def simulate_posterior(region, params, dates, initial, N = 1000, weekly = False,
parI = (1,1), parR = (1,1),parD = (1,1), random_params = False):
"""Simulate from the HMM model.
Args:
region (str): Region for the data.
params (list): Optimized parameters.
dates (tuple (2)): Date range of the data.
initial (dict): Initial values in dict with keys S,E,I,R,D.
N (int): Number of samples.
weekly (bool, optional): Weekly time step if True, otherwise daily.
parI (tuple (2)): Prior parameters for emission model I. By default (1,1).
parR (tuple (2)): Prior parameters for emission model R. By default (1,1).
parD (tuple (2)): Prior parameters for emission model D. By default (1,1).
random_params (bool, optional): Bayesian parameters if True, otherwise single point.
"""
x = _posterior_data(region, dates, weekly=weekly)\
.reset_index(drop = True)
POP = population.get_population(region)
# filter param
params = params[params.start <= dates[1]]
if (params.end > dates[1]).any():
params.loc[params.end > dates[1], 'end'] = dates[1]
latent = transition(POP, initial, params, random_params=random_params)
xx = x.merge(latent, how='left', on=['date'])
Dw = xx.shape[0]
D = (dates[1] - dates[0]).days + 1
sim_lat = np.zeros((5,N,Dw))
sim_obs = np.zeros((5,N,Dw))
for i in range(N):
if i == 0 or (i+1) % 100 == 0:
print('%4d / %d' % (i+1,N))
# transition
latent = transition(POP, initial, params, random_params=random_params)
latent[latent.I < 0]['I'] = 0
xx = x.merge(latent, how='left', on=['date'])
xx.tests = xx['tests'].apply(lambda t: t if t >= 0 else 1)
sim_lat[:,i,:] = xx[['S','E','I','R','D']].to_numpy().T
# emission
try:
sim_obs[2,i,:] = emission(np.abs(xx.I.to_numpy()), xx.tests.to_numpy(), *parI)
except:
print(xx.I)
print(xx.tests)
raise
sim_obs[3,i,:] = emission(xx.R.to_numpy(), xx.cumtests.to_numpy(), *parR)
sim_obs[4,i,:] = emission(xx.D.to_numpy(), xx.cumtests.to_numpy(), *parD)
# spare last
last_values = sim_lat[:,:,-1].mean(axis = 1)
# denormalize probability
sim_lat[1:3,:,:] = sim_lat[1:3,:,:] * x.tests.to_numpy()
sim_lat[3:5,:,:] = sim_lat[3:5,:,:] * x.cumtests.to_numpy()
sim_obs[1:3,:,:] = sim_obs[1:3,:,:] * x.tests.to_numpy()
sim_obs[3:5,:,:] = sim_obs[3:5,:,:] * x.cumtests.to_numpy()
return (sim_lat, sim_obs), last_values
def covid_deaths(save=False, name='img/data/deaths_per100K.png'):
"""Constructs the trace plot of Covid-19 deaths.
Args:
save (bool, optional): Whether to save the figure, defaultly not.
name (str, optional): Path to save the plot to.
"""
# get data
countries = ['CZ', 'PL', 'IT', 'SE']
xx = pd.concat([
posterior._posterior_data(country,
(datetime(2020, 3, 1), datetime(2021, 5, 1)))
for country in countries
])
# population
POP = {
country: population.get_population(country)
for country in countries
}
xx['POP'] = xx.region.apply(POP.get)
# normalize
xx['deaths100K'] = xx.deaths / xx.POP * 1e5
# to weekly
xx['year'] = xx.date.apply(lambda d: int(datetime.strftime(d, '%Y')))
xx['week'] = xx.date.apply(lambda d: int(datetime.strftime(d, '%W')))
def q025(x):
return x.quantile(0.)
def q975(x):
return x.quantile(1.)
xx = xx\
.groupby(['year','week','region'])\
.aggregate({'deaths100K': 'sum'})\
.reset_index(drop=False)
xx['date'] = xx.apply(
lambda r: datetime.strptime('%04d-%02d-1' %
(r.year, r.week), '%Y-%W-%w'),
axis=1)
# plot
fig, ax = plt.subplots(figsize=(8, 6))
for label, df in xx.groupby('region'):
ax.plot(df.date, df.deaths100K, label=label)
ax.set_xlabel('Date')
ax.set_ylabel('Deaths per 100K')
ax.legend()
if save: fig.savefig(name)
def _load_data(dates):
"""Load Covid-19 statistics in the appropriate format.
Args:
dates (tuple (2)): Date range of the data.
"""
global _cache
if _cache is not None:
return _cache
# regions
with open('model/regions.json') as fp:
regions = [k for k in json.load(fp) if len(k) > 2]
# fetch data
data_c, data_d, data_r = None, None, None
dateaxis = None
regions_r = []
for reg in regions:
x = posterior._posterior_data(reg, dates, weekly=True)
if dateaxis is None:
dateaxis = x.date
POP = population.get_population(reg)
# normalize by popylation
x['I1K'] = x.confirmed / POP * 1e3
x['D1K'] = x.deaths / POP * 1e3
# confirmed
c = x.I1K.to_numpy().reshape((1, -1))
data_c = np.concatenate([data_c, c],
axis=0) if data_c is not None else c
# deaths
d = x.D1K.to_numpy().reshape((1, -1))
data_d = np.concatenate([data_d, d],
axis=0) if data_d is not None else d
# recovered
if 'recovered' in x:
x['R1K'] = x.recovered / POP * 1e3
r = x.recovered.to_numpy().reshape((1, -1))
data_r = np.concatenate([data_r, r],
axis=0) if data_r is not None else r
regions_r.append(reg)
_cache = (data_c, data_d, data_r), dateaxis, (regions, regions, regions_r)
return _cache
def covid_recovered(save=False, name='img/data/recovered_per100K.png'):
"""Constructs the trace plot of Covid-19 recovered.
