Revisiting causality using stochastics: 1. Theory

Abstract

Causality is a central concept in science, in philosophy and in life. However, reviewing various approaches to it over the entire knowledge tree, from philosophy to science and to scientific and technological applications, we locate several problems, which prevent these approaches from defining sufficient conditions for the existence of causal links. We thus choose to determine necessary conditions that are operationally useful in identifying or falsifying causality claims. Our proposed approach is based on stochastics, in which events are replaced by processes. Starting from the idea of stochastic causal systems, we extend it to the more general concept of hen-or-egg causality, which includes as special cases the classic causal, and the potentially causal and anti-causal systems. Theoretical considerations allow the development of an effective algorithm, applicable to large-scale open systems, which are neither controllable nor repeatable. The derivation and details of the algorithm are described in this paper, while in a companion paper we illustrate and showcase the proposed framework with a number of case studies, some of which are controlled synthetic examples and others real-world ones arising from interesting scientific problems.

Reservoir Routing and Its Application to Atmospheric Carbon Dioxide Balance

“…For 𝑏𝑏 = 1, this corresponds the exponential distribution; indeed, by taking the limit as 𝑏𝑏 → 1, we recover equation (29). For 𝑏𝑏 < 1 the variable 𝑤𝑤 becomes bounded from above by 1 (1 − 𝑏𝑏) ⁄ , which means that the reservoir empties (and the outflow ceases) at a finite time.…”

“…A thorough and general presentation of the IRF concept in a causality framework has been presented by Koutsoyiannis et al [28,29,30]. In our case, the following particular considerations are taken into account for a reservoir: (a) the system can be studied in terms of the dimensionless quantities and the dimensional ones can then be obtained through Equation (7); (b) the response function 𝑔𝑔(𝜂𝜂) for dimensionless time lag 𝜂𝜂 = ℎ/𝑊𝑊 0 is identical to the output function 𝑞𝑞(𝜏𝜏) for 𝜂𝜂 = 𝜏𝜏, which results from the impulse of an otherwise empty reservoir; and (c) the system is causal, which means that 𝑔𝑔(𝜂𝜂) = 0 for 𝜂𝜂 < 0.…”

“…Point 3 above implies a causality direction between temperature and CO₂ concentration that is opposite to the popular one, which is the one also assumed and embedded in climate models. Specifically, the conventional wisdom that it is the increased atmospheric carbon dioxide concentration ([CO₂]) that caused the increase of temperature (T) was questioned by Koutsoyiannis and Kundzewicz [54], while later Koutsoyiannis et al [28,29,30] provided evidence, based on analyses of instrumental measurements of the last seven decades, for a unidirectional, potentially causal link between T as the cause and [CO₂] as the effect.…”

Revisiting causality using stochastics on atmospheric temperature and CO 2 concentration

“…3. 2 The conclusion in [1] is problematic: 'Clearly, the results in figure 14 suggest a (mono-directional) potentially causal system with T as the cause and [CO 2 ] as the effect. Hence the common perception that increasing [CO 2 ] causes increased T can be excluded as it violates the necessary condition for this causality direction'.…”

“…Koutsoyiannis et al . studied the causal relationship between atmospheric temperature (T) and the concentration of carbon dioxide ([CO 2 ]) [1] with their proposed causality detection methodology [2]. It is a complicated problem because entirely different mechanisms operate at different timescales.…”