相关论文: Theorems on the Geometric Definition of the Positi…
The relationship between a screening tests' positive predictive value, $\rho$, and its target prevalence, $\phi$, is proportional - though not linear in all but a special case. In consequence, there is a point of local extrema of curvature…
Bayes' Theorem imposes inevitable limitations on the accuracy of screening tests by tying the test's predictive value to the disease prevalence. The aforementioned limitation is independent of the adequacy and make-up of the test and thus…
Using Bayes' Theorem, we derive generalized equations to determine the positive and negative predictive value of screening tests undertaken sequentially. Where a is the sensitivity, b is the specificity, $\phi$ is the pre-test probability,…
In previous work by this author, the screening paradox - the loss of predictive power of screening tests over time $t$ - was mathematically formalized using Bayesian theory. Where $J$ is Youden's statistic, $b$ is the specificity of the…
Positive and negative likelihood ratios are parameters which are used to assess and compare the effectiveness of binary diagnostic tests. Both parameters only depend on the sensitivity and specificity of the diagnostic test and are…
Bayes' Theorem confers inherent limitations on the accuracy of screening tests as a function of disease prevalence. We have shown in previous work that a testing system can tolerate significant drops in prevalence, up until a certain…
A polynomial that is nonnegative over a given interval is called a positive polynomial. The set of such positive polynomials forms a closed convex cone $K$. In this paper, we consider the likelihood ratio test for the hypothesis of…
The accuracy of binary classification systems is defined as the proportion of correct predictions - both positive and negative - made by a classification model or computational algorithm. A value between 0 (no accuracy) and 1 (perfect…
In the simple vs composite hypothesis test with a proper prior, the Bayes Factor (BF) is shown to be the posterior mean of the Likelihood Ratio (LR). Therefore, the posterior standard deviation of the LR or rather its posterior cumulative…
When presenting forensic evidence, such as a DNA match, experts often use the Likelihood ratio (LR) to explain the impact of evidence . The LR measures the probative value of the evidence with respect to a single hypothesis such as 'DNA…
In this manuscript, we present various proposed methods estimate the prevalence of disease, a critical prerequisite for the adequate interpretation of screening tests. To address the limitations of these approaches, which revolve primarily…
Plausibility is a formalization of exact tests for parametric models and generalizes procedures such as Fisher's exact test. The resulting tests are based on cumulative probabilities of the probability density function and evaluate…
We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…
Scientists often use a paired comparison of the areas under the receiver operating characteristic curves to decide which continuous cancer screening test has the best diagnostic accuracy. In the paired design, all participants are screened…
Positive predictive value and negative predictive value are two widely used parameters to assess the clinical usefulness of a medical diagnostic test. When there are two diagnostic tests, it is recommendable to make a comparative assessment…
A factor model with a break in its factor loadings is observationally equivalent to a model without changes in the loadings but a change in the variance of its factors. This effectively transforms a structural change problem of high…
We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…
We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically…
We study a variant of quantum hypothesis testing wherein an additional 'inconclusive' measurement outcome is added, allowing one to abstain from attempting to discriminate the hypotheses. The error probabilities are then conditioned on a…
Background: Pleuroparenchymal fibroelastosis (PPFE) is an upper lobe predominant fibrotic lung abnormality associated with increased mortality in established interstitial lung disease. However, the clinical significance of radiologic PPFE…