raw = np.loadtxt("gfl_new_data.txt")
data = {
"x": raw[:, 0],
"y": raw[:, 1],
"r": raw[:, 2],
"theta": raw[:, 3],
"v": raw[:, 4],
"sig_v": raw[:, 5],
"N": raw.shape[0]
}
# Create the model
model = bd.Model()
# Constant velocity dispersion
model.add_node(bd.Node("velocity_dispersion", bd.Uniform(0.0, 50)))
# Constant velocity offset
model.add_node(bd.Node("v_systematic", bd.Uniform(-10.0, 10.0)))
# Rotation amplitude
model.add_node(bd.Node("A", bd.Uniform(0.0, 50.0)))
# Rotation angle
model.add_node(bd.Node("phi", bd.Uniform(0.0, 2.0 * np.pi)))
# p(data | parameters)
for i in range(0, data["N"]):
#
mean = "v_systematic + A*sin(theta{index} - phi)".format(index=i)
raw = np.loadtxt("gfl_new_data.txt")
data = {
"x": raw[:, 0],
"y": raw[:, 1],
"r": raw[:, 2],
"theta": raw[:, 3],
"v": raw[:, 4],
"sig_v": raw[:, 5],
"N": raw.shape[0]
}
# Create the model
model = bd.Model()
# Constant velocity dispersion
model.add_node(bd.Node("log10_velocity_dispersion", bd.T(1.0, 0.5, 4.0)))
model.add_node(
bd.Node("velocity_dispersion",
bd.Delta("pow(10.0, log10_velocity_dispersion)")))
# Constant velocity offset
model.add_node(bd.Node("c_v_systematic", bd.T(0.0, 0.1, 1.0)))
model.add_node(
bd.Node("v_systematic", bd.Delta("c_v_systematic*velocity_dispersion")))
# Rotation amplitude
model.add_node(bd.Node("t_A", bd.T(0.0, 2.0, 2.0)))
model.add_node(
bd.Node(
"A",
bd.Delta("pow(10.0, 1.0-\
# Data
# Ntz original data:
# data = {"y": np.array([554, 701, 749, 868, 516, 573, 978, 399]),
# "n": np.array([1183, 1510, 1597, 1924, 1178, 1324, 2173, 845]),
# "N": 8}
# Kobe Bryant's whole field goal record from NBA records:
data = {"y": np.array([176, 391, 362, 554, 701, 749, 868, 516, 573, 978, 813, 775, 800, 716, 740]),
"n": np.array([422, 913, 779, 1183, 1510, 1597, 1924, 1178, 1324, 2173, 1757, 1690, 1712, 1569, 1639]),
"N": 15}
# Create the model
model = bd.Model()
# Prior p(m)
model.add_node(bd.Node("p", bd.Uniform(0, 1)))
# Likelihood p(D|n,p) place holder.
for i in range(0, data["N"]):
suc = "y{index}".format(index=i)
atp = "n{index}".format(index=i)
model.add_node(bd.Node(suc, bd.Binomial(atp, "p"), observed=True))
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
# take1 log(Z) = -39.2245367341 with Ntz original data
# take2 log(Z) = -39.223614467 with Ntz original data
# Analytical log(Z) = -39.2308
import math
import numpy as np
import dnest4.builder as bd
# Placeholder. data not needed
data = {"D": np.array([10.0]), "u": np.array([0.01]), "v": np.array([0.1])}
# Create the model
model = bd.Model()
# Prior p(m)
model.add_node(bd.Node("th", bd.Uniform(-0.5, 0.5)))
