diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -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. + + + Copyright (C) + + 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. + + , 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. diff --git a/NestedSampling.cabal b/NestedSampling.cabal new file mode 100644 --- /dev/null +++ b/NestedSampling.cabal @@ -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 + diff --git a/README b/README new file mode 100644 --- /dev/null +++ b/README @@ -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. + diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/lib/Statistics/MiniNest.hs b/lib/Statistics/MiniNest.hs new file mode 100644 --- /dev/null +++ b/lib/Statistics/MiniNest.hs @@ -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) + diff --git a/lighthouse.hs b/lighthouse.hs new file mode 100644 --- /dev/null +++ b/lighthouse.hs @@ -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 +