User Guide

The likelihood \(L\) of a sequence of observed open and shut events \(\{t_{oi}, t_{si}\}\) can be computed as a product of open-shut, \({}^e\mathcal{G}_{AF}(t_{oi})\) and shut-open transition densities, \({}^e\mathcal{G}_{FA}(t_{oi})\), both accounting for missed events [CHS96]:

\[L(Q, \{t_{oi}, t_{si}\}) = \phi_A \left[\prod_i^{n-1}{}^e\mathcal{G}_{AF}(t_{oi}){}^e\mathcal{G}_{AF}(t_{si})\right] {}^e\mathcal{G}_{AF}(t_{on}) \phi_e\]

where \(Q\) is the transition rate matrix, and \(\phi_A\) and \(\phi_e\) are the initial and final equilibrium vectors. All these objects – as well as their components – can be accessed both from Python and from C++. In the following, we try and show how they can be created and manipulated from either language.

• The \(Q\)-matrix
• Likelihood \(L(Q)\)
• Missed-Events transition densities \({}^eG(t)\)
  • Initialization from a \(Q\)-matrix
  • Initialization from the roots and determinant equations
  • Initialization from the \(Q\)-matrix and a root finding function
  • Computing \({}^eG_{AF}(t)\) and \({}^eG_{FA}(t)\)
• Ideal transition densities \(\mathcal{G}(t)\)
• Equilibrium vectors
• Exact Survivor Function \(R_A(t)\)
• Approximate Survivor Function \(R_A(t)\)
• Determinant Equation \(W(s) = sI - H(s)\)
• Searching for Roots

How to read this manual

Each topic below is illustrated by an example in C++, and another in Python. These examples can be found in the source code of the package within the directory documentation/code. In any case, one can copy and paste.

The user guide should read using the left eye only, and keeping the right eye on the api, or vice-versa. Most of the C++ functions and Python bindings offer more functionality or parameters than mentioned in the manual.