I'm tasked with fitting the model of ODE equations to data using MCMC but can't get past the error:
TypeError Traceback (most recent call last)
<ipython-input-21-10d0a714b5f4> in <module>()
26 proposed[j] = proposed[j] + np.random.normal(0,propsigma[j])
27 if (proposed[j]>0): # automatically reject moves if proposed parameter <=0
---> 28 alpha = np.exp(logistic_loglik (proposed,time,ExRatio,sig)-logistic_loglik(par_out[i-1,],time,ExRatio,sig))
29 u = np.random.rand()
30 if (u < alpha):
<ipython-input-21-10d0a714b5f4> in logistic_loglik(params, t, data, sig)
3 # set up a function to return the log likelihood
4 def logistic_loglik(params,t,data,sig):
--> 5 return sum(norm.logpdf(logistic(params,t),data,sig))
6
7 # set standard deviations to be 10% of the population values
TypeError: logistic() missing 1 required positional argument: 'params'
the issue is with these lines:
def logistic_loglik(params,t,data,sig):
return sum(norm.logpdf(logistic(params,t),data,sig))
The function of these lines is set up a function to return the log likelihood obviously there is a logistic model involved.
It is my understanding that the issue is that the 'params' is not being called by the function but I am unsure of how to resolve this being a relative beginner to coding.
Rest of code is below to add context.
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
%matplotlib inline
def logistic(x,t,params):
S, R, A = x
r, Nmax, delta_s, beta, gamma, delta_r, delta_a, Emax, H, MICs, MICr = params
N = S + R
E_s = 1 - (Emax * A**H)/(MICs**H + A**H)
E_r = 1- (Emax * A**H)/(MICr**H + A**H)
derivs = [r * (1 - N / Nmax ) * E_s * S - delta_s * S - ((beta * S * R)/N),
r * (1 - gamma) * (1 - N/Nmax) * E_r * R - delta_r * R + ((beta * S * R)/N), - delta_a * A]
return derivs
r = 0.5
Nmax = 10**7
delta_s = 0.025
beta = 10**-2
gamma = 0.5
delta_r = 0.025
delta_a = 0.003
Emax = 2
H = 2
MICs = 8
MICr = 2000
[r, Nmax, delta_s, beta, gamma, delta_r, delta_a, Emax, H, MICs, MICr] = params
S = 9 * 10**6
R = 10**5
A = 5.6
x0 = [S, R, A]
maxt = 2000
tstep = 1
t = np.arange(0,maxt,tstep)
def logistic_resid(params,t,data):
return logistic(params,t)-data
logistic_out = odeint(logistic, x0, t, args=(params,))
time = np.array([0, 168, 336, 504, 672, 840, 1008, 1176, 1344, 1512, 1680, 1848, 2016, 2184, 2352, 2520, 2688, 2856])
ExRatio = np.array([2, 27, 43, 36, 39, 32, 27, 22, 13, 10, 14, 14, 4, 4, 7, 3, 3, 1])
ratio = 100* logistic_out[:,1]/(logistic_out[:,0]+logistic_out[:,1])
plt.plot(t,ratio)
plt.plot(time,ExRatio,'h')
xlabel('Position')
ylabel('Pollution')
New cell
from scipy.stats import norm
# set up a function to return the log likelihood
def logistic_loglik(params,t,data,sig):
return sum(norm.logpdf(logistic(params,t),data,sig))
# set standard deviations to be 10% of the population values
sig = ExRatio/10
# parameters for the MCMC
reps = 50000
nparams = 3
# output matrix
par_out = np.ones(shape=(reps,nparams))
# acceptance
accept = np.zeros(shape=(reps,nparams))
# proposal standard deviations. These have been pre-optimized.
propsigma = [0.05,20,5]
for i in range(1,reps):
# make a copy of previous parameters
par_out[i,] = par_out[i-1,]
for j in range(npars):
proposed = np.copy(par_out[i,:]) # we need to make a copy so that rejected moves don't affect the original matrix
proposed[j] = proposed[j] + np.random.normal(0,propsigma[j])
if (proposed[j]>0): # automatically reject moves if proposed parameter <=0
alpha = np.exp(logistic_loglik(proposed,time,ExRatio,sig)-logistic_loglik(par_out[i-1,],time,ExRatio,sig))
u = np.random.rand()
if (u < alpha):
par_out[i,j] = proposed[j]
accept[i,j] = 1
#print(sum(accept[range(101,reps),:])/(reps-100))
#plt.plot(par_out[:,0])
#plt.plot(par_out[range(101,reps),0])
#plt.plot(par_out[:,0],par_out[:,2])
plt.hist(par_out[range(101,reps),0],50)
print('\n')
a=np.mean(par_out[range(101,reps),0])
This my first question on here so if I have left any information out required for an answer please advise.
Any help would be greatly apprecieated
