[FIXED] Model of a Probability Distribution

Issue

I'm trying to run a python script that is used as an example on this data science site: https://www.datascience.com/blog/introduction-to-bayesian-inference-learn-data-science-tutorials

import numpy as np
from scipy.misc import factorial
import matplotlib.pyplot as plt
%matplotlib inline

plt.rcParams['figure.figsize'] = (16,7)

def likelihood(theta, n, x):
    """
    likelihood function for a binomial distribution

    n: [int] the number of experiments
    x: [int] the number of successes
    theta: [float] the proposed probability of success
    """
    return (factorial(n) / (factorial(x) * factorial(n - x))) \
            * (theta ** x) * ((1 - theta) ** (n - x))

# The number of impressions for our facebook-yellow-dress campaign
n_impressions = 10

# The number of clicks for our facebook-yellow-dress campaign
n_clicks = 7

# Observed click through rate
ctr = n_clicks / n_impressions

# 0 to 1, all possible click through rates
possible_theta_values = map(lambda x: x/100., range(100))

# Evaluate the likelihood function for possible click through rates
likelihoods = map(lambda theta: likelihood(theta, n, x)\
                                , possible_theta_values)

# Pick the best theta
mle = possible_theta_values[np.argmax(likelihoods)]

# Plot
f, ax = plt.subplots(1)
ax.plot(possible_theta_values, likelihoods)
ax.axvline(mle, linestyle = "--")
ax.set_xlabel("Theta")
ax.set_ylabel("Likelihood")
ax.grid()
ax.set_title("Likelihood of Theta for New Campaign")
plt.show()

I'm using Spyder. The errors that I am getting include:

    %matplotlib inline
    ^
SyntaxError: invalid syntax

as well as

mle = possible_theta_values[np.argmax(likelihoods)]
TypeError: 'map' object is not subscriptable

and

likelihoods = list(map(lambda theta: likelihood(theta, ctr, x)\
NameError: name 'x' is not defined

I tried a solution that I found here: Python map object is not subscriptable

# Evaluate the likelihood function for possible click through rates
likelihoods = list(map(lambda theta: likelihood(theta, n_clicks, ctr)\
                                , possible_theta_values))

But it gave the error

TypeError: object of type 'map' has no len()

How can I fix the script to run in Spyder please?

Solution

Minor modifications in the code to make it work. I had to convert your map iterable objects to lists to make your code work for the reasons you mentioned : TypeError: 'map' object is not subscriptable. I also had to define explicitly the x array to be able to use it while calculating likelihoods.

# 0 to 1, all possible click through rates
possible_theta_values = list(map(lambda x: x/100., range(100)))

n = n_impressions
x = n_clicks

# Evaluate the likelihood function for possible click through rates
likelihoods = list(map(lambda theta: likelihood(theta, n, x)\
                                , possible_theta_values))

Answered By - Sheldore