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A fundamental question in causal inference is whether it is possible to reliably infer manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most…
Observational data is increasingly used as a means for making individual-level causal predictions and intervention recommendations. The foremost challenge of causal inference from observational data is hidden confounding, whose presence…
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines…
The means by which cortical neural networks are able to efficiently solve inference problems remains an open question in computational neuroscience. Recently, abstract models of Bayesian computation in neural circuits have been proposed,…
In an effort to simplify the complexity in the studies of consciousness, the author suggests to divide the conscious experiences into a fundamental state, the intrinsic awareness (IA), and functions of this fundamental state. IA does not…
Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
The majority of the statisticians concluded many decades ago that fiducial inference was nonsensical to them. Hannig et al. (2016) and others have, however, contributed to a renewed interest and focus. Fiducial inference is similar to…
Various brain functions that are necessary to maintain life activities materialize through the interaction of countless neurons. Therefore, it is important to analyze functional neuronal network. To elucidate the mechanism of brain…
The science of consciousness has been successful over the last decades. Yet, it seems that some of the key questions remain unanswered. Perhaps, as a science of consciousness, we cannot move forward using the same theoretical commitments…
We argue that for the proof of Bell's theorem no assumptions about realism or free will are necessary. The key formula \[E(AB|a,b) = \int A(a,b,\lambda)B(a,b,\lambda)\rho(\lambda) d\lambda\] follows from the logic of plausible reasoning…
Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…
Large Language Models (LLMs) have transformed natural language processing and hold growing promise for advancing science, healthcare, and decision-making. Yet their training paradigms remain dominated by affirmation-based inference, akin to…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
Can AI systems like large language models (LLMs) replace human participants in behavioral and psychological research? Here I critically evaluate the "replacement" perspective and identify six interpretive fallacies that undermine its…
Functional data often arise as sequential temporal observations over a continuous state-space. A set of functional data with a possible change in its structure may lead to a wrong conclusion if it is not taken in to account. So, sometimes,…
A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the…
In reinforcement learning (RL), agents often operate in partially observed and uncertain environments. Model-based RL suggests that this is best achieved by learning and exploiting a probabilistic model of the world. 'Active inference' is…
Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…
The currently dominating artificial intelligence and machine learning technology, neural networks, builds on inductive statistical learning. Neural networks of today are information processing systems void of understanding and reasoning…