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49 lines
1.3 KiB
Python
49 lines
1.3 KiB
Python
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import numpy as np
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import math
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def poisson_lambda_mle(d):
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"""
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Computes the Maximum Likelihood Estimate for a given 1D training
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dataset from a Poisson distribution.
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"""
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return sum(d) / len(d)
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def likelihood_poisson(x, lam):
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"""
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Computes the class-conditional probability for an univariate
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Poisson distribution
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"""
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if x // 1 != x:
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likelihood = 0
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else:
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likelihood = math.e**(-lam) * lam**(x) / math.factorial(x)
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return likelihood
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if __name__ == "__main__":
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# Plot Probability Density Function
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from matplotlib import pyplot as plt
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training_data = [0, 1, 1, 3, 1, 0, 1, 2, 1, 2, 2, 1, 2, 0, 1, 4]
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mle_poiss = poisson_lambda_mle(training_data)
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true_param = 1.0
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x_range = np.arange(0, 5, 0.1)
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y_true = [likelihood_poisson(x, true_param) for x in x_range]
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y_mle = [likelihood_poisson(x, mle_poiss) for x in x_range]
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plt.figure(figsize=(10,8))
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plt.plot(x_range, y_true, lw=2, alpha=0.5, linestyle='--', label='true parameter ($\lambda={}$)'.format(true_param))
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plt.plot(x_range, y_mle, lw=2, alpha=0.5, label='MLE ($\lambda={}$)'.format(mle_poiss))
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plt.title('Poisson probability density function for the true and estimated parameters')
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plt.ylabel('p(x|theta)')
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plt.xlim([-1,5])
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plt.xlabel('random variable x')
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plt.legend()
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plt.show()
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