Related papers: Multivariate Confidence Intervals
We provide the asymptotic distribution of the major indexes used in the statistical literature to quantify disparate treatment in machine learning. We aim at promoting the use of confidence intervals when testing the so-called group…
A fundamental class of inferential problems are those characterised by there having been a substantial degree of pre-data (or prior) belief that the value of a model parameter was equal or lay close to a specified value, which may, for…
The goal of any estimation study is an interval estimation of a the parameter(s) of interest. These estimations are mostly expressed using empirical confidence intervals that are based on sample point estimates of the corresponding…
Though the mediums for visualization are limited, the potential dimensions of a dataset are not. In many areas of scientific study, understanding the correlations between those dimensions and their uncertainties is pivotal to mining useful…
We define interval spacing as the difference in the order statistics of data over a gap of some width. We derive its density, expected value, and variance for uniform, exponential, and logistic variates. We show that interval spacing is…
Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables…
The notion of p-value is a fundamental concept in statistical inference and has been widely used for reporting outcomes of hypothesis tests. However, p-value is often misinterpreted, misused or miscommunicated in practice. Part of the issue…
Confidence estimation, a task that aims to evaluate the trustworthiness of the model's prediction output during deployment, has received lots of research attention recently, due to its importance for the safe deployment of deep models.…
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…
Portnoy (2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation $\, X \sim {\cal{N}}(\mu , \, \sigma^2) \,$. Here we extend this result to obtaining 1-sample confidence…
Measurements are generally collected as unilateral or bilateral data in clinical trials or observational studies. For example, in ophthalmology studies, the primary outcome is often obtained from one eye or both eyes of an individual. In…
In many fields of research null hypothesis significance tests and p values are the accepted way of assessing the degree of certainty with which research results can be extrapolated beyond the sample studied. However, there are very serious…
Quantile regression has been successfully used to study heterogeneous and heavy-tailed data. Varying-coefficient models are frequently used to capture changes in the effect of input variables on the response as a function of an index or…
A key obstacle in automated analytics and meta-learning is the inability to recognize when different datasets contain measurements of the same variable. Because provided attribute labels are often uninformative in practice, this task may be…
In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…
Well-recommended methods of forming `confidence intervals' for a binomial proportion give interval estimates that do not actually meet the definition of a confidence interval, in that their coverages are sometimes lower than the nominal…
In data mining, when binary prediction rules are used to predict a binary outcome, many performance measures are used in a vast array of literature for the purposes of evaluation and comparison. Some examples include classification…
A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…
The notion of data depth has long been in use to obtain robust location and scale estimates in a multivariate setting. The depth of an observation is a measure of its centrality, with respect to a data set or a distribution. The data depths…
Consider panel data modelled by a linear random intercept model that includes a time-varying covariate. Suppose that we have uncertain prior information that this covariate is exogenous. We present a new confidence interval for the slope…