Stochastic thinking

Stochastic thinking may be looked upon as the opposite of causal thinking; however, the term stochastic thinking is rather ambiguous, because the meaning of stochastics is not clear. It can be looked upon as a branch of mathematics, or as "a cocktail of statistical ideas and probabilistic ideas",[1] or in the sense of Bernoulli stochastics. Here stochastic thinking is explained in the sense of Bernoulli stochastics.[2]

Problem solving by stochastic thinking

Stochastic thinking for problem solving proceeds in three steps:

• Stochastic thinking as basis for making decisions starts with observing an effect or problem which needs a decision. The effect is considered not as an isolated event but as an outcome of the whole system, which admitted its occurrence. Thus there are two problems, a minor one which is the actual problem, and a major one which is a problem of the system.[3]
• The second step in stochastic thinking consists of identifying the necessary system changes to avoid the recurrence of the problem or at least to reduce its probability. The identification process starts with identifying "what is not" known and proceeds by modelling the relation between past and future which are to be changed.
• The third step of stochastic thinking is to verify that the system changes are effective.

The main difference between stochastic thinking and the prevailing causal thinking is the focus: Stochastic thinking focuses on improving the whole, while causal thinking focus on improving parts. Stochastic thinking means to think in sets and structures, that is, to link the set representing the past and the sets representing the future by a set of probability distributions.[4] Improving the system means to reduce the probabilities of the occurrence of problems.

Effect of stochastic thinking

Stochastic thinking focuses on the whole system and aims at improving it step by step. The steps are essentially triggered by the occurrence of problems which are considered as system faults necessitating changes of the system. In other words, stochastic thinking results in a continual examination and improvement of the whole to prevent the recurrence of problems. Thus, stochastic thinking results in proactive strategies in contrast to the reactive strategies which are the outcome of causal thinking.

System performance is modelled by a Bernoulli space which represents the basis for stochastic thinking. The Bernoulli space shows explicitly the existing ignorance by means of the ignorance space and the inherent randomness by the variability function and the random structure function. The ignorance space specifies the possible areas of learning, while the two random functions indicate the possibilities of future changes and their impacts.[5]

Stochastic thinking is oriented towards long-term effects by means of continual improvement of the system, where improvement refers to the robustness of the system against disturbances or in other words improvements refer to the stability of the system.

References

1. ^ Andreas Eichler, Maria Gabriella Ottaviani, Floriane Wozniak and Dave Pratt, Introduction on "Stochastic Thinking", Proceedings of CERME 6, January 28th–February 1st 2009, Lyon France © INRP 2010, [1].
2. ^ Elart von Collani (ed.), Defining the Science Stochastics, Heldermann Verlag, Lemgo, 2004.
3. ^ Elart von Collani, "Science – the Great Illusion, Stochastics – the Promising Alternative."
4. ^ Elart von Collani, "Response to ‘Desired and Feared—What Do We Do Now and Over the Next 50 Years’ by Xiao-Li Meng", The American Statistician, 2010, 64(1): 23–25.
5. ^ Elart von Collani, Defining and Modelling Uncertainty, Journal of Uncertain Systems, Vol. 2, 202–211, 2008, [2].