25 papers · ranked by Valyu relevance
Michael J. Lew
The likelihood principle makes strong claims about the nature of statistical evidence but is controversial. Its claims are undermined by the existence of several examples that are assumed to show that it allows, with unity probability, domination of all other hypotheses by the uninteresting, determinist hypothesis that…
Leena Choi, Jeffrey D. Blume, William D. Dupont, Jake Olivier
To many, the foundations of statistical inference are cryptic and irrelevant to routine statistical practice. The analysis of 2 x 2 contingency tables, omnipresent in the scientific literature, is a case in point. Fisher's exact test is routinely used even though it has been fraught with controversy for over 70 years.…
Farrokh Habibzadeh, Parham Habibzadeh
Diagnostic tests are important clinical tools. Bayes’ theorem and Bayesian approach are important methods for interpreting test results. The Bayesian factor, the so-called likelihood ratio, has not always been well-understood. In this article, we try to discuss the likelihood ratio and its value for a specific test…
Paul-André Monney
Several authors have explained that the likelihood ratio measures the strength of the evidence represented by observations in statistical problems. This idea works fine when the goal is to evaluate the strength of the available evidence for a simple hypothesis versus another simple hypothesis. However, the…
André Chalom, Paulo Inácio Prado
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but they can be seen as fitting pieces of the same puzzle. In particular, analytical…
Lee, Youngjo, Pawitan, Yudi
The role of probability appears unchallenged as the key measure of uncertainty, used among other things for practical induction in the empirical sciences. Yet, Popper was emphatic in his rejection of inductive probability and of the logical probability of hypotheses; furthermore, for him, the degree of corroboration…
Oliver J. Maclaren
Profile likelihood is the key tool for dealing with nuisance parameters in likelihood theory. It is often asserted, however, that profile likelihood is not a 'true' likelihood. One implication is that likelihood theory lacks the generality of e.g. Bayesian inference, wherein marginalization is the universal tool for…
Casey Helgeson, Richard Bradley, Brian Hill
Reports of the Intergovernmental Panel on Climate Change (IPCC) employ an evolving framework of calibrated language for assessing and communicating degrees of certainty in findings. A persistent challenge for this framework has been ambiguity in the relationship between multiple degree-of-certainty metrics. We aim to…
Moritz Ingendahl, Johanna Woitzel, Hans Alves
Recent work shows that people judge an outcome as less likely when they learn the probabilities of all single pathways that lead to that outcome, a phenomenon termed the Unlikelihood Effect. The initial explanation for this effect is that the low pathway probabilities trigger thoughts that deem the outcome unlikely. We…
Van N. T. La, Stanley Nicholson, Amna Haneef, Lulu Kang + 1 more
Some data are just underappreciated. Maybe they look different or come from a different background than most other data. Maybe they don't fit neatly into common notions of what data on a ``curve'' should look like. Whatever the case, they are pigeonholed into a restricted role that limits their contributions. But if…
Authors not listed
Knowledge of the reaction rate constants can be vital in understanding electrochemical reaction mechanisms and their rate-determining processes. Although first-principles methods, such as density functional theory (DFT), provide valuable insight into reaction free energies and rate constants, they commonly use…
Daniel J. M. Crouch
A P value is conventionally interpreted either as a) the probability by chance of obtaining more extreme results than those observed or b) a tool for declaring significance at a prespecified level. Both approaches carry difficulties: b) does not allow users to make inferences based on the data in hand, and is not…
Phan H. Giang, Prakash P. Shenoy
This paper presents a decision-theoretic approach to statistical inference that satisfies the Likelihood Principle (LP) without using prior information. Unlike the Bayesian approach, which also satisfies LP, we do not assume knowledge of the prior distribution of the unknown parameter. With respect to information that…
David Heckerman
In the 1940's, a physicist named Cox provided the fir�t formal justification for the axioms of probability based on the subjective or Bayesian interpretation. He showed that if a measure of belief satisfies several fundamental properties, then the measure must be some monotonic transformation of a probability. In this…
Martin Smith
The paper is concerned with a special class of inferences, in which we draw conclusions about individual people based on evidence about the groups to which they belong. One thing that is notable about these inferences is that they are often subject to a kind of moral criticism. By judging people in this way, it is…
A. Banerjee, S. L. Jadhav, J. S. Bhawalkar
Few clinicians grasp the true concept of probability expressed in the ‘P value.’ For most, a statistically significant P value is the end of the search for truth. In fact, the opposite is the case. The present paper attempts to put the P value in proper perspective by explaining different types of probabilities, their…
Huw Llewelyn, William Speier
The prior probabilities of true outcomes for scientific replication have to be uniform by definition. This is because for replication, a study’s observations are regarded as samples taken from the set of possible outcomes of an ideally large continuation of that study. (The sampling is not done directly from some…
Wei-Hsiang Lin, Justin L. Gardner, Shih-Wei Wu
Many decisions rely on how we evaluate potential outcomes associated with the options under consideration and estimate their corresponding probabilities of occurrence. Outcome valuation is subjective as it requires consulting internal preferences and is sensitive to context. In contrast, probability estimation requires…
Jürgen Köfinger, Gerhard Hummer
The proper balancing of information from experiment and theory is a long-standing problem in the analysis of noisy and incomplete data. Viewed as a Pareto optimization problem, improved agreement with the experimental data comes at the expense of growing inconsistencies with the theoretical reference model. Here, we…
Balázs Hangya, Joshua I. Sanders, Adam Kepecs
Decision confidence is a forecast about the probability that a decision will be correct. For human decision makers, confidence is a deeply subjective sense that can be difficult to study due to its inherently introspective nature. However, confidence can be framed as an objective mathematical quantity – the Bayesian…
Jürgen Köfinger, Gerhard Hummer
The proper balancing of information from experiment and theory is a long-standing problem in the analysis of noisy and incomplete data. Viewed as a Pareto optimization problem, improved agreement with the experimental data comes at the expense of growing inconsistencies with the theoretical reference model. Here, we…
Mattias Forsgren, Peter Juslin, Ronald van den Berg
Extensive research in the behavioural sciences has addressed people’s ability to learn stationary probabilities, which stay constant over time, but only recently have there been attempts to model the cognitive processes whereby people learn – and track – non-stationary probabilities. In this context, the old debate on…
Alexandra C. Gillett, Evangelos Vassos, Cathryn M. Lewis
Stratified medicine requires models of disease risk incorporating genetic and environmental factors. These may combine estimates from different studies and models must be easily updatable when new estimates become available. The logit scale is often used in genetic and environmental association studies however the…
Emilio Salinas, Terrence R Stanford
Intuitively, combining multiple sources of evidence should lead to more accurate decisions than considering single sources of evidence individually. In practice, however, the proper computation may be difficult, or may require additional data that are inaccessible. Here, based on the concept of conditional…
Maria H. Rasmussen, Chenru Duan, Heather J. Kulik, Jan Halborg Jensen
With the increasingly more important role of machine learning (ML) models in chemical research, the need for putting a level of confidence to the model predictions naturally arises. Several methods for obtaining uncertainty estimates have been proposed in recent years but consensus on the evaluation of these have yet…