def ecdf_vals_plot(df, label = 'labeled', legend_title = "Labeled", column_label = 'time to catastrophe (s)', title = 'Labeled vs unlabeled microtubules', conf_int = True, label_bool = True):
if label_bool:
p = bokeh_catplot.ecdf(
data=df,
cats=[label],
val=column_label,
style='staircase',
conf_int = conf_int,
title = title,
width = 450,
height = 350,
)
p.legend.location = 'bottom_right'
p.legend.title = legend_title
return bokeh.io.show(p)
else:
p = bokeh_catplot.ecdf(
data=df,
val=column_label,
style='staircase',
conf_int = conf_int,
title = title,
width = 450,
height = 350,
)
p.legend.location = 'bottom_right'
p.legend.title = 'Labeled'
return bokeh.io.show(p)
def predictive_ecdf_ttc(params, data, plot_data, data_size):
n = len(data)
#draw data_size datasets with n datapoints from the distribution
parametric_bs_samples = draw_ttc(params[0], params[1], size=(data_size, n))
#compute the ECDF value for each value of n
n_theor = np.arange(0, parametric_bs_samples.max() + 1)
ecdfs = np.array(
[ecdf2(n_theor, sample) for sample in parametric_bs_samples])
#calculate confidence intervals
ecdf_low, ecdf_high = np.percentile(ecdfs, [2.5, 97.5], axis=0)
#plot the predictive ecdfs
p = bebi103.viz.fill_between(
x1=n_theor,
y1=ecdf_high,
x2=n_theor,
y2=ecdf_low,
patch_kwargs={"fill_alpha": 0.5},
x_axis_label="time (s)",
y_axis_label="ECDF",
title='Predictive ECDF of the TTC distribution')
#overlay with true data
p = bokeh_catplot.ecdf(data=plot_data,
val='time (s)',
palette=['orange'],
p=p)
bokeh.io.show(p)
def create_generated_ecdfs(beta_1, beta_2, n_samples=150):
"""
Creates a plot containing all generated ECDFs from the 2 Poisson Process
Distribution. It holds beta 1 constant.
Parameters:
beta1: An integer representing beta 1.
beta2: A list of integers representing beta 2.
n_samples: The number of samples to generate each time.
"""
times = {'times': [], 'beta 2': []}
for val in beta_2:
sampled_times = generate_samples_2pp(beta_1, val, n_samples=n_samples)
beta_2_array = [val] * n_samples
times['times'] += sampled_times
times['beta 2'] += beta_2_array
df = pd.DataFrame(data=times)
df.head()
p = bokeh_catplot.ecdf(data=df,
cats=['beta 2'],
val='times',
style='staircase',
title='Generated ECDFs for Differing Values of β')
p.legend.location = 'bottom_right'
return p
def sim_succ_poisson(process):
p = bokeh_catplot.ecdf(data=pd.DataFrame(
{'time to catastrophe (1/β1)': process}),
cats=None,
val='time to catastrophe (1/β1)',
title='ECDF of times to catastrophe',
style='staircase')
return bokeh.io.show(p)
def cdf_vs_pdf(process, time, cdf):
p = bokeh_catplot.ecdf(
data=pd.DataFrame({'time to catastrophe (1/β1)': process}),
cats=None,
val='time to catastrophe (1/β1)',
title='ECDF of times to catastrophe vs. Analytical CDF',
style='staircase')
p.line(time, cdf, color='red')
return p
def ecdf_plotter(data, title, xrange=None):
return bokeh_catplot.ecdf(
data=data,
cats=None,
val="times",
style='formal',
#palette=['#F1D4D4']
#palette=['#8c564b'],
x_range=xrange,
title=title)
def conf_ecdf(df):
p = bokeh_catplot.ecdf(data=df,
cats=['labeled'],
val='time to catastrophe (s)',
ptiles=[2.5, 97.5],
conf_int=True,
style='staircase')
p.legend.location = 'bottom_right'
return p
def plot_sim_ECDF(df_total):
# Plot ECDF of cumulative times of consecutive Poisson events
plt = bokeh_catplot.ecdf(
cats=["B2/B1"],
data=df_total,
val="C Time",
style="staircase",
title="Consecutive Poisson Processes",
)
plt.xaxis.axis_label = "Cumulative Time (β1^-1)"
plt.legend.title = "β2/β1"
bokeh.io.show(plt)
def plot_model_custom(t, beta_1, beta_2):
'''
Plots generative custom distribution against ECDF of data.
