Humans make decisions, generally, based on our knowledge of the world around us and, specifically, predicting to a greater or lesser extent the consequences of our actions. As tenuous as it may be, this requires an understanding of cause-and-effect relationships. What effects will a certain action have? What would have happened if we acted differently? Is one fact the cause of another, is there something that we are not taking into account that causes both, or is it rather pure coincidence? Understanding these causal relationships at a detailed level has important consequences at the personal, social and political levels. Judea Pearl (Israel, 1936), the new recipient of the Frontiers of Knowledge award 2022 in Information and Communication Technologies from the BBVA Foundation, is one of the creators of a formalism that extends the study of causality to numerous scenarios.
To solve a problem, we must understand which possible actions work or which do not work and why, also incorporating the uncertainty that marks our limited perspective of the world. For example, to design different medical treatments such as vaccines for polio, measles and, of course, covid-19, or antiretroviral therapy for HIV, it is essential to obtain a detailed and specific characterization of the relationship between treatment and disease. answer.
In statistics there is the famous premise that correlation does not imply causationas clearly shown by the spurious correlations. For example, there is a correlation between the number of movies featuring Nicolas Cage in the 2000s and the number of drownings in swimming pools during those same years. Does this mean that if Cage releases a new film we should be more careful in the pool? Not generally. This correlation does not imply a causal connection, it is just one of many coincidences that appear randomly.
On the other hand, sometimes there may be variables or confounding factors that affect several variables of interest at the same time, and their effect can lead to erroneous conclusions similar to the previous ones. As an example, there is a demonstrable correlation between the number of ice creams sold in a city and the number of violent crimes. In this case, there is a confounding variable: violent crimes are more frequent when temperatures rise, which also increases ice cream sales.
One of the most important “classical” techniques in the study of causality are randomized controlled trials (RCTs). In its most basic form, an RCT separates a random population into two groups: one will be treated or altered in some way and the other will remain unchanged (control group) to study the relative difference between the two. For example, in a vaccine effectiveness study, half of the participants are treated with placebo and the other half will receive the dose. Thus, under certain requirements, the randomization of both groups allows discerning whether or not said alteration has a certain effect of interest in the population.
RCTs are very versatile to clarify the causal relationships between different factors, but it is not always feasible to carry them out due to problems of time, financing, difficulty in finding case studies, etc. Faced with this, new strategies are necessary to carry out studies of causality. This is where Pearl’s work shines, providing a new way to perform these analyses.
Pearl studies causality from a new perspective, extending Bayesian network models to interpret them as models of causality. Bayesian networks, also developed by Pearl, are a graphical tool for visually representing probabilistic models. These models are widely used in statistics for their ability to describe complex probabilistic events and relationships with great accuracy and appear frequently in research in artificial intelligence, statistics, and other fundamental sciences. Outside the academic context they are also used, for example, to support health centers when deciding what treatment a patient requires.
By combining the extended Bayesian network models with the control of confounding variables, it is possible to clearly determine causal relationships under certain hypotheses. This also solves apparently paradoxical situations, where depending on who or how the data analysis is done, contradictory conclusions are obtained (what is known as Simpson’s paradox). In addition, this causal analysis is a highly effective remedy against possible manipulations, which seek to confuse or blur the conclusions of the scientific community, as happened with tobacco in the 70s of the last century, when an attempt was made to hide the relationship between tobacco and cancer.
Despite the discussions it provoked within the scientific communityPearl’s work The Why Book: The New Science of Cause and Effectwhich moves between statistics and philosophy, has popularized his language for causal analysis. Pearl’s contributions are important in different fields of science, but they also help us obtain a new way of understanding the world, with direct implications for well-being and the way we make decisions that affect others and the environment around us. surrounds.
Simon Rodriguez He is a postdoctoral researcher at the ICMAT.
Timon G Longoria Agate is coordinator of the Mathematical Culture Unit of the ICMAT.
Coffee and Theorems is a section dedicated to mathematics and the environment in which it is created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest advances in this discipline, share meeting points between mathematics and other social and cultural expressions and remember those who marked their development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: “A mathematician is a machine that transforms coffee into theorems”.
Edition and coordination: Agate A. Timón G Longoria (ICMAT).
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