Related papers: Bayesian Updating and Sequential Testing: Overcomi…
Binary observations are often repeated to improve data quality, creating technical replicates. Several scoring methods are commonly used to infer the actual individual state and obtain a probability for each state. The common practice of…
We define the information threshold as the point of maximum curvature in the prior vs. posterior Bayesian curve, both of which are described as a function of the true positive and negative rates of the classification system in question. The…
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…
Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…
Measuring neutron star radii with spectroscopic and timing techniques relies on the combination of multiple observables to break the degeneracies between the mass and radius introduced by general relativistic effects. Here, we explore a…
Sequential change diagnosis is the joint problem of detection and identification of a sudden and unobservable change in the distribution of a random sequence. In this problem, the common probability law of a sequence of i.i.d. random…
When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…
We investigate the discrimination of two candidates of an unknown parameter in quantum systems with continuous weak measurement, inspired by the application of hypothesis testing in distinguish-ing two Hamiltonians [Kiilerich and M{\o}lmer,…
In this paper we consider the problem of binary hypothesis testing with finite memory systems. Let $X_1,X_2,\ldots$ be a sequence of independent identically distributed Bernoulli random variables, with expectation $p$ under $\mathcal{H}_0$…
Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a…
The ratio of Bayesian evidences is a popular tool in cosmology to compare different models. There are however several issues with this method: Bayes' ratio depends on the prior even in the limit of non-informative priors, and Jeffrey's…
Inferences about hypotheses are ubiquitous in the cognitive sciences. Bayes factors provide one general way to compare different hypotheses by their compatibility with the observed data. Those quantifications can then also be used to choose…
The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…
Consider the following Stochastic Score Classification Problem. A doctor is assessing a patient's risk of developing a certain disease, and can perform $n$ tests on the patient. Each test has a binary outcome, positive or negative. A…
This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…
Major advances in public health have resulted from disease prevention. However, prevention of a new infectious disease by vaccination or pharmaceuticals is made difficult by the slow process of vaccine and drug development. We propose an…
We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector…
We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…