def MLE(thetas,
BaseModel,
data,
states,
parNames,
checkpoints=None,
samples=None):
"""
A function to return the maximum likelihood estimator given a model object and a dataset
Parameters
-----------
BaseModel: model object
correctly initialised model to be fitted to the dataset
thetas: np.array
vector containing estimated parameter values
thetas: list
names of parameters to be fitted
data: list
list containing dataseries
states: list
list containg the names of the model states to be fitted to data
Returns
-----------
MLE : float
total sum of squared errors
Notes
-----------
An explanation of the difference between SSE and MLE can be found here: https://emcee.readthedocs.io/en/stable/tutorials/line/
Brief summary: if measurement noise is unbiased, Gaussian and independent than the MLE and SSE are identical.
Example use
-----------
MLE = MLE(model,thetas,data,parNames,positions)
"""
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# assign estimates to correct variable
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
initN, Nc_home, Nc_work, Nc_schools, Nc_transport, Nc_leisure, Nc_others, Nc_total = polymod.get_interaction_matrices(
)
# by defenition, if N is the number of data timeseries then the first N parameters are the estimated variances of these timeseries!
i = 0
sigma = []
for param in parNames:
if param == 'extraTime': # don't know if there's a way to make this function more general due to the 'extraTime', can this be abstracted in any way?
setattr(BaseModel, param, int(round(thetas[i])))
elif param == 'prevention':
checkpoints.update({
'Nc': [
thetas[i] *
(1.0 * Nc_home + (1 - 0.60) * Nc_work +
(1 - 0.70) * Nc_transport + (1 - 0.30) * Nc_others +
(1 - 0.80) * Nc_leisure)
]
})
# The following section is needed to perform a recalibration of beta
#elif param == 'beta':
# estimate_beta = thetas[i]
# checkpoints.update(
# {'beta':
# [
# np.random.choice(samples[param]),
# thetas[i],
# thetas[i],
# thetas[i],
# thetas[i],
# thetas[i],
# thetas[i]
# ]
# })
else:
if i < len(data):
sigma.append(thetas[i])
else:
BaseModel.parameters.update({param: thetas[i]})
i = i + 1
# ~~~~~~~~~~~~~~
# Run simulation
# ~~~~~~~~~~~~~~
# number of dataseries
n = len(data)
# Compute simulation time
data_length = []
for i in range(n):
data_length.append(data[i].size)
T = max(data_length) + BaseModel.extraTime - 1
# Use previous samples
if samples:
for param in samples:
if param == 'prevention':
prevention = np.random.choice(samples[param])
checkpoints.update({
'Nc': [
prevention * (1.0 * Nc_home + (1 - 0.60) * Nc_work +
(1 - 0.70) * Nc_transport +
(1 - 0.30) * Nc_others +
(1 - 0.80) * Nc_leisure), prevention *
(1.0 * Nc_home + (1 - 0.50) * Nc_work +
(1 - 0.60) * Nc_transport + (1 - 0.30) * Nc_others +
(1 - 0.70) * Nc_leisure), prevention *
(1.0 * Nc_home + (1 - 0.40) * Nc_work +
(1 - 0.55) * Nc_transport + (1 - 0.25) * Nc_others +
(1 - 0.65) * Nc_leisure), prevention *
(1.0 * Nc_home + (1 - 0.30) * Nc_work +
(1 - 0.50) * Nc_transport + (1 - 0.20) * Nc_others +
(1 - 0.60) * Nc_leisure), prevention *
(1.0 * Nc_home + (1 - 0.30) * Nc_work +
(1 - 0.45) * Nc_transport + (1 - 0.85) * Nc_schools +
(1 - 0.15) * Nc_others + (1 - 0.50) * Nc_leisure),
prevention *
(1.0 * Nc_home + (1 - 0.25) * Nc_work +
(1 - 0.35) * Nc_transport + (1 - 0.35) * Nc_schools +
(1 - 0.10) * Nc_others + (1 - 0.30) * Nc_leisure),
prevention * (1.0 * Nc_home + (1 - 0.20) * Nc_work +
(1 - 0.15) * Nc_transport +
(1 - 0.00) * Nc_others +
(1 - 0.00) * Nc_leisure)
]
})
#checkpoints.update({'Nc': [prevention*(1.3*Nc_home + (1-0.60)*Nc_work + (1-0.70)*Nc_transport + (1-0.30)*Nc_others + (1-0.80)*Nc_leisure)]})
else:
BaseModel.parameters[param] = np.random.choice(samples[param],
1,
replace=False)
# Perform simulation
out = BaseModel.sim(T, checkpoints=checkpoints)
# -------------
# calculate MLE
# -------------
ymodel = []
MLE = 0
for i in range(n):
som = 0
# sum required states
for j in range(len(states[i])):
som = som + out[states[i][j]].sum(dim="stratification").values
ymodel.append(som[BaseModel.extraTime:])
# calculate simga2 and log-likelihood function
MLE = MLE - 0.5 * np.sum(
(data[i] - ymodel[i])**2 / sigma[i]**2 + np.log(sigma[i]**2))
return abs(MLE) # must be positive for pso
def get_COVID19_SEIRD_parameters(stratified=True):
"""
Extracts and returns the parameters for the age-stratified deterministic model
This function returns all parameters needed to run the age-stratified model.
