def plot_power(effect_sizes, empirical_power, ax=None):
"""Function for plotting empirical power as a function of effect size.
Input arguments:
================
effect_sizes : ndarray [n_effect_sizes, ]
The evaluated effect sizes.
empirical_power : ndarray[n_effect_sizes, ]
The empirical power at each effect size.
ax : Axes
(Optional) Axes to plot to. If not specified, a new figure with new
axes will be created.
"""
"""Fit a logistic function to the data."""
logistic_k, logistic_x0 = curve_fit(logistic_function, effect_sizes,
empirical_power)[0]
logistic_x = np.linspace(effect_sizes[0], effect_sizes[-1], 100)
logistic_y = logistic_function(logistic_x, logistic_k, logistic_x0)
"""Plot the data and fitted line."""
if (ax is None):
fig = plt.figure(figsize=(8, 5))
ax = fig.add_subplot(121)
ax.plot(effect_sizes, empirical_power, '.', markersize=9)
ax.plot(logistic_x, logistic_y, '-', linewidth=1.5)
"""Label the axes etc."""
ax.set_xlim([effect_sizes[0] - 0.05, effect_sizes[-1] + 0.05])
ax.set_ylim([-0.05, 1.05])
ax.set_xlabel('Effect size $\Delta$', fontsize=14)
ax.set_ylabel('Empirical power', fontsize=14)
def plot_two_group_reproducibility(effect_sizes, emphasis_primary,
reproducibility):
"""Function for visualizing reproducibility in the two-group model.
Input arguments:
================
effect_sizes : ndarray [n_effect_sizes, ]
The tested effect sizes.
emphasis_primary : ndarray [n_emphasis_values, ]
The tested primary study emphases.
reproducibility ndarray [n_effect_sizes, n_emphasis_values]
The observed reproducibility at each combination of effect size and
emphasis of primary study.
Output arguments:
=================
fig : Figure
Instance of matplotlib Figure class.
"""
n_emphs = len(emphasis_primary)
"""Fit logistic functions to the data."""
logistic_k, logistic_x0 = np.zeros(n_emphs), np.zeros(n_emphs)
for i in np.arange(0, n_emphs):
params = curve_fit(logistic_function, effect_sizes,
reproducibility[:, i])[0]
logistic_k[i], logistic_x0[i] = params
"""Visualize the results."""
sns.set_style('darkgrid')
fig = plt.figure(figsize=(8, 5))
ax = fig.add_subplot(111)
ax.plot(effect_sizes, reproducibility, '.')
for i in np.arange(0, n_emphs):
logistic_x = np.linspace(effect_sizes[0], effect_sizes[-1], 100)
logistic_y = logistic_function(logistic_x, logistic_k[i],
logistic_x0[i])
plt.plot(logistic_x, logistic_y, '-')
ax.set_xlim([effect_sizes[0]-0.05, effect_sizes[-1]+0.05])
ax.set_ylim([0.0, 1.0])
ax.set_xlabel('Effect size')
ax.set_ylabel('Reproducibility rate')
ax.set_title('Two-stage FDR')
ax.legend(emphasis_primary, loc='lower right')
fig.tight_layout()
return fig
def plot_logistic(x,
y,
ax,
legend=None,
xlabel=None,
ylabel=None,
xlim=None,
ylim=None,
**kwargs):
"""Function for drawing a scatter plot of the (x, y) tuples and
fitting a logistic function.
Input arguments:
================
x, y : ndarray
The visualize data points.
ax : Matplotlib Axes
The axes to draw to.
legend : ndarray
Legend added to the axes, e.g. different parameter selection when
drawing several overlaid datasets at once.
xlabel, ylabel : str
Labels for the x- and y-axes.
xlim, ylim : ndarray
Limits for the axes.
**kwargs : keyword arguments
Possible additional keyword arguments for plotting (ax.plot).
"""
"""Find number of samples and variables."""
if (len(np.shape(x)) == 1):
x = x[:, None]
if (len(np.shape(y)) == 1):
y = y[:, None]
print np.shape(x), np.shape(y)
n_samples, n_vars = np.shape(y)
"""Fit a logistic function to the data."""
for i in np.arange(0, n_vars):
xdata, ydata = np.squeeze(x), np.squeeze(y[:, i])
logistic_k, logistic_x0 = curve_fit(logistic_function, xdata, ydata)[0]
logistic_x = np.linspace(x[0], x[-1], 100)
logistic_y = logistic_function(logistic_x, logistic_k, logistic_x0)
"""Plot the data and the fitted line."""
ax.plot(x, y[:, i], '.', markersize=9, **kwargs)
ax.plot(logistic_x, logistic_y, '-', linewidth=1.5, **kwargs)
"""Label the axes etc."""
ax.set_xlim(xlim)
ax.set_ylim(ylim)
ax.set_xlabel(xlabel, fontsize=14)
ax.set_ylabel(ylabel, fontsize=14)
return ax
##########################################################
########## Predict population data
#######################
prev_pop = pop_data[2014]
mort_fixed = mort_data[2014]
imm_fixed = imm_rate[2014]
NUM_COLORS = 2500 + 1 - 2015
cm = plt.get_cmap('Blues')
cNorm = colors.Normalize(vmin=0, vmax=NUM_COLORS-1)
scalarMap = mplcm.ScalarMappable(norm=cNorm, cmap=cm)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.set_prop_cycle(color=[scalarMap.to_rgba(i) for i in range(NUM_COLORS)])
for year in range(2015, 2500):
beta = util.logistic_function(year - 1, L_MLE_beta, k_MLE_beta, x_MLE_beta) + min(betas)
m = util.logistic_function(year - 1, L_MLE_m, k_MLE_m, x_MLE_m) + min(ms)
year_adj_alpha = - (year - 1 - x_MLE_alpha) + x_MLE_alpha
alpha = util.logistic_function(year_adj_alpha, L_MLE_alpha, k_MLE_alpha, x_MLE_alpha) + min(alphas)
year_adj_scale = - (year - 1 - x_MLE_scale) + x_MLE_scale
scale = util.logistic_function(year_adj_scale, L_MLE_scale, k_MLE_scale, x_MLE_scale) + min(scales)
ages = np.linspace(14, 50, 37)
fert = util.gen_gamma_fun_pdf(ages, alpha, beta, m)
fert = fert_data[2014]
births = fert * prev_pop[14:51]
births = np.sum(births)
deaths = mort_fixed * prev_pop
deaths = np.roll(deaths, 1)