How To Implement Conflation For Probability Distribution In Python?

I looked online for performing the combining several continuous probability distributions into one continuous probability distribution. This method is called Conflation, the method

Solution 1:

Disclaimer: there's a good chance I'm misunderstanding either you or the paper authors, in which case please suggest an edit to this answer.

Here is a trivial, not-especially-performant implementation of what I think conflation might look like

##define pdfs for discrete RV X = {1,2,3,4}import numpy as np

defmult_list(pdfs):
    prod=np.ones(pdfs[0].shape[0])
    for pdf in pdfs:
        prod=prod*pdf
    return prod

defconflate(pdfs):
    return mult_list(pdfs)/sum(mult_list(pdfs))

pdf_1=np.array([.25,.25,.25,.25])
pdf_2=np.array([.33,.33,.33,.00])
pdf_3=np.array([.25,.12,.13,.50])

print(conflate([pdf_1,pdf_2,pdf_3]))

which yields the resulting conflated pdf

>>>[0.50.240.260.  ]

which passes a cursory sniff test.

On the continuous side of things, the above translates to

from scipy.integrate import quad
from scipy import stats
import numpy as np

def prod_pdf(x,dists):
    p_pdf=1
    for dist in dists:
        p_pdf=p_pdf*dist.pdf(x)
    return p_pdf

def conflate_pdf(x,dists,lb,ub):
    denom = quad(prod_pdf, lb, ub, args=(dists))[0]
    return prod_pdf(x,dists)/denom

dists=[stats.norm(2,1),stats.norm(4,2)]
lb=-10
ub=10
domain=np.arange(lb,ub,.01)
graph=conflate_pdf(domain,dists,lb,ub)

from matplotlib import pyplot as plt
plt.plot(domain,graph)
plt.xlabel("domain")
plt.ylabel("pdf")
plt.title("Conflated PDF")
plt.show()
plt.savefig("conflatedpdf.png")

which gives

As you can see, the distribution is not bimodal, just as one would hope.