Related papers: Using Random Variables to Predict Experimental Out…
Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in…
We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis,'' randomization…
Probabilistic metrology attempts to improve parameter estimation by occasionally reporting an excellent estimate and the rest of the time either guessing or doing nothing at all. Here we show that probabilistic metrology can never improve…
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…
Elections involving a very large voter population often lead to outcomes that surprise many. This is particularly important for the elections in which results affect the economy of a sizable population. A better prediction of the true…
This paper introduces an open-ended sequential algorithm for computing the p-value of a test using Monte Carlo simulation. It guarantees that the resampling risk, the probability of a different decision than the one based on the theoretical…
How should social scientists understand and communicate the uncertainty of statistically estimated causal effects? I propose we utilize the posterior distribution of a causal effect and present the probability of the effect being greater…
The Poisson probability distribution is frequently encountered in physical science measurements. In spite of the simplicity and familiarity of this distribution, there is considerable confusion among physicists concerning the description of…
Given independent random variables $Y_1, \ldots, Y_n$ with $Y_i \in \{0,1\}$ we test the hypothesis whether the underlying success probabilities $p_i$ are constant or whether they are periodic with an unspecified period length of $r \ge 2$.…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
It is widely acknowledged that the biomedical literature suffer from a surfeit of false positive results. Part of the reason for this is the persistence of the myth that observation of a p value less than 0.05 is sufficient justification to…
We generalise the randomness test definitions in the literature for both the Martin-L\"of and Schnorr randomness of a series of binary outcomes, in order to allow for interval-valued rather than merely precise forecasts for these outcomes,…
Likelihood methods for measuring statistical evidence obey the likelihood principle while maintaining bounded and well-controlled frequency properties. These methods lend themselves to sequential study designs because they measure the…
Randomness is a central concept to statistics and physics. Here, a statistical analysis shows experimental evidence that tossing coins and finding last digits of prime numbers are identical regarding statistics for equally likely outcomes.…
For n>=1 let X_n be a vector of n independent Bernoulli random variables. We assume that X_n consists of M "blocks" such that the Bernoulli random variables in block i have success probability p_i. Here M does not depend on n and the size…
We consider the classical last-success problem for sequential Bernoulli trials in the homogeneous setting where $X_1,\ldots,X_n$ are i.i.d. $\mathrm{Bernoulli}(p)$ but the success probability $p\in(0,1)$ is unknown to the decision maker.…
Let $(X_1,X_2,...)$ be a random partition of the unit interval $[0,1]$, i.e. $X_i\geq0$ and $\sum_{i\geq1} X_i=1$, and let $(\varepsilon_1,\varepsilon_2,...)$ be i.i.d. Bernoulli random variables of parameter $p \in (0,1)$. The Bernoulli…
We treat success runs of independent identically distributed Bernoulli trials (with success parameter $p$) distributed according to the Type II binomial distribution of order $k$. However, the success runs are separated by a gap $g\ge1$ (a…
Statistical prediction plays an important role in many decision processes such as university budgeting (depending on the number of students who will enroll), capital budgeting (depending on the remaining lifetime of a fleet of systems), the…
In algorithmic randomness, when one wants to define a randomness notion with respect to some non-computable measure $\lambda $, a choice needs to be made. One approach is to allow randomness tests to access the measure $\lambda $ as an…