# Likelihood p(D|mu) place holder. Will have to enter egg-box likelihood by hand.
name = "D{index}".format(index=0)
model.add_node(bd.Node(name, bd.Normal("mu", 1), observed=True))
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
# Run result: log(Z) = 0.684022078176
# Mathematica result: = log(2) = 0.693147
import math
import numpy as np
import dnest4.builder as bd
# Placeholder. data not needed
data = {
"Xb": 1.517116,
"sCS": 0.0004726074,
"Yb": 1.517456,
"sSP": 0.001038594
}
# Create the model
model = bd.Model()
# Prior p(m)
model.add_node(bd.Node("mucssp", bd.Normal(1.5, 0.5)))
# Likelihood
model.add_node(bd.Node("Xb", bd.Normal("mucssp", "sCS"), observed=True))
model.add_node(bd.Node("Yb", bd.Normal("mucssp", "sSP"), observed=True))
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
# Run result: log(Z) = XXXXX
import numpy as np
import dnest4.builder as bd
data = {
"x": np.array([1.0, 2.0, 3.0, 4.0, 5.0]),
"y": np.array([1.0, 2.0, 3.0, 3.9, 5.1]),
"N": 5
}
# Create the model
model = bd.Model()
# Slope and intercept
model.add_node(bd.Node("m", bd.Uniform(-100.0, 100.0)))
model.add_node(bd.Node("b", bd.Uniform(-100.0, 100.0)))
# Noise standard deviation
model.add_node(bd.Node("log_sigma", bd.Uniform(-10.0, 10.0)))
model.add_node(bd.Node("sigma", bd.Delta("exp(log_sigma)")))
# p(data | parameters)
for i in range(0, data["N"]):
name = "y{index}".format(index=i)
mean = "m*x{index} + b".format(index=i)
model.add_node(bd.Node(name, bd.Normal(mean, "sigma"), observed=True))
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
# Compile the C++ code so it's ready to go
import math
import numpy as np
import dnest4.builder as bd
# Placeholder. data not needed
data = {"D": np.array([1.0])}
# Create the model
model = bd.Model()
# Prior p(m)
model.add_node(bd.Node("r", bd.Uniform(0.0, 20.0)))
model.add_node(bd.Node("th", bd.Uniform(0.0, math.pi)))
model.add_node(bd.Node("ph", bd.Uniform(0.0, 2.0 * math.pi)))
# Likelihood p(D|mu) place holder. Will have to enter likelihood by hand.
name = "D{index}".format(index=0)
model.add_node(bd.Node(name, bd.Normal("mu", 1), observed=True))
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
# Run result: log(Z) = about -6.0....
data["N"] = 40
data["N_groups"] = 4
data["group"] = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\
2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\
3, 3, 3, 3, 3, 3, 3, 3, 3, 3], dtype="int64")
data["y"] = np.array([78, 88, 87, 88, 83, 82, 81, 80, 80, 89, 78, 78, 83,\
81, 78, 81, 81, 82, 76, 76, 79, 73, 79, 75, 77, 78,\
80, 78, 83, 84, 77, 69, 75, 70, 74, 83, 80, 75, 76,\
75], dtype="float64")
# A model
model = bd.Model()
# Hyperparameters
model.add_node(bd.Node("grand_mean", bd.Normal(0.0, 1000.0)))
model.add_node(bd.Node("diversity", bd.LogUniform(1E-3, 1E3)))
# Group mean parameters
for i in range(0, data["N_groups"]):
model.add_node(bd.Node("n{i}".format(i=i), bd.Normal(0.0, 1.0)))
model.add_node(\
bd.Node("mu{i}".format(i=i),\
bd.Delta("grand_mean + diversity*n{i}".format(i=i))\
)\
)
# Noise sd
model.add_node(bd.Node("sigma", bd.LogUniform(1E-3, 1E3)))
# Data nodes
import math
import numpy as np
import dnest4.builder as bd
# Daniel Azevedo GC-Ethanol Data:
data = {"x": np.array([0.1716393, 0.2905149, 0.5521852, 0.8684159, 1.046752, 1.279638]), # AreaRatio
"y": np.array([0.05, 0.1, 0.2, 0.3, 0.4, 0.5]), # Concentration
"N": 6}
# Create the model
model = bd.Model()
# Prior p(m). Need to modify C++ for Half-Cauchy on beta1
model.add_node(bd.Node("beta0", bd.Cauchy(0, 1)))
model.add_node(bd.Node("beta1", bd.Cauchy(0, 5))) # Should be Half-Cauchy
model.add_node(bd.Node("epsilon", bd.Normal(0, 1)))
# Likelihood p(data | parameters)
for i in range(0, data["N"]):
name = "y{index}".format(index=i)
mean = "beta1*x{index} + beta0".format(index=i)
model.add_node(bd.Node(name, bd.Normal(mean, "epsilon"), observed=True))
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
# Run result: log(Z) = 2.24468713205
# Mathematica result: = XXXX
import math
import numpy as np
import dnest4.builder as bd
# Placeholder. data not needed
data = {"D": np.array([1.0])}
# Create the model
model = bd.Model()
# Prior p(m)
model.add_node(bd.Node("a", bd.Uniform(0, 10 * math.pi)))
model.add_node(bd.Node("b", bd.Uniform(0, 10 * math.pi)))
