def plot_surface(tdata_agg, surface_result, num_levels=11):
"""plot the 3D surface and the level set"""
# calculate the 3D surface
num_mt = 101
num_dt = 101
mean_temp = np.linspace(tdata_agg.mean_temp.min(),
tdata_agg.mean_temp.max(), num_mt)
daily_temp = np.linspace(tdata_agg.daily_temp.min(),
tdata_agg.daily_temp.max(), num_dt)
MT, DT = np.meshgrid(mean_temp, daily_temp)
mt = MT.flatten()
dt = DT.flatten()
# compute residual surface
scaled_dt = utils.scale_daily_temp(mt, dt, surface_result.scale_params)
invalid_id = (scaled_dt <= -1.0) | (scaled_dt > 0.75)
surface = surface_result.surface_func(mt, dt)
surface[invalid_id] = np.inf
surface = surface.reshape(num_mt, num_dt)
# plot 3D surface
fig = plt.figure(figsize=(16, 8))
ax = fig.add_subplot(121, projection='3d')
ax.scatter(tdata_agg.mean_temp,
tdata_agg.daily_temp,
tdata_agg.obs_mean,
s=1.0 / tdata_agg.obs_std,
c=tdata_agg.obs_mean)
ax.plot_surface(MT, DT, surface)
ax.set_xlabel('mean temp degree')
ax.set_ylabel('daily temp cat')
ax.set_zlabel('ln rr')
# plot the level set
ax = fig.add_subplot(122)
ax.scatter(tdata_agg.mean_temp,
tdata_agg.daily_temp,
s=1.0 / tdata_agg.obs_std,
c=tdata_agg.obs_mean)
c = ax.contour(MT, DT, surface, levels=np.linspace(-0.5, 0.5, num_levels))
ax.set_xlabel('mean temp degree')
ax.set_ylabel('daily temp cat')
ax.clabel(c)
# min_daily_temp_id = np.array([np.argmin(surface[:, i])
# for i in range(num_mt)])
# min_daily_temp = daily_temp[min_daily_temp_id]
min_daily_temp = np.array([
surface_result.tmrl_at_mean_temp(mean_temp[i]) for i in range(num_mt)
])
ax.scatter(mean_temp, min_daily_temp, c='r', marker='.')
def fit_surface(tdata_agg, scale_params=[40.0, 1.25], linear_no_mono=False):
"""fit the mean surface"""
# unpack data
mt = tdata_agg.mean_temp
dt = tdata_agg.daily_temp
scaled_dt = utils.scale_daily_temp(mt, dt, scale_params)
obs_mean = tdata_agg.obs_mean
obs_std = tdata_agg.obs_std
study_sizes = tdata_agg.study_sizes
# create spline
mt_knots = np.linspace(mt.min(), mt.max(), 2)
mt_degree = 3
if linear_no_mono:
dt_degree = 1
dt_knots = np.linspace(scaled_dt.min(), scaled_dt.max(), 2)
else:
dt_degree = 3
dt_knots = np.linspace(scaled_dt.min(), scaled_dt.max(), 3)
spline_list = [
xspline.ndxspline(2, [mt_knots, dt_knots], [mt_degree, dt_degree])
]
# create mrbrt object
x_cov_list = [{
'cov_type': 'ndspline',
'spline_id': 0,
'mat': np.vstack((mt, scaled_dt))
}]
z_cov_list = [{'cov_type': 'linear', 'mat': np.ones(mt.size)}]
mr = mrbrt.MR_BRT(obs_mean, obs_std, study_sizes, x_cov_list, z_cov_list,
spline_list)
# add priors
prior_list = [{
'prior_type':
'ndspline_shape_function_uprior',
'x_cov_id':
0,
'interval': [[mt.min(), mt.max()], [scaled_dt.min(),
scaled_dt.max()]],
'indicator': [-1.0, 1.0],
'num_points': [20, 20]
}, {
'prior_type': 'ndspline_shape_monotonicity',
'x_cov_id': 0,
'dim_id': 1,
'interval': [[mt.min(), mt.max()], [0.7, scaled_dt.max()]],
'indicator': 'increasing',
'num_points': [20, 10]
}, {
'prior_type': 'z_cov_uprior',
'z_cov_id': 0,
'prior': np.array([[0.0] * mr.k_gamma, [0.0] * mr.k_gamma])
}]
if not linear_no_mono:
prior_list += [
{
'prior_type': 'ndspline_shape_monotonicity',
'x_cov_id': 0,
'dim_id': 1,
'interval': [[mt.min(), mt.max()], [scaled_dt.min(), -0.75]],
'indicator': 'decreasing',
'num_points': [20, 10]
},
]
mr.addPriors(prior_list)
# initialization
k_beta = mr.lt.k_beta
k_gamma = mr.lt.k_gamma
X = mr.lt.JF(mr.lt.beta)
S = mr.lt.S
