squash before rebase

.gitmodules

@@ -1,3 +1,4 @@
 [submodule "stan"]
 	path = stan
         url = https://github.com/stan-dev/stan
+        branch = mpi_warmup_v2

examples/arK-arK/arK-arK.data.R

@@ -0,0 +1,46 @@
+K <- 5
+
+T <- 200
+
+y <- c(
+  0.7293852753,  0.8297635923,  0.7839527091,  1.0259589105,  0.9696824412,
+  1.0828859218,  0.7063891465,  0.7769243971,  0.4618029476,  0.6385997565,
+  0.3742344429,  0.0854966416, -0.1260149233, -0.2934151326, -0.2617308802,
+ -0.3359221372, -0.5019895766, -0.6417399532, -0.6224629523, -0.8508997238,
+ -0.8678351807, -1.0163853144, -1.0558901454, -0.9694812319, -1.0672519169,
+ -0.8430989055, -0.6827006149, -0.4446573489, -0.5920387090, -0.5105689815,
+ -0.4178858435, -0.1736168751, -0.1072500940, -0.0355025516,  0.3432168459,
+  0.3841903414,  0.4960876950,  0.7084511605,  0.5962806615,  0.6414424152,
+  0.6513222735,  0.5942153484,  0.7779414176,  0.7307762325,  0.4822472694,
+  0.5320372234,  0.4851022175,  0.3685521219,  0.3533268113,  0.1633690002,
+  0.2530389410,  0.0006621430, -0.0157674958, -0.0144909054, -0.0252628993,
+ -0.0056256128, -0.3189177332, -0.0227791612, -0.0716865707, -0.1850182514,
+ -0.2350075682, -0.1243111880, -0.1304923565, -0.1994777726,  0.0775739320,
+ -0.1628522111,  0.0234645663, -0.0646807914,  0.0845324981,  0.0550150773,
+  0.1417424074,  0.0876638222, -0.0528467198,  0.0695217092, -0.1014499970,
+ -0.0688806547, -0.2512073227, -0.3902872828, -0.1676283611, -0.2791635517,
+ -0.3121253506, -0.2865502547, -0.4117701622, -0.4982098458, -0.5028522787,
+ -0.7394004480, -0.2492280924, -0.4710158859, -0.4645727076, -0.4457058117,
+ -0.2844237121, -0.0227786998, -0.0605507196,  0.0662256249,  0.1405232927,
+  0.2763394882,  0.3772233671,  0.6103044598,  0.8808694697,  0.7885174270,
+  0.8013632395,  0.6609678195,  0.8097669196,  0.8205077274,  0.9807562966,
+  0.7240388847,  0.9318587166,  0.8504881551,  0.4805918638,  0.5085811342,
+  0.4161126092,  0.3146685518, -0.0281539189, -0.0717016521, -0.1439206592,
+ -0.5223661051, -0.4033621109, -0.6886329349, -0.6947170572, -0.6496557077,
+ -0.9926992981, -0.9354098817, -0.8969864546, -0.9781523572, -1.0668406080,
+ -0.9535621424, -0.7570773682, -0.8425755431, -0.6977697431, -0.3165581858,
+ -0.3878217300, -0.0671166462, -0.0385154999,  0.0895646813,  0.1454578935,
+  0.1852131654,  0.3956127617,  0.6852644284,  0.5563107812,  0.7108445288,
+  0.7462804690,  0.6684519285,  0.6936535333,  0.7379992741,  0.6627708128,
+  0.6900939802,  0.6807304694,  0.3733191989,  0.4536740601,  0.3137682260,
+  0.4500334320, -0.0337947734,  0.0047340737, -0.0856874439,  0.1082543270,
+ -0.1398269720, -0.0429735449, -0.4541637356, -0.3326428149, -0.2333534103,
+ -0.2014612607, -0.1826792426, -0.2278848137, -0.0415383584, -0.1210077677,
+ -0.0724354048, -0.0482025571,  0.1580149098,  0.0583926960, -0.1117559432,
+ -0.0381725259,  0.1789819529, -0.0148415779,  0.0500966207, -0.1980592117,
+ -0.1400114013, -0.1746734639, -0.1767850853, -0.2154143864, -0.4144745850,
+ -0.3405434088, -0.4482790416, -0.6571159536, -0.3546433053, -0.5257081174,
+ -0.6564372310, -0.5245263017, -0.4758655851, -0.3631316786, -0.3366915389,
+ -0.3254437415,  0.0006694692,  0.2080422414,  0.0023164951,  0.1124752107,
+  0.3494037146,  0.4717023945,  0.5906600432,  0.6048634064,  0.9331979099)
+