# Likelihood p(D|mu) place holder. Will have to enter egg-box likelihood by hand.
name = "D{index}".format(index=0)
model.add_node(bd.Node(name, bd.Normal("mu", 1), observed=True))
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
# Run result: log(Z) = 235.85129744
# Feroz numerical integration result = 235.856
# Feroz Multinest result = 235.835 and 235.839
# Mathematica result: = 231.944
-0.32019000, 1.59480235, -0.23412293, -0.08350555, -1.46057870,
-0.62142475, 0.84171547, 1.25053406, 1.22901729, -1.28844456,
-0.79355889, 0.64806456, 2.43395630, -1.18086072, 0.36834657,
0.51896395, 0.99233285, -0.19108939, -1.15934395, 0.64806456,
0.82019870, -0.90114273, 0.75564840, -0.64294152, -1.80484699,
0.56199749, 0.30379627
]),
"N":
42
}
# Create the model
model = bd.Model()
# Prior p(m)
model.add_node(bd.Node("a", bd.Normal(0, 1000)))
model.add_node(bd.Node("b", bd.Normal(0, 100)))
# Need to modify C++ for Half-Cauchy on sigma_1
#model.add_node(bd.Node("sig1", bd.Cauchy(0, 5)))
model.add_node(bd.Node("sig1", bd.Uniform(0, 1e8)))
# Likelihood p(data | parameters)
for i in range(0, data["N"]):
name = "y{index}".format(index=i)
mean = "b*x{index} + a".format(index=i)
model.add_node(bd.Node(name, bd.Normal(mean, "sig1"), observed=True))
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
import numpy as np
import dnest4.builder as bd
import pandas as pd
CHD = pd.read_csv('CHD.csv')
data = {"CHD": np.array(CHD["CHD"]).astype("int64"),\
"Age": np.array(CHD["Age"]).astype("int64"),\
"AgeGrp": np.array(CHD["AgeGrp"]).astype("int64")}
data["N"] = len(data["CHD"])
# Create the model
model = bd.Model()
# Coefficients
model.add_node(bd.Node("beta_0", bd.Normal(0, 10)))
model.add_node(bd.Node("beta_1", bd.Normal(0, 10)))
# Sampling Distribution
for i in range(0, data["N"]):
name = "CHD{i}".format(i=i)
#prob = "exp(beta_0 + beta_1 * Age{i})/(1.0 + exp(beta_0 + beta_1 * Age{i}))"
prob = "exp(beta_0 + beta_1 * Age{i})"
prob += "/(1.0 + exp(beta_0 + beta_1 * Age{i}))"
prob = prob.format(i=i)
distribution = bd.Binomial(1, prob)
node = bd.Node(name, distribution, observed=True)
model.add_node(node)
# Extra node for prediction
name = "CHDnew"
import numpy as np
import dnest4.builder as bd
# Placeholder. data not needed
data = {
"Xb": 1.517116,
"sCS": 0.0004726074,
"Yb": 1.517456,
"sSP": 0.001038594
}
# Create the model
model = bd.Model()
# Prior p(m)
model.add_node(bd.Node("mucssp", bd.Normal(1.51, 0.01))) # Hp
# model.add_node(bd.Node("mucs", bd.Normal(1.51, 0.01))) # Hd
# model.add_node(bd.Node("musp", bd.Normal(1.51, 0.01))) # Hd
# Likelihood
model.add_node(bd.Node("Xb", bd.Normal("mucssp", "sCS"), observed=True)) # Hp
model.add_node(bd.Node("Yb", bd.Normal("mucssp", "sSP"), observed=True)) # Hp
# model.add_node(bd.Node("Xb", bd.Normal("mucs", "sCS"), observed=True)) # Hd
# model.add_node(bd.Node("Yb", bd.Normal("musp", "sSP"), observed=True)) # Hd
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
