Related papers: Bayesian Updating and Sequential Testing: Overcomi…
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…
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…
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…
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…
We identify the critical deviation scale governing Bayesian evidence accumulation in regular parametric testing. Under integrated Bayes risk with zero-one loss, the risk-optimal rejection boundary lies in a moderate deviation regime, with a…
Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…
In the last year more than 70,000 people have been brought to the UK hospitals with serious injuries. Each time a clinician has to urgently take a patient through a screening procedure to make a reliable decision on the trauma treatment.…
AB testing aids business operators with their decision making, and is considered the gold standard method for learning from data to improve digital user experiences. However, there is usually a gap between the requirements of practitioners,…
Sequential hypothesis testing asks for decision rules that update as data arrive. A natural goal is \emph{eventual correctness}: the rule may change its mind early on, but it should make only finitely many wrong decisions almost surely.…
In multiple testing scenarios, typically the sign of a parameter is inferred when its estimate exceeds some significance threshold in absolute value. Typically, the significance threshold is chosen to control the experimentwise type I error…
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…
Bayes factors for composite hypotheses have difficulty in encoding vague prior knowledge, as improper priors cannot be used and objective priors may be subjectively unreasonable. To address these issues I revisit the posterior Bayes factor,…
Sequential inspection is a technique employed to monitor product quality during the production process. For smaller batch sizes, the Acceptable Quality Limit(AQL) inspection theory is typically applied, whereas for larger batch sizes, the…
When the infection prevalence of a disease is low, Dorfman showed 80 years ago that testing groups of people can prove more efficient than testing people individually. Our goal in this paper is to propose new group testing algorithms that…
Datasets are rarely a realistic approximation of the target population. Say, prevalence is misrepresented, image quality is above clinical standards, etc. This mismatch is known as sampling bias. Sampling biases are a major hindrance for…
In many derivative-free optimization algorithms, a sufficient decrease condition decides whether to accept a trial step in each iteration. This condition typically requires that the potential objective function value decrease of the trial…
We consider the problem of computing reach-avoid probabilities for iterative predictions made with Bayesian neural network (BNN) models. Specifically, we leverage bound propagation techniques and backward recursion to compute lower bounds…
The Bayes Error Rate (BER) is the fundamental limit on the achievable generalizable classification accuracy of any machine learning model due to inherent uncertainty within the data. BER estimators offer insight into the difficulty of any…
We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…