Tools for Markov Chain Monte Carlo analysis

Here are collected some useful tools for Markov Chain data analysis. Currently have been implemented:

• Bootstrap ( $\sim O(lkr)$ )
• Jackknife ( $\sim O(2lk)$ )
• Integrated autocorrelation time calculator

with $l =$ len(primary_functions), $k =$ blocks and $r =$ boot_samples.

Both Bootstrap and Jackknife accept two keyword arguments: primary function : list(callable) and function : callable.The first one is the list of primary functions $g_{\alpha}(x)$ from which $F(x)$, passed through function, depends.

Example: for $F(x) = \langle x ^4\rangle/\langle x^2 \rangle^2$, the inputs are primary_functions = [lambda x: x**4, lambda x: x**2] and lastly function = lambda a,b : a/b**2. In other words, primary_funtions contains all the functions whose means are computed, while function defines and registers the relation between these mean values.