'''
t_theor = np.linspace(0, 2000, 200)
cdf = (beta_1 * beta_2 / (beta_2 - beta_1) *
((1 - np.exp(-beta_1 * t_theor)) / beta_1 -
(1 - np.exp(-beta_2 * t_theor)) / beta_2))
p = bokeh_catplot.ecdf(data=pd.DataFrame({"t": t}), val="t", conf_int=True)
p.line(t_theor, cdf, line_width=2, color="orange")
bokeh.io.show(p)
def plot_ecdf(tub_df):
'''
Plots ECDFs for catastrophe time at different concentrations.
'''
p = bokeh_catplot.ecdf(data=tub_df,
cats=['concentration'],
val='catastrophe time',
style='staircase',
x_axis_label='catastrophe time (s)')
p.legend.location = 'bottom_right'
bokeh.io.show(p)
def display_ecdf(df, cats, val):
p = bokeh_catplot.ecdf(
data=df,
cats=cats,
val=val,
style='staircase',
height=400,
width=500,
conf_int=True
)
p.legend.location = 'bottom_right'
bokeh.io.show(p)
def plot_ECDF(df):
# Plot ECDF of labeled and unlabeled tubulin catastrophe times
plt = bokeh_catplot.ecdf(
cats=["labeled"],
data=df,
val="time to catastrophe (s)",
conf_int=True,
style="staircase",
title="",
)
plt.xaxis.axis_label = "Time to Catastrophe (s)"
plt.legend.title = "Labeled"
return bokeh.io.show(plt)
def plot_model_gamma(t, alpha_mle, beta_mle):
'''
Plots generative Gamma distribution against ECDF of data.
'''
p = bokeh_catplot.ecdf(
pd.DataFrame({'t (s)': t}),
val='t (s)',
conf_int=True,
x_axis_label='catastrophe time (s)',
)
t_theor = np.linspace(0, 2000, 200)
cdf = st.gamma.cdf(t_theor, alpha_mle, loc=0, scale=1 / beta_mle)
p.line(t_theor, cdf, line_width=2, color='orange')
bokeh.io.show(p)
def plot_DKW_inequal(data):
p = bokeh_catplot.ecdf(
data=pd.DataFrame({'time to catastrophe (s)': data}),
cats=None,
val='time to catastrophe (s)',
conf_int=True,
title='Computed 95% confidence interval vs. DKW inequality',
x_axis_label='time to catastrophe (s)',
y_axis_label='ECDF',
style='staircase')
# actual distribution
p.circle(labeled, labeled_lower, color='red', legend_label='lower bound')
p.circle(labeled, labeled_upper, color='blue', legend_label='upper bound')
p.legend.location = 'bottom_right'
return p
def plot_ecdf(tidy_data, cats, val, title, width=550, conf_int=False):
"""
Plots an ECDF of tidy data.
tidy_data: Set of tidy data.
cats: Categories to plot
val: The value to plot
title: Title of plot
width: width of plot
conf_int: Whether or not to bootstrap a CI.
"""
p = bokeh_catplot.ecdf(
data=tidy_data,
cats=cats,
val=val,
title=title,
width=width,
conf_int=conf_int,
)
return p
def theo_empirical_cdf(beta_1, beta_2, n_samples=150):
"""
Overlays empirical and theoretical ECDFs for the 2 Poisson Process Distribution.
Parameters:
beta_1: The beta 1 value
beta_2: The beta 2 value.
n_samples: The number of samples to generate.
