Survival Analysis, Master Equation, Efficient Simulation of Path-Related Quantities, and Hidden State Concept of Transitions

TL;DR

This paper explores the relationship between survival analysis and master equations, introducing new formulas and simulation tools to efficiently analyze path-related quantities and hidden states in stochastic systems.

Contribution

It derives new formulas linking survival analysis and master equations, and presents an efficient simulation approach for path-related quantities and hidden states.

Findings

New formulas for path-related quantities like occurrence probability and time distribution.

Efficient evaluation of these quantities using the EPIS simulation tool.

Introduction of a hidden state concept for behavioral change analysis.

Abstract

This paper presents and derives the interrelations between survival analysis and master equation. Survival analysis deals with modeling the transitions between succeeding states of a system in terms of hazard rates. Questions related with this are the timing and sequencing of the states of a time series. The frequency and characteristics of time series can be investigated by Monte-Carlo simulations. If one is interested in cross-sectional data connected with the stochastic process under consideration, one needs to know the temporal evolution of the distribution of states. This can be obtained by simulation of the associated master equation. Some new formulas allow the determination of path-related (i.e. longitudinal) quantities like the occurence probability, the occurence time distribution, or the effective cumulative life-time distribution of a certain sequencing of states (path). These can be efficiently evaluated with a recently developed simulation tool (EPIS). The effective cumulative life-time distribution facilitates the formulation of a hidden state concept of behavioral changes which allows an interpretation of the respective time-dependence of hazard rates. Hidden states represent states which are either not phenomenological distinguishable from other states, not externally measurable, or simply not detected.