The standard Bayesian story goes something like this: probabilities represent a rational agent's degrees of belief. When the agent learns something new she conditions on it, meaning that she updates her probabilities according to Bayes' rule. Importantly, the interpretation of the probability function is that it represents the agent's degrees of belief about how likely… Continue reading Paper Review: New Semantics for Bayesian Inference: The Interpretive Problem
Can one rationally choose to have a child?
Is it rational for me to want to have a child if I cannot know what it will be like to have a child? Laurie Paul, in her book Transformative Experience, argues that this question poses a significant problem for traditional theories of decision-making. Paul holds that many major life decisions are ones in which… Continue reading Can one rationally choose to have a child?
Paper Review: Subjective Probability and the Theory of Games: Comments on Kadane and Larkey’s Paper
Last week I reviewed Kadane and Larkey's paper. In short, the main claim of their paper was that since the solution concepts used in game theory do not depend on the beliefs of the players they are irrelevant to game theory. Haranyi wrote a response to this paper, which it what I will review today.… Continue reading Paper Review: Subjective Probability and the Theory of Games: Comments on Kadane and Larkey’s Paper
Paper Review: Subjective Probability and the Theory of Games
Game theory is the study of the strategic interaction of rational agents. Decision theory is the study of the decision making of a rational agent. Clearly there is something similar about these two fields. What, exactly, is the relationship though? Do they study different aspects of rational action, or do they overlap? If they overlap,… Continue reading Paper Review: Subjective Probability and the Theory of Games
Paper Review: Philosophy and the practice of Bayesian statistics
One of the more interesting things I've learned in my life is that our best account of epistemology is that rational beliefs are governed by the probability axioms. Furthermore, there is a specific way in a rational agent updates her beliefs given new evidence---Bayesian conditionalization. Of course there is disagreement on this. At this point… Continue reading Paper Review: Philosophy and the practice of Bayesian statistics
Paper Review: Objective versus Subjective Probability
Hugh Everett III proposed his many worlds (or as he preferred to call it, relative state) formulation of quantum mechanics back in the mid 50s in order to solve the quantum measurement problem. Although it took a while for the theory to gain traction, it (or some form of it) is one of the more… Continue reading Paper Review: Objective versus Subjective Probability
Paper Review: Contribution to discussion on Probability
Probability can seem like a slippery notion. Indeed, though we have an intuitive notion of various aspects of probability, it took a long time for humanity to develop a rigorous formal theory. And even with the mathematics of probability on surer footing, the interpretation of probability -- what does it mean -- is still plagued… Continue reading Paper Review: Contribution to discussion on Probability
Paper Review: Agreeing to Disagree
Can two rational people agree to disagree? This question seems really important to me. When having a conversation with a friend, for example, if we are both good-faith rational actors who are engaged in a collective truth-seeking endeavor (as is my hope!), is it possible that we can agree to disagree? Of course, in the… Continue reading Paper Review: Agreeing to Disagree
Paper Review: Difficulties in the Theory of Personal Probability
Readers of the blog will know that I am a fan of the Bayesian approach to probability. This approach is also sometimes called "personal probability", because it takes probabilities to be the degrees of belief (or credences) of rational agents. We can think of using probability like this as a framework for managing uncertainty in… Continue reading Paper Review: Difficulties in the Theory of Personal Probability
Paper Review: Why Conditionalize?
How should we change our beliefs in the light of new information? This is one of the central questions of epistemology, and has great practical importance. For example, consider a doctor who has a patient who is concerned he might have cancer. The doctor has certain beliefs: for example, she may think that her patient… Continue reading Paper Review: Why Conditionalize?