# Copyright (c) 2022 The BayesFlow Developers
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# The above copyright notice and this permission notice shall be included in all
# copies or substantial portions of the Software.
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.
# Corresponds to Task T.9 from the paper https://arxiv.org/pdf/2101.04653.pdf
import numpy as np
from scipy.integrate import odeint
bayesflow_benchmark_info = {
"simulator_is_batched": False,
"parameter_names": [r"$\beta$", r"$\gamma$"],
"configurator_info": "posterior",
}
[docs]
def prior(rng=None):
"""Generates a random draw from a 2-dimensional (independent) lognormal prior
which represents the contact and recovery rate parameters of a basic SIR model.
Parameters
----------
rng : np.random.Generator or None, default: None
An optional random number generator to use.
Returns
-------
theta : np.ndarray of shape (2,)
A single draw from the 2-dimensional prior.
"""
if rng is None:
rng = np.random.default_rng()
theta = rng.lognormal(mean=[np.log(0.4), np.log(1 / 8)], sigma=[0.5, 0.2])
return theta
def _deriv(x, t, N, beta, gamma):
"""Helper function for scipy.integrate.odeint."""
S, I, R = x
dS = -beta * S * I / N
dI = beta * S * I / N - gamma * I
dR = gamma * I
return dS, dI, dR
[docs]
def simulator(theta, N=1e6, T=160, I0=1.0, R0=0.0, subsample=10, total_count=1000, scale_by_total=True, rng=None):
"""Runs a basic SIR model simulation for T time steps and returns `subsample` evenly spaced
points from the simulated trajectory, given disease parameters (contact and recovery rate) `theta`.
See https://arxiv.org/pdf/2101.04653.pdf, Benchmark Task T.9.
Note, that the simulator will scale the outputs between 0 and 1.
Parameters
----------
theta : np.ndarray of shape (2,)
The 2-dimensional vector of disease parameters.
N : float, optional, default: 1e6 = 1 000 000
The size of the simulated population.
T : T, optional, default: 160
The duration (time horizon) of the simulation.
I0 : float, optional, default: 1.
The number of initially infected individuals.
R0 : float, optional, default: 0.
The number of initially recovered individuals.
subsample : int or None, optional, default: 10
The number of evenly spaced time points to return. If None,
no subsampling will be performed and all T timepoints will be returned.
total_count : int, optional, default: 1000
The N parameter of the binomial noise distribution. Used just
for scaling the data and magnifying the effect of noise, such that
max infected == total_count.
scale_by_total : bool, optional, default: True
Scales the outputs by ``total_count`` if set to True.
rng : np.random.Generator or None, default: None
An optional random number generator to use.
Returns
-------
x : np.ndarray of shape (subsample,) or (T,) if subsample=None
The time series of simulated infected individuals. A trailing dimension of 1 should
be added by a BayesFlow configurator if the data is (properly) to be treated as time series.
"""
# Use default RNG, if None specified
if rng is None:
rng = np.random.default_rng()
# Create vector (list) of initial conditions
x0 = N - I0 - R0, I0, R0
# Unpack parameter vector into scalars
beta, gamma = theta
# Prepate time vector between 0 and T of length T
t_vec = np.linspace(0, T, T)
# Integrate using scipy and retain only infected (2-nd dimension)
irt = odeint(_deriv, x0, t_vec, args=(N, beta, gamma))[:, 1]
# Subsample evenly the specified number of points, if specified
if subsample is not None:
irt = irt[:: (T // subsample)]
# Truncate irt, so that small underflow below zero becomes zero
irt = np.maximum(irt, 0.0)
# Add noise and scale, if indicated
x = rng.binomial(n=total_count, p=irt / N)
if scale_by_total:
x = x / total_count
return x
[docs]
def configurator(forward_dict, mode="posterior", as_summary_condition=False):
"""Configures simulator outputs for use in BayesFlow training."""
# Case only posterior configuration
if mode == "posterior":
input_dict = _config_posterior(forward_dict, as_summary_condition)
# Case only likelihood configuration
elif mode == "likelihood":
input_dict = _config_likelihood(forward_dict)
# Case posterior and likelihood configuration
elif mode == "joint":
input_dict = {}
input_dict["posterior_inputs"] = _config_posterior(forward_dict, as_summary_condition)
input_dict["likelihood_inputs"] = _config_likelihood(forward_dict)
# Throw otherwise
else:
raise NotImplementedError('For now, only a choice between ["posterior", "likelihood", "joint"] is available!')
return input_dict
def _config_posterior(forward_dict, as_summary_condition):
"""Helper function for posterior configuration."""
input_dict = {}
input_dict["parameters"] = forward_dict["prior_draws"].astype(np.float32)
if as_summary_condition:
input_dict["summary_conditions"] = forward_dict["sim_data"].astype(np.float32)[:, :, np.newaxis]
else:
input_dict["direct_conditions"] = forward_dict["sim_data"].astype(np.float32)
return input_dict
def _config_likelihood(forward_dict):
"""Helper function for likelihood configuration."""
input_dict = {}
input_dict["conditions"] = forward_dict["prior_draws"].astype(np.float32)
input_dict["observables"] = forward_dict["sim_data"].astype(np.float32)
return input_dict
