Suppose we observe many emeralds which are all green. This observation usually provides good evidence that all emeralds are green. However, the emeralds we have observed are also all grue, which means that they are either green and already observed or blue and not yet observed. We usually do not think that our observation provides good evidence that all emeralds are grue. Why? I argue that if we are in the best case for inductive reasoning, we have reason to assign (...) low probability to the hypothesis that all emeralds are grue before seeing any evidence. My argument appeals to random sampling and the observation-independence of green, understood as probabilistic independence of whether emeralds are green and when they are observed. (shrink)

Suppose we observe many emeralds which are all green. This observation usually provides good evidence that all emeralds are green. However, the emeralds we have observed are also all grue, which means that they are either green and already observed or blue and not yet observed. We usually do not think that our observation provides good evidence that all emeralds are grue. Why? I argue that if we are in the best case for inductive reasoning, we have reason to assign (...) low probability to the hypothesis that all emeralds are grue before seeing any evidence. My argument appeals to random sampling and the observation-independence of green, understood as probabilistic independence of whether emeralds are green and when they are observed. (shrink)

My dissertation is about Bayesian rationality for non-ideal agents. I show how to derive subjective probabilities from preferences using much weaker rationality assumptions than other standard representation theorems. I argue that non-ideal agents might be uncertain about how they will update on new information and consider two consequences of this uncertainty: such agents should sometimes reject free information and make choices which, taken together, yield sure loss. The upshot is that Bayesian rationality for non-ideal agents makes very different normative demands (...) than ideal Bayesian rationality. (shrink)

Developing new ways to estimate probabilities can be valuable for science, statistics, engineering, and other fields. By considering the information content of different output patterns, recent work invoking algorithmic information theory inspired arguments has shown that a priori probability predictions based on pattern complexities can be made in a broad class of input-output maps. These algorithmic probability predictions do not depend on a detailed knowledge of how output patterns were produced, or historical statistical data. Although quantitatively fairly accurate, a main (...) weakness of these predictions is that they are given as an upper bound on the probability of a pattern, but many low complexity, low probability patterns occur, for which the upper bound has little predictive value. Here, we study this low complexity, low probability phenomenon by looking at example maps, namely a finite state transducer, natural time series data, RNA molecule structures, and polynomial curves. Some mechanisms causing low complexity, low probability behaviour are identified, and we argue this behaviour should be assumed as a default in the real-world algorithmic probability studies. Additionally, we examine some applications of algorithmic probability and discuss some implications of low complexity, low probability patterns for several research areas including simplicity in physics and biology, a priori probability predictions, Solomonoff induction and Occam’s razor, machine learning, and password guessing. (shrink)