Question

Normalizing weights

Given a set of weights, we want to nromalize them so that the sum = 1.

def normalize(ws):
    """Returns normalized set of weights that sum to 1."""
    s = sum(ws)
    return [w/s for w in ws]

ws = [1,2,3,4,5]
normalize(ws)

[0, 0, 0, 0, 0]

Comparing likleihoods

Assuming indepdnece, the likelihood of observing some data points given a distributional model for each data point is the product of the likelihood for each data point.

from scipy.stats import norm

rv1 = norm(0, 1)
rv2 = norm(0, 3)

xs = np.random.normal(0, 3, 1000)
likelihood1 = np.prod(rv1.pdf(xs))
likelihood2 = np.prod(rv2.pdf(xs))
likelihood2 > likelihood1

False

Equality comparisons

We use an equality condition to exit some loop.

s = 0.0

for i in range(1000):
    s += 1.0/10.0
    if s == 1.0:
        break
print i

999

Calculating variance

\[s^2 = \frac{\sum_{i=1}^{n} x_i^2 - (\sum_{i=1}^n x_i)^2/n}{n-1}\]

def var(xs):
    """Returns variance of sample data."""
    n = 0
    s = 0
    ss = 0

    for x in xs:
        n +=1
        s += x
        ss += x*x

    v = (ss - (s*s)/n)/(n-1)
    return v

# What is the sample variance for numbers from a normal distribution with variance 1?
np.random.seed(4)
xs = np.random.normal(1e9, 1, 1000)
var(xs)

-262.4064