相关论文: A relation between log-likelihood and cross-valida…

We describe a fast computation method for leave-one-out cross-validation (LOOCV) for $k$-nearest neighbours ($k$-NN) regression. We show that, under a tie-breaking condition for nearest neighbours, the LOOCV estimate of the mean square…

Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…

As a convention, p-value is often computed in frequentist hypothesis testing and compared with the nominal significance level of 0.05 to determine whether or not to reject the null hypothesis. The smaller the p-value, the more significant…

A method is introduced for the verification of nonclassicality in terms of moments of nonclassicality quasiprobability distributions. The latter are easily obtained from experimental data and will be denoted as nonclassicality moments.…

How predictable a word is can be quantified in two ways: using human responses to the cloze task or using probabilities from language models (LMs).When used as predictors of processing effort, LM probabilities outperform probabilities…

Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…

We discuss a general definition of likelihood function in terms of Radon-Nikod\'{y}m derivatives. The definition is validated by the Likelihood Principle once we establish a result regarding the proportionality of likelihood functions under…

The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…

A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…

Process mining is a scientific discipline that analyzes event data, often collected in databases called event logs. Recently, uncertain event logs have become of interest, which contain non-deterministic and stochastic event attributes that…

Reliability is an essential measure of how closely observed scores represent latent scores (reflecting constructs), assuming some latent variable measurement model. We present a general theoretical framework of reliability, placing emphasis…

Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the…

A profile likelihood ratio test is proposed for inferences on the index coefficients in generalized single-index models. Key features include its simplicity in implementation, invariance against parametrization, and exhibiting substantially…

We present a method for estimating the correlation between log-rank test statistics evaluating separate null hypotheses for two time-to-event endpoints. The correlation is estimated using subject-level data by a non-parametric approach…

We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a…

Likelihood-based methods of statistical inference provide a useful general methodology that is appealing, as a straightforward asymptotic theory can be applied for their implementation. It is important to assess the relationships between…

Many clustering methods, including k-means, require the user to specify the number of clusters as an input parameter. A variety of methods have been devised to choose the number of clusters automatically, but they often rely on strong…

The combined universal probability $\mathbf{m}(D)$ of strings $x$ in sets $D$ is close to max $\mathbf{m}(x)$ over $x$ in $D$: their logs differ by at most $D$'s information $\mathbf{I}(D:\mathcal{H})$ about the halting sequence…

The combination of evidence in Dempster-Shafer theory is compared with the combination of evidence in probabilistic logic. Sufficient conditions are stated for these two methods to agree. It is then shown that these conditions are minimal…

Nonprobability (convenience) samples are increasingly sought to stabilize estimations for one or more population variables of interest that are performed using a randomized survey (reference) sample by increasing the effective sample size.…