V = S**2
Y = mr.lt.Y
beta0 = np.linalg.solve((X.T / V).dot(X), (X.T / V).dot(Y))
gamma0 = np.zeros(k_gamma)
x0 = np.hstack((beta0, gamma0))
# fit the model and store the result
mr.fitModel(x0=x0)
# compute posterior variance for the beta
# extract the matrix
beta_var = (X.T / V).dot(X)
if mr.lt.use_regularizer:
H = np.vstack([
mr.lt.H(
np.hstack(
np.eye(1, k_beta, i).reshape(k_beta, ), np.zeros(k_gamma)))
for i in range(k_beta)
]).T
SH = mr.lt.h[1]
VH = SH**2
beta_var += (H.T / VH).dot(VH)
beta_var = np.linalg.inv(beta_var)
mean_temp = tdata_agg.unique_mean_temp
daily_temp_range = []
for mt in mean_temp:
tdata_agg_mt = mtslice.extract_mtslice(tdata_agg, mt)
daily_temp_range.append(
[tdata_agg_mt.daily_temp.min(),
tdata_agg_mt.daily_temp.max()])
surface_result = utils.SurfaceResult(mr.beta_soln,
beta_var,
spline_list[0],
mean_temp,
daily_temp_range,
scale_params=scale_params)
return surface_result
def fit_surface(tdata, scale_params=[40.0, 1.25]):
"""fit the mean surface"""
agg_tdata = aggregate_data(tdata)
# unpack data
mt = agg_tdata.mean_temp
dt = agg_tdata.daily_temp
scaled_dt = utils.scale_daily_temp(mt, dt, scale_params)
obs_mean = agg_tdata.obs_mean
obs_std = agg_tdata.obs_std * 15.0
study_sizes = agg_tdata.study_sizes
# mt = tdata.mean_temp
# dt = tdata.daily_temp
# scaled_dt = utils.scale_daily_temp(mt, dt, scale_params)
# obs_mean = tdata.obs_mean
# obs_std = tdata.obs_std
# study_sizes = np.array([1]*obs_mean.size)
# create spline
mt_knots = np.linspace(mt.min(), mt.max(), 2)
dt_knots = np.linspace(scaled_dt.min(), scaled_dt.max(), 2)
mt_degree = 3
dt_degree = 3
spline_list = [
xspline.ndxspline(2, [mt_knots, dt_knots], [mt_degree, dt_degree])
]
# create mrbrt object
x_cov_list = [{
'cov_type': 'ndspline',
'spline_id': 0,
'mat': np.vstack((mt, scaled_dt))
}]
z_cov_list = [{'cov_type': 'linear', 'mat': np.ones(mt.size)}]
mr = mrbrt.MR_BRT(obs_mean, obs_std, study_sizes, x_cov_list, z_cov_list,
spline_list)
# add priors
prior_list = [
{
'prior_type': 'ndspline_shape_function_uprior',
'x_cov_id': 0,
'interval': [[mt.min(), mt.max()],
[scaled_dt.min(), scaled_dt.max()]],
'indicator': [-1.0, 1.0],
'num_points': [20, 20]
},
# {
# 'prior_type': 'x_cov_gprior',
# 'x_cov_id': 0,
# 'prior': np.array([[0.0]*mr.k_beta, [10.0]*mr.k_beta])
# },
{
'prior_type': 'ndspline_shape_monotonicity',
'x_cov_id': 0,
'dim_id': 1,
'interval': [[mt.min(), mt.max()], [0.5, scaled_dt.max()]],
'indicator': 'increasing',
'num_points': [20, 10]
},
{
'prior_type': 'ndspline_shape_monotonicity',
'x_cov_id': 0,
'dim_id': 1,
'interval': [[mt.min(), mt.max()], [scaled_dt.min(), -0.75]],
'indicator': 'decreasing',
'num_points': [20, 10]
},
{
'prior_type': 'z_cov_uprior',
'z_cov_id': 0,
'prior': np.array([[1e-6] * mr.k_gamma, [1e-6] * mr.k_gamma])
}
]
mr.addPriors(prior_list)
# fit the model and store the result
mr.fitModel()
# compute posterior variance for the beta
# extract the matrix
k_beta = mr.lt.k_beta
k_gamma = mr.lt.k_gamma
X = mr.lt.JF(mr.lt.beta)
S = mr.lt.S
V = S**2
beta_var = (X.T / V).dot(X)
if mr.lt.use_regularizer:
H = np.vstack([
mr.lt.H(
np.hstack(
np.eye(1, k_beta, i).reshape(k_beta, ), np.zeros(k_gamma)))
for i in range(k_beta)
]).T
SH = mr.lt.h[1]
VH = SH**2
beta_var += (H.T / VH).dot(VH)
beta_var = np.linalg.inv(beta_var)
surface_result = utils.SurfaceResult(mr.beta_soln,
beta_var,
spline_list[0],
scale_params=scale_params)
return surface_result, agg_tdata