# Run result: log(Z) = XXXXX
# Hp: log(Z) = -4.29510326831 # Super Wide prior, mu = 0, sigma = 10000
import math
import numpy as np
import dnest4.builder as bd
# Data, shell centers:
data = {"cx": np.array([3.5,-3.5]),
"cy": np.array([0.0,0.0])}
# Create the model
model = bd.Model()
# Prior p(m)
model.add_node(bd.Node("m1", bd.Uniform(-6.0, 6.0)))
model.add_node(bd.Node("m2", bd.Uniform(-6.0, 6.0)))
# Likelihood p(D|mu) place holder. Will have to enter shell likelihood by hand.
name = "D{index}".format(index=0)
model.add_node(bd.Node(name, bd.Normal("mu", 1), observed=True))
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
# Run result: log(Z) = -1.72298793735, -1.74864668478, -1.75171455818
# Feroz analytical integration result = −1.75
# Feroz Multinest result = -1.61, -1.71, -1.72, -1.69 depending on control params
# Mathematica result: =
1949, 1950, 1951, 1952, 1953, 1954, 1955,
1956, 1957, 1958, 1959, 1960, 1961, 1962])\
.astype("float64")
data["y"] = np.array([4, 5, 4, 1, 0, 4, 3, 4, 0, 6, 3, 3, 4, 0,
2, 6, 3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5,
3, 4, 2, 5, 2, 2, 3, 4, 2, 1, 3, 2, 2, 1,
1, 1, 1, 3, 0, 0, 1, 0, 1, 1, 0, 0, 3, 1,
0, 3, 2, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0,
0, 2, 1, 0, 0, 0, 1, 1, 0, 2, 3, 3, 1, 1,
2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 0, 1, 4, 0,
0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])\
.astype("float64")
data["N"] = int(len(data["t"]))
model = bd.Model()
model.add_node(bd.Node("log_mu1", bd.Cauchy(0.0, 5.0)))
model.add_node(bd.Node("diff", bd.Cauchy(0.0, 1.0)))
model.add_node(bd.Node("log_mu2", bd.Delta("log_mu1 + diff")))
model.add_node(bd.Node("mu1", bd.Delta("exp(log_mu1)")))
model.add_node(bd.Node("mu2", bd.Delta("exp(log_mu2)")))
model.add_node(bd.Node("change_year", bd.Uniform(1851.0, 1962.0)))
model.add_node(bd.Node("L", bd.LogUniform(1E-2, 1E2)))
# Data nodes
for i in range(0, data["N"]):
name = "y{i}".format(i=i)
mean = "mu1 + (mu2 - mu1)/(1.0 + exp(-(t{i} - change_year)/L))"\
.format(i=i)
model.add_node(bd.Node(name, bd.Poisson(mean), observed=True))
# Create the C++ code
import numpy as np
import dnest4.builder as bd
data = {"D": np.array([90.0])}
# Create the model
model = bd.Model()
# Prior p(m)
model.add_node(bd.Node("mu", bd.Cauchy(0.3, 10)))
# Likelihood p(D|mu)
name = "D{index}".format(index=0)
# Start with this and modify the log likelihood that gets written in MyModel.cpp
model.add_node(bd.Node(name, bd.Normal("mu", 0.5), observed=True))
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
import dnest4.builder as bd
import pandas as pd
# The data, as a dictionary
Clocks = pd.read_csv('Clocks.csv')
data = {}
data = {'log_age': np.log(np.array(Clocks['age']).astype('float64')),\
'log_num_bidders': np.log(np.array(Clocks['num_bidders'])).astype('float64'),\
'log_y': np.log(np.array(Clocks['y']).astype('float64'))}
data["N"] = int(len(data["log_y"]))
# Model
model = bd.Model()
# Slopes and Intercept
model.add_node(bd.Node("beta0", bd.Normal(0, 100)))
