Related papers: Why do we change whatever amount we found in the f…
The literature on "mechanism design from samples," which has flourished in recent years at the interface of economics and computer science, offers a bridge between the classic computer-science approach of worst-case analysis (corresponding…
In the absence of empirical confirmation, scientists may judge a theory's chances of being viable based on a wide range of arguments. The paper argues that such arguments can differ substantially with regard to their structural similarly to…
The data supporting neutrino oscillations are reexamined empirically, ignoring the phase space of the usual theory. An absolutely minimum description can be constructed easily without assuming oscillations. An empirical fit to a simplified…
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…
Explanations of Machine Learning (ML) models often address a 'Why?' question. Such explanations can be related with selecting feature-value pairs which are sufficient for the prediction. Recent work has investigated explanations that…
Following Fisher, it is widely believed that randomization "relieves the experimenter from the anxiety of considering innumerable causes by which the data may be disturbed." In particular, it is said to control for known and unknown…
Given a dollar, how many ways are there to make change using pennies, nickels, dimes, and quarters? What if you are given a different amount of money? What if you use different coin denominations? This is a well known problem and formulas…
There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured.…
We investigate how robust the results of committee elections are to small changes in the input preference orders, depending on the voting rules used. We find that for typical rules the effect of making a single swap of adjacent candidates…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
The problem of combining p-values is an old and fundamental one, and the classic assumption of independence is often violated or unverifiable in many applications. There are many well-known rules that can combine a set of arbitrarily…
We introduce a framework uniting algorithmic randomness with exchangeable credences to address foundational questions in philosophy of probability and philosophy of science. To demonstrate its power, we show how one might use the framework…
We consider the urn setting with two different objects, ``good'' and ``bad'', and analyze the number of draws without replacement until a good object is picked. Although the expected number of draws for this setting is a standard textbook…
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
We introduce uncertainty into a pure exchange economy and establish a connection between Shannon's differential entropy and uniqueness of price equilibria. The following conjecture is proposed under the assumption of a uniform probability…
Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…
This paper is about the Coupon collector's problem. There are some coupons, or baseball cards, or other plastic knick-knacks that are put into bags of chips or under soda bottles, etc. A collector starts collecting these trinkets and wants…
We introduce the dependent doors problem as an abstraction for situations in which one must perform a sequence of possibly dependent decisions, without receiving feedback information on the effectiveness of previously made actions.…
The role of an expert in the decision-making process is crucial, as the final recommendation depends on his disposition, clarity of mind, experience, and knowledge of the problem. However, the recommendation also depends on their honesty.…
We investigate the potential of deliberation to create consensus among fully-informed citizens. Our approach relies on two cognitive assumptions: i. citizens need a thinking frame (or perspective) to consider an issue; and ii. citizens…