examples/arK-arK/arK-arK.stan

@@ -0,0 +1,27 @@
+data {
+  int<lower=0> K;
+  int<lower=0> T;
+  real y[T];
+}
+
+parameters {
+  real alpha;
+  real beta[K];
+  real<lower=0> sigma;
+}
+
+model {
+  alpha ~ normal(0, 10);
+  beta ~ normal(0, 10);
+  sigma ~ cauchy(0, 2.5);
+
+  for (t in (K+1):T) {
+    real mu;
+    mu = alpha;
+
+    for (k in 1:K)
+      mu = mu + beta[k] * y[t - k];
+
+    y[t] ~ normal(mu, sigma);
+  }
+}

examples/arK/arK.data.R

@@ -0,0 +1,46 @@
+K <- 5
+
+T <- 200
+
+y <- c(
+ 0.7293852753,  0.8297635923,  0.7839527091,  1.0259589105,  0.9696824412,
+ 1.0828859218,  0.7063891465,  0.7769243971,  0.4618029476,  0.6385997565,
+ 0.3742344429,  0.0854966416, -0.1260149233, -0.2934151326, -0.2617308802,
+-0.3359221372, -0.5019895766, -0.6417399532, -0.6224629523, -0.8508997238,
+-0.8678351807, -1.0163853144, -1.0558901454, -0.9694812319, -1.0672519169,
+-0.8430989055, -0.6827006149, -0.4446573489, -0.5920387090, -0.5105689815,
+-0.4178858435, -0.1736168751, -0.1072500940, -0.0355025516,  0.3432168459,
+ 0.3841903414,  0.4960876950,  0.7084511605,  0.5962806615,  0.6414424152,
+ 0.6513222735,  0.5942153484,  0.7779414176,  0.7307762325,  0.4822472694,
+ 0.5320372234,  0.4851022175,  0.3685521219,  0.3533268113,  0.1633690002,
+ 0.2530389410,  0.0006621430, -0.0157674958, -0.0144909054, -0.0252628993,
+-0.0056256128, -0.3189177332, -0.0227791612, -0.0716865707, -0.1850182514,
+-0.2350075682, -0.1243111880, -0.1304923565, -0.1994777726,  0.0775739320,
+-0.1628522111,  0.0234645663, -0.0646807914,  0.0845324981,  0.0550150773,
+ 0.1417424074,  0.0876638222, -0.0528467198,  0.0695217092, -0.1014499970,
+-0.0688806547, -0.2512073227, -0.3902872828, -0.1676283611, -0.2791635517,
+-0.3121253506, -0.2865502547, -0.4117701622, -0.4982098458, -0.5028522787,
+-0.7394004480, -0.2492280924, -0.4710158859, -0.4645727076, -0.4457058117,
+-0.2844237121, -0.0227786998, -0.0605507196,  0.0662256249,  0.1405232927,
+ 0.2763394882,  0.3772233671,  0.6103044598,  0.8808694697,  0.7885174270,
+ 0.8013632395,  0.6609678195,  0.8097669196,  0.8205077274,  0.9807562966,
+ 0.7240388847,  0.9318587166,  0.8504881551,  0.4805918638,  0.5085811342,
+ 0.4161126092,  0.3146685518, -0.0281539189, -0.0717016521, -0.1439206592,
+-0.5223661051, -0.4033621109, -0.6886329349, -0.6947170572, -0.6496557077,
+-0.9926992981, -0.9354098817, -0.8969864546, -0.9781523572, -1.0668406080,
+-0.9535621424, -0.7570773682, -0.8425755431, -0.6977697431, -0.3165581858,
+-0.3878217300, -0.0671166462, -0.0385154999,  0.0895646813,  0.1454578935,
+ 0.1852131654,  0.3956127617,  0.6852644284,  0.5563107812,  0.7108445288,
+ 0.7462804690,  0.6684519285,  0.6936535333,  0.7379992741,  0.6627708128,
+ 0.6900939802,  0.6807304694,  0.3733191989,  0.4536740601,  0.3137682260,
+ 0.4500334320, -0.0337947734,  0.0047340737, -0.0856874439,  0.1082543270,
+-0.1398269720, -0.0429735449, -0.4541637356, -0.3326428149, -0.2333534103,
+-0.2014612607, -0.1826792426, -0.2278848137, -0.0415383584, -0.1210077677,
+-0.0724354048, -0.0482025571,  0.1580149098,  0.0583926960, -0.1117559432,
+-0.0381725259,  0.1789819529, -0.0148415779,  0.0500966207, -0.1980592117,
+-0.1400114013, -0.1746734639, -0.1767850853, -0.2154143864, -0.4144745850,
+-0.3405434088, -0.4482790416, -0.6571159536, -0.3546433053, -0.5257081174,
+-0.6564372310, -0.5245263017, -0.4758655851, -0.3631316786, -0.3366915389,
+-0.3254437415,  0.0006694692,  0.2080422414,  0.0023164951,  0.1124752107,
+ 0.3494037146,  0.4717023945,  0.5906600432,  0.6048634064,  0.9331979099)
+