"""
# Gets our analytical ECDF
times = np.arange(0, 20, .1)
prob_times = cdf_points(times, beta_1, beta_2)
t = {'times': [], 'beta 2': []}
sampled_times = generate_samples_2pp(beta_1, beta_2, n_samples=n_samples)
beta_2_array = [beta_2] * n_samples
t['times'] += sampled_times
t['beta 2'] += beta_2_array
df = pd.DataFrame(data=t)
df['label'] = 'Empirical CDF'
p = bokeh_catplot.ecdf(data=df,
cats='label',
val='times',
style='staircase',
show_legend=True,
conf_int=True,
title='Empirical and Theoretical CDFs')
p.circle(
x=times,
y=prob_times,
size=2,
color='orange',
legend='Theoretical CDF',
)
p.yaxis.axis_label = 'CDF value'
return p
def plot_all_concentrations(tub_df, mle_data):
t = tub_df.loc[tub_df["concentration (int)"] ==
7]["catastrophe time"].values
alpha_mle, beta_mle = mle_data["alpha MLE"][0], mle_data["beta MLE"][0]
p7 = bokeh_catplot.ecdf(pd.DataFrame({'t (s)': t}),
val='t (s)',
conf_int=True,
x_axis_label='catastrophe time (s)')
t_theor = np.linspace(0, 2000, 200)
cdf = st.gamma.cdf(t_theor, alpha_mle, loc=0, scale=1 / beta_mle)
p7.line(t_theor, cdf, line_width=2, color='orange')
title7 = Title()
title7.text = '7 uM tubulin'
p7.title = title7
t = tub_df.loc[tub_df["concentration (int)"] ==
9]["catastrophe time"].values
alpha_mle, beta_mle = mle_data["alpha MLE"][1], mle_data["beta MLE"][1]
p9 = bokeh_catplot.ecdf(pd.DataFrame({'t (s)': t}),
val='t (s)',
conf_int=True,
x_axis_label='catastrophe time (s)')
t_theor = np.linspace(0, 2000, 200)
cdf = st.gamma.cdf(t_theor, alpha_mle, loc=0, scale=1 / beta_mle)
p9.line(t_theor, cdf, line_width=2, color='orange')
title9 = Title()
title9.text = '9 uM tubulin'
p9.title = title9
t = tub_df.loc[tub_df["concentration (int)"] ==
10]["catastrophe time"].values
alpha_mle, beta_mle = mle_data["alpha MLE"][2], mle_data["beta MLE"][2]
p10 = bokeh_catplot.ecdf(pd.DataFrame({'t (s)': t}),
val='t (s)',
conf_int=True,
x_axis_label='catastrophe time (s)')
t_theor = np.linspace(0, 2000, 200)
cdf = st.gamma.cdf(t_theor, alpha_mle, loc=0, scale=1 / beta_mle)
p10.line(t_theor, cdf, line_width=2, color='orange')
title10 = Title()
title10.text = '10 uM tubulin'
p10.title = title10
t = tub_df.loc[tub_df["concentration (int)"] ==
12]["catastrophe time"].values
alpha_mle, beta_mle = mle_data["alpha MLE"][3], mle_data["beta MLE"][3]
p12 = bokeh_catplot.ecdf(pd.DataFrame({'t (s)': t}),
val='t (s)',
conf_int=True,
x_axis_label='catastrophe time (s)')
t_theor = np.linspace(0, 2000, 200)
cdf = st.gamma.cdf(t_theor, alpha_mle, loc=0, scale=1 / beta_mle)
p12.line(t_theor, cdf, line_width=2, color='orange')
title12 = Title()
title12.text = '12 uM tubulin'
p12.title = title12
t = tub_df.loc[tub_df["concentration (int)"] ==
14]["catastrophe time"].values
alpha_mle, beta_mle = mle_data["alpha MLE"][4], mle_data["beta MLE"][4]
p14 = bokeh_catplot.ecdf(pd.DataFrame({'t (s)': t}),
val='t (s)',
conf_int=True,
x_axis_label='catastrophe time (s)')
t_theor = np.linspace(0, 2000, 200)
cdf = st.gamma.cdf(t_theor, alpha_mle, loc=0, scale=1 / beta_mle)
p14.line(t_theor, cdf, line_width=2, color='orange')
title14 = Title()
title14.text = '14 uM tubulin'
p14.title = title14
l = bokeh.layouts.layout([[p7, p9], [p10, p12], [p14]])
bokeh.io.show(l)
