Maximizing Likelihood, Part 2
In Part 1, you computed a single log-likelihood for a single mu
. In this Part 2, you will apply the predefined function compute_loglikelihood()
to compute an array of log-likelihood values, one for each element in an array of possible mu
values.
The goal then is to determine which single mu
guess leads to the single maximum value of the loglikelihood array.
To get started, use the preloaded data sample_distances
, sample_mean
, sample_stdev
and a helper function compute_loglikelihood()
.
This exercise is part of the course
Introduction to Linear Modeling in Python
Exercise instructions
- Construct
mu_guesses
by taking values centered onsample_mean
and spread bysample_stdev
. - For each guess value
mu_guess
inmu_guesses
, usecompute_loglikelihood()
for allsample_distances
, holdingsigma
fixed atsample_stdev
. - Find the maximum value in the
loglikelihoods
array and use its index to find thebest_mu
from ourmu_guesses
. - Print the
best_mu
and visualize it by plotting theloglikelihoods
.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Create an array of mu guesses, centered on sample_mean, spread out +/- by sample_stdev
low_guess = sample_mean - 2*sample_stdev
high_guess = sample_mean + 2*sample_stdev
mu_guesses = np.linspace(____, ____, 101)
# Compute the loglikelihood for each model created from each guess value
loglikelihoods = np.zeros(len(mu_guesses))
for n, mu_guess in enumerate(____):
loglikelihoods[n] = compute_loglikelihood(____, mu=____, sigma=sample_stdev)
# Find the best guess by using logical indexing, the print and plot the result
best_mu = mu_guesses[loglikelihoods==np.max(____)]
print('Maximum loglikelihood found for best mu guess={}'.format(____))
fig = plot_loglikelihoods(mu_guesses, loglikelihoods)