples: Objects defining posterior+-- logZ: Evidence (= total weight = SUM[Samples] Weight)+getStats :: [Lighthouse] -> Double -> Stats+getStats samples logZ =+ Stats {meanX=x,+ meanY=y,+ stddevX=sqrt $ xx - x*x,+ stddevY=sqrt $ yy - y*y }+ where weightsSamples = [(exp (lhLogWt s - logZ), s) | s <- samples]+ x = sum [w*(lhX s) | (w,s) <- weightsSamples]+ y = sum [w*(lhY s) | (w,s) <- weightsSamples]+ xx = sum [w*(lhX s)^2 | (w,s) <- weightsSamples]+ yy = sum [w*(lhY s)^2 | (w,s) <- weightsSamples]++main = do+ let n = 100 -- # number of candidate lighthouses+ let maxIterations = 1000 -- # iterates+ priorSamples <- mapM (\_ -> sampleFromPrior) [1..n] + result <- nestedSampling priorSamples explore maxIterations+ let stats = getStats (nsSamples result) (nsLogZ result) + print result+ print stats+