model.add_node(bd.Node("beta1", bd.Normal(0, 100)))
model.add_node(bd.Node("beta2", bd.Normal(0, 100)))
model.add_node(bd.Node("beta3", bd.Normal(0, 100)))
# Noise standard deviation
model.add_node(bd.Node("sigma", bd.LogUniform(0.001, 100)))
# Sampling distribution
for i in range(0, data["N"]):
name = "log_y{i}".format(i=i)
mean = "beta0 + beta1 * log_age{i} + beta2 * log_num_bidders{i} +"
mean += "beta3 * log_age{i} * log_num_bidders{i}"
mean = mean.format(i=i)
model.add_node(bd.Node(name, bd.Normal(mean, "sigma"), observed=True))
237, 257, 261, 248, 219, 244, 283, 293, 312, 272, 280, 298, 275, 297,
350, 260, 313, 273, 289, 326, 281, 288, 280, 283, 307, 286, 298, 267,
272, 285, 286, 303, 295, 289, 258, 286, 320, 354, 328, 297, 323, 331,
305, 338, 376, 296, 352, 314, 325, 358, 312, 324, 316, 317, 336, 321,
334, 302, 302, 323, 331, 345, 333, 316, 291, 324
]).astype("float64"),
"x":
np.array([8.0, 15.0, 22.0, 29.0, 36.0])
}
data["x_bar"] = float(data["x"].mean()) # Convert from numpy.float64 to float
# A model
model = bd.Model()
# Priors
model.add_node(bd.Node("alpha_mu", bd.Normal(0.0, 100.0)))
model.add_node(bd.Node("beta_mu", bd.Normal(0.0, 100.0)))
model.add_node(bd.Node("tau_c", bd.Gamma(1E-3, 1E3)))
model.add_node(bd.Node("alpha_tau", bd.Gamma(1E-3, 1E3)))
model.add_node(bd.Node("beta_tau", bd.Gamma(1E-3, 1E3)))
# Transformations
model.add_node(bd.Node("alpha_sigma", bd.Delta("1.0/sqrt(alpha_tau)")))
model.add_node(bd.Node("beta_sigma", bd.Delta("1.0/sqrt(beta_tau)")))
model.add_node(bd.Node("sigma_c", bd.Delta("1.0/sqrt(tau_c)")))
model.add_node(bd.Node("a0", bd.Delta("alpha_mu - beta_mu*x_bar")))
# Sampling distribution
for i in range(0, data["N"]):
model.add_node(bd.Node("n_alpha{i}".format(i=i), bd.Normal(0.0, 1.0)))
model.add_node(bd.Node("n_beta{i}".format(i=i), bd.Normal(0.0, 1.0)))
data["N_Species"] = len(np.unique(data["Species"]))
data["N"] = len(data["Species"])
data["N_Input"] = 6
# Add Some Ones to the Data for the One Trick
data["ones"] = np.ones(data["N"], dtype="int64")
# Create the model
model = bd.Model()
# Coefficients
for j in range(0, data["N_Species"]):
for k in range(0, data["N_Input"]):
name = "beta_{j}_{k}".format(j=j, k=k)
prior = bd.Normal(0.0, 10.0)
node = bd.Node(name, prior)
model.add_node(node)
# Sampling distribution
for i in range(0, data["N"]):
# Probability Distribution over Categories
for j in range(0, data["N_Species"]):
name = "p_{j}_{i}".format(i=i, j=j)
formula = ""
formula += "beta_{j}_0 +"
formula += "beta_{j}_1 * SL{i} + beta_{j}_2 * SW{i} + "
formula += "beta_{j}_3 * PL{i} + beta_{j}_4 * PW{i} + "
formula += "beta_{j}_5 * SW{i} * PL{i}"
formula = formula.format(i=i, j=j)
model.add_node(bd.Node(name, bd.Delta(formula)))
"n":
np.array([
422, 913, 779, 1183, 1510, 1597, 1924, 1178, 1324, 2173, 1757, 1690,
1712, 1569, 1639
]),
"N":
15
}
# Create the model
model = bd.Model()
# Prior p(m)
for i in range(0, data["N"]):
ppi = "ppi{index}".format(index=i)
model.add_node(bd.Node(ppi, bd.Uniform(0, 1)))
