mh.ipynb

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       "Stochaskell, version 0.1.0\n",
       "Copyright (C) 2015-2020 David A Roberts\n",
       "This program comes with ABSOLUTELY NO WARRANTY.\n",
       "This is free software, and you are welcome to redistribute it\n",
       "under certain conditions; see the LICENSE for details.\n",
       "\n",
       "Using installation directory at \n",
       "  /home/jovyan/stochaskell"
      ]
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     "output_type": "display_data"
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   "source": [
    "{-# LANGUAGE FlexibleContexts, MonadComprehensions, NoImplicitPrelude, RebindableSyntax, TypeFamilies #-}\n",
    "import Language.Stochaskell\n",
    "stochaskell"
   ]
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   "source": [
    "mhStep :: P R -> (R -> P R) -> R -> P R\n",
    "mhStep target proposal x = do\n",
    "  y <- proposal x\n",
    "  let f = lpdf target; q = lpdfCond proposal\n",
    "      a = exp (f y - f x + q y x - q x y)\n",
    "  accept <- bernoulli (min' 1 a)\n",
    "  return (if accept then y else x)"
   ]
  },
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   "source": [
    "import IHaskell.Display"
   ]
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    "target :: P R\n",
    "target = do\n",
    "  z <- normal 2 0.75\n",
    "  return (exp z)\n",
    "\n",
    "svg <$> (vizIR . return . lpdf target $ symbol \"x\")"
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   ],
   "source": [
    "proposal :: R -> P R\n",
    "proposal x = do\n",
    "  u <- uniform (-2) 2\n",
    "  return (x + u)\n",
    "\n",
    "svg <$> (vizIR . mhStep target proposal $ symbol \"x\")"
   ]
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  {
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   "metadata": {},
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    {
     "data": {
      "text/plain": [
       "[runStep]\n",
       "let v_0_0 = getExternal x_sim_0_0 :: R\n",
       "    v_0_1 = i_9_0 + x_sim_0_0 :: R\n",
       "    v_0_2 = log v_0_1 :: R\n",
       "    v_0_3 = normal_lpdf v_0_2 2.0 0.75 :: R\n",
       "    v_0_4 = v_0_3 - v_0_2 :: R\n",
       "    v_0_5 = log i_9_0 :: R\n",
       "    v_0_6 = normal_lpdf v_0_5 2.0 0.75 :: R\n",
       "    v_0_7 = v_0_6 - v_0_5 :: R\n",
       "    v_0_8 = v_0_4 - v_0_7 :: R\n",
       "    v_0_9 = i_9_0 - v_0_1 :: R\n",
       "    v_0_10 = uniform_lpdf v_0_9 -2.0 2.0 :: R\n",
       "    v_0_11 = v_0_8 + v_0_10 :: R\n",
       "    v_0_12 = v_0_1 - i_9_0 :: R\n",
       "    v_0_13 = uniform_lpdf v_0_12 -2.0 2.0 :: R\n",
       "    v_0_14 = v_0_11 - v_0_13 :: R\n",
       "    v_0_15 = exp v_0_14 :: R\n",
       "    v_0_16 = min 1.0 v_0_15 :: R\n",
       "    v_0_17 = getExternal x_sim_0_1 :: B\n",
       "    v_0_18 = ifThenElse x_sim_0_1 v_0_1 i_9_0 :: R\n",
       " in do x_sim_0_0 <- uniform -2.0 2.0 :: P R\n",
       "       x_sim_0_1 <- bernoulli v_0_16 :: P B\n",
       "       return [v_0_18]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples <- iterateLimit 10000 (runStep (mhStep target proposal)) 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[runStep]\n",
       "let v_0_0 = getExternal x_sim_0_0 :: R\n",
       "    v_0_1 = i_9_0 * x_sim_0_0 :: R\n",
       "    v_0_2 = log v_0_1 :: R\n",
       "    v_0_3 = normal_lpdf v_0_2 2.0 0.75 :: R\n",
       "    v_0_4 = v_0_3 - v_0_2 :: R\n",
       "    v_0_5 = log i_9_0 :: R\n",
       "    v_0_6 = normal_lpdf v_0_5 2.0 0.75 :: R\n",
       "    v_0_7 = v_0_6 - v_0_5 :: R\n",
       "    v_0_8 = v_0_4 - v_0_7 :: R\n",
       "    v_0_9 = i_9_0 / v_0_1 :: R\n",
       "    v_0_10 = uniform_lpdf v_0_9 0.5 2.0 :: R\n",
       "    v_0_11 = v_0_10 - v_0_2 :: R\n",
       "    v_0_12 = v_0_8 + v_0_11 :: R\n",
       "    v_0_13 = uniform_lpdf x_sim_0_0 0.5 2.0 :: R\n",
       "    v_0_14 = v_0_13 - v_0_5 :: R\n",
       "    v_0_15 = v_0_12 - v_0_14 :: R\n",
       "    v_0_16 = exp v_0_15 :: R\n",
       "    v_0_17 = min 1.0 v_0_16 :: R\n",
       "    v_0_18 = getExternal x_sim_0_1 :: B\n",
       "    v_0_19 = ifThenElse x_sim_0_1 v_0_1 i_9_0 :: R\n",
       " in do x_sim_0_0 <- uniform 0.5 2.0 :: P R\n",
       "       x_sim_0_1 <- bernoulli v_0_17 :: P B\n",
       "       return [v_0_19]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "proposal :: R -> P R\n",
    "proposal x = do\n",
    "  u <- uniform (1/2) 2\n",
    "  return (x * u)\n",
    "\n",
    "samples' <- iterateLimit 10000 (runStep (mhStep target proposal)) 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Language.Stochaskell.Plot\n",
    ":opt svg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "toRenderable $ do\n",
    "  plotHist \"symmetric proposal\" (real <$> samples) (0,80) 0.5\n",
    "  plotHist \"asymmetric proposal\" (real <$> samples') (0,80) 0.5\n",
    "  plotpdf \"target\" target (0,80)\n",
    "  xlabel \"location\"\n",
    "  ylabel \"density\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "toRenderable $ do\n",
    "  liftCState $ colors %= map (dissolve 0.7)\n",
    "  plot $ line \"symmetric proposal\" [zip [0..] $ real <$> samples]\n",
    "  plot $ line \"asymmetric proposal\" [zip [0..] $ real <$> samples']\n",
    "  xlabel \"time\"\n",
    "  ylabel \"location\"\n",
    "  ylim (0,80)"
   ]
  }
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