PDF Summary:Everything Is Predictable, by Tom Chivers

How do we make decisions when we're uncertain? How does our brain process and interpret the world around us? In Everything Is Predictable, Tom Chivers explores Bayesian logic—a mathematical framework for updating beliefs based on new information. Rather than thinking in absolutes, Bayesian reasoning works with probabilities that shift as evidence accumulates.

Chivers explains how this framework applies beyond statistics, showing how Bayesian thinking can correct common misinterpretations in research and how the brain itself operates like a Bayesian machine. From adjusting confidence levels based on evidence to understanding how our minds combine sensory information and generate predictions about reality, this guide demonstrates how Bayesian models shape everything from scientific inquiry to conscious experience itself.

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(Shortform note: In Evidence and Evolution, philosopher Elliott Sober argues that this principle breaks down when the process that would reveal the thing to you is unreliable. For example, if you were looking for a rare fossil, the fact that you haven’t found one yet doesn’t mean that it doesn’t exist. This is because the process of fossilization is so unreliable that the fossil could exist without you ever finding it.)

Applications and Implications of Bayesian Inference

Next, let's go over two applications of Bayesian methods.

Correcting Misinterpretations Through Bayesian Thinking

Chivers explains that Bayesian reasoning can correct misinterpretations of p-value statistics. A p-value represents the probability of obtaining results as extreme as the ones you've observed, assuming the null hypothesis is true. However, a p-value of 0.05 merely indicates your data are unexpected, not the likelihood of the null hypothesis given your data.

The problem is that researchers frequently interpret statistically significant results as strong support for their hypothesis, but that’s not always true. In some cases, observing a p-value of 0.05 is more probable under the null hypothesis than the alternative hypothesis. In the absence of solid justification for favoring a specific hypothesis, a statistically significant outcome could support the null more than it argues against it. Chivers clarifies that this doesn’t imply the idea of p-values is inherently flawed; the two frameworks simply address different questions.

How to Interpret a P-Value Using Bayesian Reasoning

To use Bayesian reasoning to reinterpret a p-value, statisticians first specify a model for the alternative hypothesis. Then, they use mathematical formulas to convert each p-value into a minimum Bayes factor, which quantifies the strength of evidence against the null hypothesis. This Bayes factor is then plugged into Bayes’ theorem to update the odds of the null hypothesis being true. For example, a research article shows that a p-value of 0.05 corresponds to a minimum Bayes factor of about 2.5, meaning the data are only 2.5 times more likely under the alternative hypothesis than the null. This demonstrates that a p-value of 0.05 provides much weaker evidence against the null hypothesis than many researchers assume.

Bayesian Models of Cognition and Prediction

Chivers also explains that the mind uses Bayesian models to forecast and interpret sensory information. It’s constantly making predictions about the world and verifying them using sensory data. When the predictions align with the data, the brain is satisfied. When they do not, the brain experiences a "prediction error" and sends signals up the neural hierarchy to update its model. The brain pays more attention to predictions and data that are more precise and applies Bayes' theorem to combine top-down predictions with bottom-up sensory data at each level of processing. Chivers continues by saying that if the two match, the brain doesn't send many signals up or down.

(Shortform note: The idea that the brain forecasts and interprets sensations using Bayesian models emerged from computational neuroscience research on the “Bayesian brain” hypothesis. In a 2004 paper, David C. Knill and Alexandre Pouget argued that the nervous system represents information about the world in the form of probability distributions and combines these probabilistic representations according to the rules of probability theory, so that perception and action can be understood as the outcome of Bayesian inference operating on uncertain sensory data. For example, they showed that combining two noisy visual cues is mathematically identical to multiplying two probability distributions, suggesting that patterns of neural firing can be interpreted as probability distributions over possible sensory causes.)

When there's a misalignment, the brain sends a "surprisal" signal up the hierarchy. The bigger the discrepancy, the stronger the signal. The brain's goal is to minimize errors in its predictions. It accomplishes this by revising its representation of reality upon encountering novel data. The brain also pursues data to test its predictions. It navigates its surroundings and interacts with objects to collect information. This requires the mind to anticipate the impact of its movements and decide what actions to take to maximize knowledge.

(Shortform note: The term "surprisal" comes from information theory, where it refers to the negative logarithm of the probability of an event. In other words, the more unlikely an event is, the higher its surprisal value. Friston, who developed the free energy principle, explains that the brain can't directly calculate the probability of every possible sensory input. Instead, it uses a mathematical technique called variational inference to estimate an upper bound on surprisal, which it then tries to minimize.)

Additionally, the brain combines data from various senses using a Bayesian approach, assigning greater importance to the one that offers the most accurate information. This has been demonstrated in experiments where the precision of sensory inputs is manipulated. The brain combines the inputs similarly to the approach of a perfect Bayesian observer. Chivers adds that the mind's use of Bayesian models extends to high-level thinking like science. Science involves forecasting and verifying those forecasts, a method that follows Bayesian principles. However, Bayesian models are subjective because they rely on personal estimates of prior likelihoods.

(Shortform note: The brain’s ability to combine sensory inputs in a Bayesian manner is well-documented, but the exact neural mechanisms remain unclear. One theory, proposed by Pouget et al., suggests that the brain encodes the reliability of sensory information in the activity of large populations of neurons. Each sense’s reliability is reflected in the variability and gain of these neural populations. When the brain combines inputs from different senses, it pools the activity of these populations. This pooling process naturally gives more weight to signals with higher gain and lower variability, effectively implementing a reliability-weighted average without requiring individual neurons to explicitly calculate weights.)

This doesn't imply that science is devoid of knowledge. We can evaluate the reasonableness of our prior assumptions by assessing them against others' and seeing if our conclusions hold up with different starting assumptions. Finally, Chivers argues that using Bayesian models in the brain also explains consciousness. Our experiences in life are shaped by our expectations of it, our pre-existing Bayesian assumptions. Our awareness is a representation of reality rather than reality itself. What we perceive consists of our predictions. The brain's primary motivation is to reduce errors in its predictions. All our desires and necessities can be seen as an effort to lessen the gap between our expectations and our sensory information. This constitutes life's essential motivating force. All living beings aim to lessen the gap between their expectations and their actual experiences.

The Bayesian Brain Hypothesis and Consciousness

Psychologists Jeffrey S. Bowers and Colin J. Davis argue that the Bayesian brain hypothesis, which suggests that the brain operates as a Bayesian inference machine, is not sufficient to explain consciousness. They contend that while Bayesian models can describe how the brain processes information and updates beliefs based on new evidence, they do not address the subjective experience of consciousness itself. They argue that Bayesian models are often too flexible and can be adjusted to fit any data, making them difficult to falsify. Additionally, they point out that Bayesian models do not explain how the brain generates conscious experiences or why certain neural processes are associated with consciousness. They also challenge the idea that all desires and necessities in living beings can be explained by reducing the gap between expectations and sensory information.