Parton distributions with LHC data

In coming to understand the world-in learning concepts, acquiring language, and grasping causal relations-our minds make inferences that appear to go far beyond the data available. How do we do it? This review describes recent approaches to reverse-engineering human learning and cognitive development and, in parallel, engineering more humanlike machine learning systems. Computational models that perform probabilistic inference over hierarchies of flexibly structured representations can address some of the deepest questions about the nature and origins of human thought: How does abstract knowledge guide learning and reasoning from sparse data? What forms does our knowledge take, across different domains and tasks? And how is that abstract knowledge itself acquired?

/pdf/how-to-grow-a-mind-statistics-structure-and-abstraction-21o338o2i1.pdf

How to Grow a Mind: Statistics, Structure, and Abstraction

The degree of confidence in a decision provides a graded and probabilistic assessment of expected outcome. Although neural mechanisms of perceptual decisions have been studied extensively in primates, little is known about the mechanisms underlying choice certainty. We have shown that the same neurons that represent formation of a decision encode certainty about the decision. Rhesus monkeys made decisions about the direction of moving random dots, spanning a range of difficulties. They were rewarded for correct decisions. On some trials, after viewing the stimulus, the monkeys could opt out of the direction decision for a small but certain reward. Monkeys exercised this option in a manner that revealed their degree of certainty. Neurons in parietal cortex represented formation of the direction decision and the degree of certainty underlying the decision to opt out.

/pdf/representation-of-confidence-associated-with-a-decision-by-3ly6oggi94.pdf

Representation of Confidence Associated with a Decision by Neurons in the Parietal Cortex

LSST Science Book, Version 2.0

Does psi exist? D. J. Bem (2011) conducted 9 studies with over 1,000 participants in an attempt to demonstrate that future events retroactively affect people’s responses. Here we discuss several limitations of Bem’s experiments on psi; in particular, we show that the data analysis was partly exploratory and that one-sided p values may overstate the statistical evidence against the null hypothesis. We reanalyze Bem’s data with a default Bayesian t test and show that the evidence for psi is weak to nonexistent. We argue that in order to convince a skeptical audience of a controversial claim, one needs to conduct strictly confirmatory studies and analyze the results with statistical tests that are conservative rather than liberal. We conclude that Bem’s p values do not indicate evidence in favor of precognition; instead, they indicate that experimental psychologists need to change the way they conduct their experiments and analyze their data.

/pdf/why-psychologists-must-change-the-way-they-analyze-their-22b8wvn2na.pdf

Why psychologists must change the way they analyze their data: the case of psi: comment on Bem (2011).

This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. Now results are discussed, along with the application of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book is not restricted to one particular discipline but rather will be of interest to scientists working in any area where inference from incomplete information is necessary.

/pdf/probability-theory-the-logic-of-science-47cb0ykp0x.pdf

Ralph Baierlein

Papers

Probability Theory: The Logic of Science

Meeting Them on Their Own Ground