# A Statistical Approach to Discovering Process Regime Shifts and Their Determinants
## 1 Introduction  
Real-world processes involve internal and external determinants, which act together to produce a certain expected output. These determinants, independently or in response to other factors, change over time, causing systematic and long-term shifts in their actual output patterns. Discovering these shifts and their determinants is thus a vital issue in understanding and managing the behavior of such processes. We note here that the term process is used in a broader sense, not restricted to just business or technological systems [1; 2; 3] that conform to well-defined aims such as producing specific quantities or qualities [4]. We also consider processes that have complex social, physical, economic or other determinants and interactions within or across their environments [5]. For instance, commodity price or demand generation is a process that has socio-economic determinants such as collective human behavior and geopolitical, economic or even health-related events [6; 7; 8]. Although there is no well-defined central control in such processes, stakeholders still seek to discover behavioral shifts for obvious reasons. It may also refer to socio-technical processes such as in information systems development and/or adoption [9; 10] in timetabling, transportation and healthcare [11; 12] and in road traffic systems, in which the output may be in the form of accidents or injuries [13]. In such systems, the concerned stakeholders are interested in discovering process dynamics and their conformity to intended behavior while taking appropriate enhancement measures [14]. In this context, we observe that the related process-mining literature has primarily taken a predominantly technological perspective. More precisely, the evaluated processes are well-defined, centrally managed, isolated from their wider environment (e.g., social or economic), and they behave mechanistically. The literature is rich in this direction, coveringprocess discovery, conformance and enhancement [15], where significant progress has been made in algorithm development, improvement and scalability [16; 17; 18]. A gap thus exists, as process mining of socio-economic or socio-technical systems has received minimal attention. Understanding overall behavioral dynamics is vital for such systems, in which behavioral regime shift discovery and analysis are crucial unaddressed questions. This has been recently highlighted by [PERSON], [PERSON] and [PERSON] [15] in the business context, pinpointing a lack of coverage of the social side of business problems. In this work, we aim to address this gap, and we propose a methodology that applies to studying behavioral regime shifts or changes in processes of such varied nature. Specifically, we aim to deal with these dynamic and temporally shifting processes at two levels. The _first_ level involves finding all the behavioral regime shifts [19]. To illustrate, we use the time series event log of two different processes (Figure 1), in which regime changes are evident. In the first example (Figure 1a), we see three distinct regimes: A, B and C, in which the process output _level_ significantly and systematically increased between regimes A and B. Later, between regimes B and C, the level significantly decreased. Similarly, regime A shows a stable behavior in the direction or trend example (Figure 1b). In contrast, regime B shows a systematic rising trend. We also note that we mainly focus on significant, systematic and potentially explainable shifts and not on small random fluctuations. As all regime shifts are discovered in the first level, the _second_ level focuses on _statistically_ finding their determinants. Although details are presented later, in summary, this phase involves identifying potential determinants, which are then statistically evaluated for their role in the formation of these regime shifts. Clearly, a lack of such knowledge only leads to inaccurate process understanding, predictability and inevitably its management and control.