# Likelihood p(D|n,p) place holder.
for i in range(0, data["N"]):
suc = "y{index}".format(index=i)
atp = "n{index}".format(index=i)
ppi = "ppi{index}".format(index=i)
model.add_node(bd.Node(suc, bd.Binomial(atp, ppi), observed=True))
# Create the C++ code
bd.generate_h(model, data)
bd.generate_cpp(model, data)
# take1 log(Z) = -58.0551362482 with Ntz original data
# take2 log(Z) = -57.9893885883 with Ntz original data
# take3 log(Z) = -57.9826848935 with Ntz original data
# Plot the data
plt.plot(data["t"], data["adult"], "ko-", label="Adult")
plt.plot(data["t"], data["youth"], "go-", label="Youth")
plt.xlabel("Time (quarters)")
plt.ylabel("Unemployment rate (logit)")
plt.legend()
plt.xlim([data["t"].min() - 0.5, data["t"].max() + 0.5])
plt.ylim([-4.0, 0.0])
plt.show()
# A model (of the prior information!)
model = bd.Model()
# AR(1) parameters for adult unemployment rate
model.add_node(bd.Node("mu1", bd.Uniform(-10.0, 0.0)))
model.add_node(bd.Node("L1", bd.LogUniform(1.0, 1E4)))
model.add_node(bd.Node("beta1", bd.LogUniform(1E-3, 1E3)))
model.add_node(bd.Node("alpha1", bd.Delta("exp(-1.0/L1)")))
model.add_node(bd.Node("sigma1", bd.Delta("beta1/sqrt(1.0 - alpha1*alpha1)")))
# Sampling distribution for adult data
model.add_node(bd.Node("adult0",\
bd.Normal("mu1", "sigma1"), observed=True))
for i in range(1, data["N"]):
name = "adult{i}".format(i=i)
dist = bd.Normal("mu1 + alpha1*(adult{k} - mu1)".format(k=(i-1)), "beta1")
model.add_node(bd.Node(name, dist, observed=True))
# Parameters relating to youth data
model.add_node(bd.Node("offset", bd.Normal(0.0, 1.0)))
CHD = pd.read_csv('CHD.csv')
data = {"CHD": np.array(CHD["CHD"]).astype("int64"),\
"Age": np.array(CHD["Age"]).astype("int64")}
data["N"] = len(data["CHD"])
data["N_Input"] = 2
data["N_CHD"] = 2
# Add Some Ones to the Data for the One Trick
data["ones"] = np.ones(data["N"], dtype="int64")
# Create the model
model = bd.Model()
# Coefficients
model.add_node(bd.Node("beta_0_0", bd.Normal(0, 10)))
model.add_node(bd.Node("beta_0_1", bd.Normal(0, 10)))
model.add_node(bd.Node("beta_1_0", bd.Normal(0, 10)))
model.add_node(bd.Node("beta_1_1", bd.Normal(0, 10)))
# Sampling distribution
for i in range(0, data["N"]):
for j in range(0, data["N_CHD"]):
name = "p_{j}_{i}".format(i=i, j=j)
formula = ""
formula += "beta_{j}_0 + beta_{j}_1 * Age{i} "
formula = formula.format(i=i, j=j)
model.add_node(bd.Node(name, bd.Delta(formula)))
# Probability Distribution over Categories
#name = "p_0_{i}".format(i=i)
#formula = ""