Args:
save (bool, optional): Whether to save the figure, defaultly not.
name (str, optional): Path to save the plot to.
"""
# get data
countries = ['CZ', 'PL', 'IT']
xx = pd.concat([
posterior._posterior_data(country,
(datetime(2020, 3, 1), datetime(2021, 5, 1)))
for country in countries
])
# population
POP = {
country: population.get_population(country)
for country in countries
}
xx['POP'] = xx.region.apply(POP.get)
# normalize
xx['deaths100K'] = xx.deaths / xx.POP * 1e5
# to weekly
xx['year'] = xx.date.apply(lambda d: int(datetime.strftime(d, '%Y')))
xx['week'] = xx.date.apply(lambda d: int(datetime.strftime(d, '%W')))
def q025(x):
return x.quantile(0.)
def q975(x):
return x.quantile(1.)
# plot
fig, ax = plt.subplots(figsize=(8, 6))
for label, df in xx.groupby('region'):
alpha = 1 if label != 'PL' else .5
ax.plot(df.date, df.deaths100K, label=label, alpha=alpha)
ax.set_xlabel('Date')
ax.set_ylabel('Deaths per 100K')
ax.legend()
if save: fig.savefig(name)
def posterior_objective(params, region, dates, initial, fixparams = None, weekly=False,
attributes = 'IRD', parI = (1,1), parR = (1,1), parD = (1,1)):
"""Objective function of the HMM model for optimization.
Args:
params (list): Optimized parameters.
region (str): Region for the data.
dates (tuple (2)): Date range of the data.
initial (dict): Initial values in dict with keys S,E,I,R,D.
fixparams (list): Fixed parameters.
weekly (bool, optional): Weekly time step if True, otherwise daily.
attributes (str, optional): Attributes used for optimization, 'I', 'R' or 'D'.
parI (tuple (2)): Prior parameters for emission model I.
parR (tuple (2)): Prior parameters for emission model R.
parD (tuple (2)): Prior parameters for emission model D.
"""
x = _posterior_data(region, dates, weekly=weekly)
POP = population.get_population(region)
# construct params dataframe
a,c,b,d = _parse_params(params, fixparams)
params = pd.DataFrame({'start': [dates[0]], 'end': [dates[1]],
'a': [a], 'b': [b], 'c': [c], 'd': [d]})
# compute score
D = (dates[1] - dates[0]).days + 1
score = 0
latent = transition(POP, initial, params)
latent.loc[latent.I < 0,'I'] = 0
x = x.merge(latent, how='left', on=['date'])
if 'I' in attributes:
score += emission_objective(x.confirmed.to_numpy() / x.tests.to_numpy(),
np.abs(x.I.to_numpy()), x.tests.to_numpy(), *parI)
if 'D' in attributes:
score += emission_objective(x.deaths.cumsum().to_numpy() / x.cumtests.to_numpy(),
x.D.to_numpy(), x.cumtests.to_numpy(), *parD)
if 'R' in attributes:
score += emission_objective(x.recovered.cumsum().to_numpy() / x.cumtests.to_numpy(),
x.R.to_numpy(), x.cumtests.to_numpy(), *parR)
return score / D
def run(region, N=1000):
"""Run model simulation.
Args:
region (str): Region to run the simulation for.
N (int, optional): Number of samples.
"""
region = region.upper().strip()
print(region)
# load config
with open("model/regions.json") as fp:
_config = json.load(fp)
config = _config[region]
config = {
'dates': ('2020-08-01', '2021-03-13'),
'window': 7,
'weekly': False,
'attributes': 'IRD',
'initial': {
'E': .1,
'I': .1,
'R': 0,
'D': 0
},
'emission': {
'I': (1, 1),
'R': (1, 1),
'D': (1, 1)
},
**config
}
POP = population.get_population(region)
# parse
dates = [datetime.strptime(d, "%Y-%m-%d") for d in config['dates']]
window = config['window']
weekly = config.get('weekly', False)
attributes = config['attributes'].upper()
initial = [
1 - sum(config['initial'].values()), # S
config['initial'].get('E', 0), # E
config['initial'].get('I', 0), # I
config['initial'].get('R', 0), # R
config['initial'].get('D', 0)
] # D
emission = [
config['emission'].get('I',
(1, 1)), config['emission'].get('R', (1, 1)),
config['emission'].get('D', (1, 1))
]
# optimize
params = optimize_spline(region,
dates,
initial=initial,
attributes=attributes,
emission=emission,
window=window,
weekly=weekly)
# simulate result
(sim_lat,
sim_obs), last_values = posterior.simulate_posterior(region=region,
params=params,
dates=dates,
N=N,
initial=initial,
parI=emission[0],
parR=emission[1],
parD=emission[2])
# save result
_results.save((sim_lat, sim_obs), dates, region, params)