This function was created to group all parameters in one centralised location.
Parameters
----------
stratified : boolean
If True: returns parameters stratified by age, for agestructured model
If False: returns parameters for non-agestructured model
Returns
-----------
A dictionary with following keys and values:
Nc: np.array
9x9 social interaction matrix; by default, the total interaction
matrix Nc_total from the Polymod study is assigned to the parameters dictionary
h : np.array
fraction of the cases that require hospitalisation (-)
icu: np.array
fraction of the hospitalized in ICU
c: np.array
fraction of the hospitalized in Cohort, calculated as (c = 1 - icu) (-)
m0: np.array
fraction of the patients in ICU who die (-)
a: np.array
fraction of asymptomatic cases (-)
m: np.array
fraction of (mild) symptomatic cases (-)
da: float64
length of infectiousness in case of asymptomatic infection (days)
dm: float64
length of infectiousness in case of mild symptomatic infection (days)
dc: float64
length of stay in Cohort when symptoms don't worsen (days)
dICU: float64
length of stay in ICU (days)
dICUrec: float64
length of recovery stay in Cohort after stay in ICU (days)
dhospital: float64
time between first symptom and hospitalization (days)
beta: float64
chance of transmission when coming into contact with an infectious person (-)
sigma: float64
length of latent period (days)
omega: float64
length of pre-symptomatic infectious period (days)
dq: float64
length of quarantine when patient does not develop symptoms (days)
Example use
-----------
parameters = get_COVID19_SEIRD_parameters()
"""
abs_dir = os.path.dirname(__file__)
par_path = os.path.join(abs_dir, "../../../data/raw/model_parameters/")
# Initialize parameters dictionary
pars_dict = {}
if stratified == True:
# Assign Nc_total from the Polymod study to the parameters dictionary
Nc_total = polymod.get_interaction_matrices()[-1]
pars_dict['Nc'] = Nc_total
# Verity_etal
df = pd.read_csv(os.path.join(par_path, "verity_etal.csv"),
sep=',',
header='infer')
pars_dict['h'] = np.array(
df.loc[:, 'symptomatic_hospitalized'].astype(float).tolist()) / 100
pars_dict['icu'] = np.array(
df.loc[:, 'hospitalized_ICU'].astype(float).tolist()) / 100
# Molenberghs_etal
df = pd.read_csv(os.path.join(par_path, "molenberghs_etal.csv"),
sep=',',
header='infer')
pars_dict['m0'] = np.array(df.loc[:, 'IFR_general_population'].astype(
float).tolist()) / 100 / pars_dict['h']
# Wu_etal
df_asymp = pd.read_csv(os.path.join(par_path, "wu_etal.csv"),
sep=',',
header='infer')
pars_dict['a'] = np.array(
df_asymp.loc[:, 'fraction asymptomatic'].astype(float).tolist())
else:
pars_dict['Nc'] = np.array([11.2])
non_strat = pd.read_csv(os.path.join(par_path, "non_stratified.csv"),
sep=',',
header='infer')
pars_dict.update({
key: np.array(value)
for key, value in non_strat.to_dict(orient='list').items()
})
# deduced parameters
pars_dict['c'] = 1 - pars_dict['icu']
pars_dict['m'] = 1 - pars_dict['a']
# Other parameters
df_other_pars = pd.read_csv(os.path.join(par_path, "others.csv"),
sep=',',
header='infer')
pars_dict.update(df_other_pars.T.to_dict()[0])
# Fitted parameters
pars_dict['beta'] = 0.03492
return pars_dict
import math
import xarray as xr
import emcee
import json
import corner
from covid19model.optimization import objective_fcns
from covid19model.optimization import MCMC
from covid19model.models import models
from covid19model.data import google
from covid19model.data import sciensano
from covid19model.data import polymod
from covid19model.data import model_parameters
from covid19model.visualization.optimization import traceplot
initN, Nc_home, Nc_work, Nc_schools, Nc_transport, Nc_leisure, Nc_others, Nc_total = polymod.get_interaction_matrices(
)
def full_calibration(model,
timeseries,
spatial_unit,
start_date,
end_beta,
end_ramp,
fig_path,
samples_path,
maxiter=50,
popsize=50,
steps_mcmc=10000):
"""
model : object