Related papers: On the Probability of Immunity
The relationship between three probability distributions and their maximizable entropy forms is discussed without postulating entropy property. For this purpose, the entropy I is defined as a measure of uncertainty of the probability…
It is known that the hazard ratio lacks a useful causal interpretation. Even for data from a randomized controlled trial, the hazard ratio suffers from built-in selection bias as, over time, the individuals at risk in the exposed and…
Opinion formation in the population has attracted extensive research interest. Various models have been introduced and studied, including the ones with individuals' free will allowing them to change their opinions. Such models, however,…
This contribution to the debate on confidence limits focuses mostly on the case of measurements with `open likelihood', in the sense that it is defined in the text. I will show that, though a prior-free assessment of {\it confidence} is, in…
I propose novel partial identification bounds on infection prevalence from information on test rate and test yield. The approach utilizes user-specified bounds on (i) test accuracy and (ii) the extent to which tests are targeted, formalized…
Starting from considerations about meaning and subsequent use of asymmetric uncertainty intervals of experimental results, we review the issue of uncertainty propagation. We show that, using a probabilistic approach (the so-called Bayesian…
This paper develops upper and lower bounds for the probability of Boolean functions by treating multiple occurrences of variables as independent and assigning them new individual probabilities. We call this approach dissociation and give an…
We define the Probability of Tiered Benefit in scenarios with a binary exposure and an outcome that is either categorical with $K \geq 2$ ordered tiers or continuous partitioned by $K-1$ fixed thresholds into disjoint intervals. Similarly…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…
We introduce and study a model stemming from game theory for the spread of an epidemic throughout a given population. Each agent is allowed to choose an action whose value dictates to what extent they limit their social interactions, if at…
We provide novel bounds on average treatment effects (on the treated) that are valid under an unconfoundedness assumption. Our bounds are designed to be robust in challenging situations, for example, when the conditioning variables take on…
The topic of this paper is prevalence estimation from the perspective of active information. Prevalence among tested individuals has an upward bias under the assumption that individuals' willingness to be tested for the disease increases…
This paper is motivated by the questions of how to give the concept of probability an adequate real-world meaning, and how to explain a certain type of phenomenon that can be found, for instance, in Ellsberg's paradox. It attempts to answer…
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…
The test-negative design has become popular for evaluating the effectiveness of post-licensure vaccines using observational data. In addition to its logistical convenience on data collection, the design is also believed to control for the…
Unobserved confounders are a long-standing issue in causal inference using propensity score methods. This study proposed nonparametric indices to quantify the impact of unobserved confounders through pseudo-experiments with an application…
Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…
An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to…
This article extends the hypotheses assessment method to the case with two competing simple hypotheses. In doing so we further clarify the benefits that hypotheses assessments can bring to classical statistical analyses. Given that…