# Why does the MAP estimate of the parameter vector of the dirichlet sum to 1?

``````    #Example for Pymc3 forums
import pymc3 as pm
import theano.tensor as tt
import pandas as pd
import numpy as np

pred_arr = [[2,3,4],[5,1,9]]
data = [2,3]
with pm.Model() as model:
a_vec = np.array([100 for i in range(3)])

prior = pm.Dirichlet('a',a = a_vec,shape=(3))

likelihood = pm.Normal('y',mu = tt.dot(np.array(pred_arr),prior),sd = 0.1,observed = np.array(data).T)

abra = pm.find_MAP()
trace = pm.fit(1000,start = abra)
``````

In the above example of dirichlet regression (note the numbers are just nonsense), I don’t understand why the posterior values of the concentration parameters of the dirichlet sum to 1. Why is this?

EDIT: I am very sorry, my brain had a massive derp. obviously the MAP values are not the MAPs of the concentration parameters, rather the actual values for which the posterior is maxed. Please close this.

No problem Thumbs up for finding out the solution/reason yourself.