Log uniform prior

# Parameters
func_name = "Log_uniform_prior"
positive_prior = True

Description

func.display()

• description: A function which is K/x on the interval lower_bound - upper_bound and 0 outside the interval. The extremes of the interval are NOT counted as part of the interval. Lower_bound must be >= 0.
• formula: $ f(x)=K~\begin{cases}0 & x \le \text{lower_bound} \\\frac{1}{x} & \text{lower_bound} < x < \text{upper_bound} \\ 0 & x \ge \text{upper_bound} \end{cases}$
• parameters:
  • lower_bound:
    • value: 1e-20
    • desc: Lower bound for the interval
    • min_value: 1e-30
    • max_value: inf
    • unit:
    • is_normalization: False
    • delta: 1e-21
    • free: True
  • upper_bound:
    • value: 100.0
    • desc: Upper bound for the interval
    • min_value: 1e-30
    • max_value: inf
    • unit:
    • is_normalization: False
    • delta: 10.0
    • free: True
  • K:
    • value: 1.0
    • desc: Normalization
    • min_value: None
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: False

Shape

The shape of the function.

If this is not a photon model but a prior or linear function then ignore the units as these docs are auto-generated

fig, ax = plt.subplots()


ax.plot(energy_grid, func(energy_grid), color=blue, lw=3)

ax.set_xlabel("x")
ax.set_ylabel("probability")

Text(0, 0.5, 'probability')

Random Number Generation

This is how we can generate random numbers from the prior.

u = np.random.uniform(0,1, size=5000)

draws = [func.from_unit_cube(x) for x in u]


fig, ax = plt.subplots()


ax.hist(draws, color=green, bins=50)

ax.set_xlabel("value")
ax.set_ylabel("N")

Text(0, 0.5, 'N')