The **Bayesian method** is the natural approach to inference, yet it is hidden from readers behind chapters of slow, mathematical analysis. Nevertheless, **mathematical analysis** is only one way to *“think Bayes”*. With cheap computing power, we can now afford to take an alternate route via **probabilistic programming**.

Cam Davidson-Pilon wrote the **book ****Bayesian Methods for Hackers** as a introduction to Bayesian inference from a computational and understanding-first, mathematics-second, point of view.

The book is available via Amazon, but you can access an **online e-book** **for free**. There’s also an associated GitHub repo.

The book explains Bayesian principles with code and visuals. For instance:

```
%matplotlib inline
from IPython.core.pylabtools import figsize
import numpy as np
from matplotlib import pyplot as plt
figsize(11, 9)
import scipy.stats as stats
dist = stats.beta
n_trials = [0, 1, 2, 3, 4, 5, 8, 15, 50, 500]
data = stats.bernoulli.rvs(0.5, size=n_trials[-1])
x = np.linspace(0, 1, 100)
for k, N in enumerate(n_trials):
sx = plt.subplot(len(n_trials)/2, 2, k+1)
plt.xlabel("$p$, probability of heads") \
if k in [0, len(n_trials)-1] else None
plt.setp(sx.get_yticklabels(), visible=False)
heads = data[:N].sum()
y = dist.pdf(x, 1 + heads, 1 + N - heads)
plt.plot(x, y, label="observe %d tosses,\n %d heads" % (N, heads))
plt.fill_between(x, 0, y, color="#348ABD", alpha=0.4)
plt.vlines(0.5, 0, 4, color="k", linestyles="--", lw=1)
leg = plt.legend()
leg.get_frame().set_alpha(0.4)
plt.autoscale(tight=True)
plt.suptitle("Bayesian updating of posterior probabilities",
y=1.02,
fontsize=14)
plt.tight_layout()
```

I can only recommend you start with the **online version** of *Bayesian Methods for Hackers*, but note that the print version helps sponsor the author ánd includes some additional features:

- Additional Chapter on Bayesian A/B testing
- Updated examples
- Answers to the end of chapter questions
- Additional explanation, and rewritten sections to aid the reader.

If you’re interested in learning more about Bayesian analysis, I recommend these other books:

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