Stochastic Modeling in the Life and Social Science
Stochastic Modeling in the Life and Social Science
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Introduction
Even though stochastic modeling is associated mainly with the study of uncertainty in natural sciences, views a higher substantial level concerning stochastic modeling function and applications are not similar. This is not surprising, owing to the multidisciplinary nature of science. Basing on the application under consideration, stochastic models can be referred to as hydrologic, atmospheric, ecological, and geological genetic and so forth. A common aspect in all these situations is that stochastic modeling related to mathematically vigorous and scientifically logically representation, justification and projection of natural systems in unpredictable situations (unpredictability may be because of measurements errors, insufficient knowledge or changes in space/time of underlying processes). In this kind of a situation, the main objective of SM is providing a practical system with spatiotemporal continuity and internal physical consistency. Barley and Cherif (2011) explain that, to attain such an objective stochastic modeling depends on the powerful mixture of two aspects. First, a formal aspect, that focuses on mathematical framework, rational process and theoretical representation, secondly, interpretive aspect, which deals with the application of the formal component in real-world circumstances.
Formal stochastic modeling is concerned with a big range of mathematical topics that include random fractals and wavelets, stochastic differential and integro-differential equations, estimation methods, rules of logical reasoning, among others.
Stochastic modeling and Science
The use of stochastic modeling is more and more being applied in the social sciences as well as epidemiology, to represent the random attribute of these processes. As pointed by Barley and Cherif (2011), previous studies carried out by Reed and Frost (1928) on disease spreading within a locked human population lead to initial use of simplified stochastic models. In their research, they applied chain binomials models as a way of basic stochastic models for examining discrete epidemic processes in a regular population. Stochastic models are characterized by two main components, which help in understanding the process at hand and justifying the methodological approach taken to model the process as a system. The first component is the formal component, and which Christakos (n.d.) argues that it focuses on the mathematical structure of the process or natural system, brings out the logicalness and helps in coming up with a theoretical representation of the system in general. The second component is the interpretive component. This component relates to the application of the formal form in real world situation. Despite the instrumental role of these components in stochastic modeling, application of SM is met with several challenges in the various fields of science.
The multidisciplinary characteristic of science gives stochastic modeling a special role to play in science in general. Many terms can be used to describe the general characteristics of stochastic models, as has been highlighted earlier. For instance, Christakos et al (2005), observe that stochastic models are of diverse nature just as the science field is multifaceted in nature and thus the models could be described with such terms as epidemic, genetic or atmospheric, among other terms as long as the main object of the models is to come up with a mathematically rigorous representation and prediction of natural systems in light of uncertainty and need for scientific meaningfulness in the explanation of the models. Prediction is called for in such environments because the natural systems are a function of uncertainties that may arise from aspects such as measurement errors, irregular fluctuations in the time and/or space of the process being modeled and also due to insufficient knowledge. Therefore, with this understanding, stochastic modeling comes in as a handy tool to present the natural systems in a way that guarantees a higher degree of spatiotemporal continuity and achieve a consistent internal physical environment (Dickinson 2007).
Sociological and Biological Process Modeling
Due to high degree of diversity in human behavior and the erratic nature of most variables that encompass the behavior, modeling predictive models in the fields of sociology and biology can be challenging given the numerous aspects of the scientific method that have to be incorporated. For instance, as observed by Barley and Cherif (2011), formulating a predictive model for a romantic relationship would incorporate aspects of behavior and emotions and therefore proper methods of data collection and estimation of parameters yet not all parameters can be predicted at present since some methods are yet to be developed.
There are social processes that are also represented using stochastically modeled systems. An example of such processes is the political stability of states. While the main object of a stochastic model is to make an accurate representation of a natural system given the underlying factors, one big challenge that faces modeling for social processes such as political stability is that variability of state stability has to be adequately characterized. Despite this challenge, it is agreeable that deterministic models are not fit for predicting the stability of states (Dickinson 2007).
Even though some studies (e.g. Barley & Cheri 2011), have shown that deterministic models can be used to present dynamic features of certain social processes such as romantic dynamics, some authors have argued that deterministic models are not the best for these processes due to the randomness of variability that would require probabilistic approach to model the states given the nature of variables involved (e.g. Dickinson 2007; also Christakos n.d).
Epidemiological Process Modeling
Stochastic modeling is appropriate for modeling epidemiological processes like the spread of a communicable disease after an outbreak. In fact, as has already been mentioned, the studies carried out by Reed and Frost (1928) examining the spread of communicable disease within a closed human population provided the first simplified probabilistic models for the study of epidemic processes. After this application many other stochastic models were developed and used for the study of disease spread and other social processes; either as discrete or continuous-time processes (Christakos et al 2005).
We have seen that stochastic modeling requires the use of variables and parameters that must be estimated. Therefore, parameter estimation is a very essential part of the model formulation. Since model formulation generally relies on the use of the observed data and model it in such a way that the parameters we model fit appropriately in the data that has been observed, accuracy is of paramount concern. Among the methods that are used in parameter estimation includes least squares method and the maximum likelihood method.
Reference:
Christakos, G., R.A. Olea, M.L. Serre, H.L. Yu and L-L. Wang (2005) Interdisciplinary Public Health Reasoning and Epidemic Modelling: The Case of Black Death. Springer-Verlag, New York, N.Y.
Dickinson R. E., (2007) Exact Solution to the Stochastic Spread of Social Contagion — Using Rumours. University of Adelaide
Christakos G., (nd) STOCHASTIC MODELING IN LIFE SUPPORT SYSTEMS, San Diego State University, CA, USA
Barley, K., Cherif, A. (2011), Stochastic nonlinear dynamics of interpersonal and romantic relationships, Appl. Math. Comput. doi:10.1016/j.amc.2010.12.117