examples/arK/arK.stan

@@ -0,0 +1,27 @@
+data {
+  int<lower=0> K;
+  int<lower=0> T;
+  real y[T];
+}
+
+parameters {
+  real alpha;
+  real beta[K];
+  real<lower=0> sigma;
+}
+
+model {
+  alpha ~ normal(0, 10);
+  beta ~ normal(0, 10);
+  sigma ~ cauchy(0, 2.5);
+
+  for (t in (K+1):T) {
+    real mu;
+    mu = alpha;
+
+    for (k in 1:K)
+      mu = mu + beta[k] * y[t - k];
+
+    y[t] ~ normal(mu, sigma);
+  }
+}

examples/eight_schools/eight_schools.data.R

@@ -0,0 +1,6 @@
+J <- 8
+
+y <- c(28,  8, -3,  7, -1,  1, 18, 12)
+
+sigma <- c(15, 10, 16, 11,  9, 11, 10, 18)
+

examples/eight_schools/eight_schools.stan

@@ -0,0 +1,21 @@
+data {
+  int <lower=0> J; // number of schools
+  real y[J]; // estimated treatment
+  real<lower=0> sigma[J]; // std of estimated effect
+}
+parameters {
+  vector[J] theta_trans; // transformation of theta
+  real mu; // hyper-parameter of mean
+  real<lower=0> tau; // hyper-parameter of sd
+}
+transformed parameters{
+  vector[J] theta;
+  // original theta
+  theta=theta_trans*tau+mu;
+}
+model {
+  theta_trans ~ normal (0,1);
+  y ~ normal(theta , sigma);
+  mu ~ normal(0, 5); // a non-informative prior
+  tau ~ cauchy(0, 5);
+}

