example_MCMC_logistic_growth.py

import numpy as np

from PAID.EulerMethod.euler import euler
from PAID.data.generator import DataGenerator
from PAID.InferenceMethod.inference import MCMCInferenceProblem
from tests.exact_models.models import logistic_growth_dimensionless

### exact parameters
exact_parameters = [1.0, 0.1, 0.05]
Lambda, x_0, scale = exact_parameters

### generate data
data_time = np.linspace(0, 10, 100)
exact_solution = logistic_growth_dimensionless(times=data_time, x_0=x_0, Lambda=Lambda)

gen = DataGenerator()
data_y = gen.generate_data(exact_solution, scale=scale)
data = np.vstack(tup=(data_time, data_y))

ODEmodel = lambda t, x, Lambda: Lambda * x * (1 - x)

problem = MCMCInferenceProblem(ODEmodel, data)

initial_parameters = [1.0] # initial lambda
initial_y0 = 0.1
initial_noise = 0.05
step_size = 0.1

lambda_interval = np.array([0.0, 10.0])
y0_interval = np.array([0.0, 1.0])
std_interval = np.array([1.0e-5, 10])
valid_parameter_interval = np.vstack(tup=(lambda_interval, y0_interval, std_interval))

sampling_stepsize = np.array([0.01, 0.01, 0.005])
estimated_parameters, mean, std = problem.infer_parameters(initial_parameters=initial_parameters,
                                                y_0=initial_y0,
                                                initial_noise=initial_noise,
                                                valid_parameter_interval=valid_parameter_interval,
                                                sampling_stepsize=sampling_stepsize,
                                                max_iterations=500)

print('infered parameters: ', estimated_parameters)
print('mean of posteriors: ', mean)
print('std of posteriors: ', std)
print('exact parameters: ', exact_parameters)

problem.plot()