Related papers: Testing for dice control at craps
Gambits are central to human decision-making. Our goal is to provide a theory of Gambits. A Gambit is a combination of psychological and technical factors designed to disrupt predictable play. Chess provides an environment to study gambits…
Two possibly unfair $n$-sided dice, both labelled $1, 2, \ldots, n$, are rolled, and the sum is recorded. How should the dice's sides be weighted so that the resulting sum is closest to the uniform distribution on $2, 3, \ldots, 2n$? We…
The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…
The traditional approaches to false discovery rate (FDR) control in multiple hypothesis testing are usually based on the null distribution of a test statistic. However, all types of null distributions, including the theoretical,…
Given a controlled diffusion and a connected, bounded, Lipschitz set, when is it possible to guarantee controlled set invariance with probability one? In this work, we answer this question by deriving the necessary and sufficient conditions…
Knockoffs are a popular statistical framework that addresses the challenging problem of conditional variable selection in high-dimensional settings with statistical control. Such statistical control is essential for the reliability of…
In 1970, Statistics giant, Bradley Efron, amazed the world by coming up with a set of four dice, let's call them A,B,C,D, whose faces are marked with [0,0,4,4,4,4], [3,3,3,3,3,3],[2,2,2,2,6,6],[1,1,1,5,5,5] respectively, where die A beats…
When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability's fundamental principle for testing by betting says yes, provided…
We study the problem of controlling a general complex network towards an assigned synchronous evolution, by means of a pinning control strategy. We define the pinning-controllability of the network in terms of the spectral properties of an…
Suppose we have $n$ dice, each with $s$ faces (assume $s\geq n$). On the first turn, roll all of them, and remove from play those that rolled an $n$. Roll all of the remaining dice. In general, if at a certain turn you are left with $k$…
Consider the following experiment: a deck with $m$ copies of $n$ different card types is randomly shuffled, and a guesser attempts to guess the cards sequentially as they are drawn. Each time a guess is made, some amount of "feedback" is…
The problem of testing mutually exclusive hypotheses with dependent test statistics is considered. Bayesian and frequentist approaches to multiplicity control are studied and compared to help gain understanding as to the effect of test…
The problem of stock hedging is reconsidered in this paper, where a put option is chosen from a set of available put options to hedge the market risk of a stock. A formula is proposed to determine the probability that the potential loss…
The score test statistic using the observed information is easy to compute numerically. Its large sample distribution under the null hypothesis is well known and is equivalent to that of the score test based on the expected information, the…
We consider a stochastic impulse control problem that is motivated by applications such as the optimal exploitation of a natural resource. In particular, we consider a stochastic system whose uncontrolled state dynamics are modelled by a…
This note is addressed to giving a short introduction to control theory of stochastic systems, governed by stochastic differential equations in both finite and infinite dimensions. We will mainly explain the new phenomenon and difficulties…
Controlling a complex network is of great importance in many applications. The network can be controlled by inputting external control signals through some selected nodes, which are called input nodes. Previous works found that the majority…
The limit of a sequence by the definition with $\varepsilon$ is introduced by the notion of checkmate in two moves. The idea is also extended to define the limit of a function with $\varepsilon$ and $\delta$.
Testing for association or dependence between pairs of random variables is a fundamental problem in statistics. In some applications, data are subject to selection bias that causes dependence between observations even when it is absent from…
We consider statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses, under the assumption that a suitable single test (and corresponding $p$-value) is known for each…