How to implement automatic model determination and two state model fitting in python?

问题

Currently, I've been doing model fitting in Prism manually for all my data. It's quite tedious and time consuming. I wonder if there is any way to improve the efficiency in data analysis. I'm familiar with Python so I'd like to start with python to think of a better workflow. Your help is much appreciated.

Two questions:

How to do two state model fitting in python (figure 1)? In my case, it will has an initial linear increase followed by horizontal plateau state. I wish to the way of implementation in python and the way to automatically detect the turning point where the changes occurs (Ideally I can get the time where it occurs and the slope as well)
Another case is when the state become exponentially or polynomial. Is there any way in python to automatically tell which model is the best.

Figure 1

回答1:

Scipy provides a least square curve fit method that supports custom defined functions. Here is an example for the first model:

import numpy as np
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

#custom fit function - first slope steeper than second slope
def two_lin(x, m1, n1, m2, n2):
    return np.min([m1 * x + n1, m2 * x + n2], axis = 0)

#x/y data points
x = np.asarray([0, 1, 2,  3,  4,  5,  6,  7,  8,  9,  10])
y = np.asarray([2, 4, 8, 12, 14, 18, 20, 21, 22, 23,  24])
#initial guess for a steep rising and plateau phase
start_values = [3, 0, 0, 3]
#curve fitting
fit_param, pcov = curve_fit(two_lin, x, y, p0 = start_values)

#output of slope/intercept for both parts
m1, n1, m2, n2 = fit_param
print(m1, n1, m2, n2)
#calculating sum of squared residuals as parameter for fit quality
r = y - two_lin(x, *fit_param)
print(np.sum(np.square(r)))

#point, where the parts intersect 
if m1 != m2:
    x_intersect = (n2 - n1) / (m1 - m2)
    print(x_intersect)
else:
    print("did not find two linear components")

#plot data and fit function
x_fit = np.linspace(-1, 11, 100)  
plt.plot(x, y, 'o', label='data')
plt.plot(x_fit, two_lin(x_fit, *fit_param), '--', label='fit')

plt.axis([-2, 12, 0, 30])
plt.legend()
plt.show()

More information about scipy.optimize.curve_fit can be found in the reference guide. For polynomials, numpy provides standard functions with numpy.polyfit and numpy.poly1d, but you still have to provide the expected degree.

The sum of squared residuals can be used to compare the accuracy of different fit functions.

来源：https://stackoverflow.com/questions/48674558/how-to-implement-automatic-model-determination-and-two-state-model-fitting-in-py

标签

python

scipy

modeling

model-fitting