examples/garch-garch11/garch-garch11.data.R

@@ -0,0 +1,37 @@
+T <- 200
+sigma1 <- 0.5
+y <- c(
+ 4.9376697,  4.8899168,  5.0254610,  4.3556765,  3.8357394,  6.4251189,
+ 6.2174959,  5.3789445,  6.1202710,  5.1143114,  7.6245731, -1.8588047,
+ 5.5093409,  6.4493257,  5.1634192,  3.4463904,  4.1698488,  4.1064708,
+ 4.3614838,  5.9580466,  4.0459563,  3.1268747,  3.0014272,  7.2568532,
+ 0.6181061, -0.1529171,  9.1520129,  4.2929169,  8.4797655,  3.4712109,
+-0.7844602,  6.3643689,  7.3924605,  7.4482162,  7.9462958,  7.4520089,
+ 4.9160684,  7.0783740,  2.2755717,  4.3338510,  5.3356670,  7.7133457,
+ 3.8465556,  6.5227739,  3.8073106,  5.5854836,  4.0171510,  3.9905454,
+ 5.3564230,  5.6389753,  5.8895307,  6.0430888,  7.0166372,  5.2398473,
+ 7.5704829,  7.1371788,  5.0647421,  3.9293894,  3.4554177,  4.3275448,
+ 8.2122458,  5.4182330,  4.7841770,  3.9840486,  8.2691524,  3.3376053,
+ 2.0656949,  1.5275422,  1.8313308,  3.4272586, 10.6728548,  9.1516989,
+ 5.0237735,  9.3370065,  6.2413672,  6.0495085,  5.1750646,  3.5839200,
+ 2.5954829,  4.8390738,  3.9602637,  5.8275888,  4.2354627,  7.2289368,
+ 2.6012532,  4.6906417,  1.9171748,  4.6100141,  5.4795416,  5.1599669,
+ 6.1819383,  4.3444092,  4.4134581,  6.6869847,  3.3489950,  6.8327026,
+ 4.1952444,  6.7873446,  3.3809638,  6.9186328,  3.6888826,  6.2622409,
+ 3.4474512,  0.5621525, 12.0983927, -3.9476306, -3.2151898,  8.9190162,
+ 6.9925151,  8.6113043,  0.7972950,  0.7407605,  6.6504390, -1.0102533,
+ 6.0100541,  1.0596830,  6.8292719,  4.1636762,  5.1217723,  5.3588360,
+ 2.9456964,  3.0978778,  4.2588637,  7.3676196,  2.1469861,  7.3753851,
+ 4.8272418,  4.5120439,  5.7304457,  4.4193964,  2.7559061,  4.3644689,
+ 7.1601115,  8.2984161,  2.8166543,  3.9179671,  9.7952480, -4.7242886,
+ 5.4548679,  6.5446901,  6.5973368,  6.2416000,  3.0396850,  1.2093547,
+ 5.2636842,  8.6437868,  7.4910598,  6.4736415,  4.5251063,  6.7226653,
+ 4.9341330,  4.1566114,  4.5100764,  6.2950699,  3.1982652,  5.0967501,
+ 3.2661672,  5.5375760,  6.2441927,  7.2051307,  3.0704887,  2.7454787,
+ 0.9819569,  5.2894448,  3.8637890,  3.2133096,  5.9141655,  7.2122398,
+ 5.7235900,  6.8712588,  2.7826501,  3.9139987,  5.8714783,  4.8225299,
+ 6.4460635,  4.9013858,  4.7609188,  6.5644727,  2.6157804,  7.2306003,
+ 4.3068921,  3.9418201,  8.9272450,  3.4283380,  1.1672301,  0.8543514,
+12.1460656, -6.3507524,  7.7055931,  4.5136553,  4.9229184,  6.4621882,
+ 0.2856913,  3.6447997,  6.2438314,  7.6303149,  8.8403182,  6.9152914,
+ 4.1049014,  5.2848041)

examples/garch-garch11/garch-garch11.stan

@@ -0,0 +1,24 @@
+/* stan_code(posterior("garch-garch11", pdb = pd)) */
+data {
+  int<lower=0> T;
+  real y[T];
+  real<lower=0> sigma1;
+}
+
+parameters {
+  real mu;
+  real<lower=0> alpha0;
+  real<lower=0, upper=1> alpha1;
+  real<lower=0, upper=(1-alpha1)> beta1;
+}
+
+model {
+  real sigma[T];
+  sigma[1] = sigma1;
+  for (t in 2:T)
+    sigma[t] = sqrt(  alpha0
+                    + alpha1 * square(y[t - 1] - mu)
+                    + beta1 * square(sigma[t - 1]));
+
+  y ~ normal(mu, sigma);
+}