scholarly journals A Mathematical Framework for Statistical Decision Confidence

2016 ◽  
Vol 28 (9) ◽  
pp. 1840-1858 ◽  
Author(s):  
Balázs Hangya ◽  
Joshua I. Sanders ◽  
Adam Kepecs
Keyword(s):  
Bayesian Posterior Probability ◽  
Mathematical Framework ◽  
Statistical Decision ◽  
Decision Confidence ◽  
Statistical Framework ◽  
Neural Representations ◽  
Starting Point ◽  
Common Framework ◽  
Rigorous Treatment ◽  
Research Domains

Decision confidence is a forecast about the probability that a decision will be correct. From a statistical perspective, decision confidence can be defined as the Bayesian posterior probability that the chosen option is correct based on the evidence contributing to it. Here, we used this formal definition as a starting point to develop a normative statistical framework for decision confidence. Our goal was to make general predictions that do not depend on the structure of the noise or a specific algorithm for estimating confidence. We analytically proved several interrelations between statistical decision confidence and observable decision measures, such as evidence discriminability, choice, and accuracy. These interrelationships specify necessary signatures of decision confidence in terms of externally quantifiable variables that can be empirically tested. Our results lay the foundations for a mathematically rigorous treatment of decision confidence that can lead to a common framework for understanding confidence across different research domains, from human and animal behavior to neural representations.

scholarly journals A mathematical framework for statistical decision confidence

2015 ◽  
Author(s):  
Balázs Hangya ◽  
Joshua I. Sanders ◽  
Adam Kepecs
Keyword(s):  
Statistical Treatment ◽  
Bayesian Posterior Probability ◽  
Mathematical Framework ◽  
Statistical Decision ◽  
Decision Confidence ◽  
Starting Point ◽  
Common Framework ◽  
Subjective Confidence ◽  
Rigorous Treatment ◽  
Definition Of

Decision confidence is a forecast about the probability that a decision will be correct. Despite this description is suggestive of a potential statistical treatment, a theoretical foundation of subjective confidence evaluation is missing. Nevertheless, confidence can be framed as an objective mathematical quantity, the Bayesian posterior probability, providing a formal definition of statistical decision confidence. Here we use this definition as a starting point to develop a normative statistical framework for decision confidence. We analytically prove interrelations between statistical decision confidence and other observable decision measures. Among these is a counterintuitive property of confidence - that the lowest average confidence occurs when classifiers err in the presence of the strongest evidence. These results lay the foundations for a mathematically rigorous treatment of decision confidence that can lead to a common framework for understanding confidence across different research domains, from human behavior to neural representations.

scholarly journals The World in the Post-Truth Era or How Too Much Love of TINA Will Kill You

2017 ◽  
Vol 1 (2) ◽  
pp. 7 ◽  
Author(s):  
Jarl K Kampen
Keyword(s):  
Fossil Fuels ◽  
Design Research ◽  
Social Research ◽  
Global Level ◽  
Global Context ◽  
Starting Point ◽  
Alternative Facts ◽  
Research Domains ◽  
Research Domain ◽  
The Eu

Aim: The temptation to provide simple answers to complex problems exists for politicians and scientists alike. This essay attempts to briefly outline the complexity of present day problems at global level, taking as a starting point the question “how quick will the EU collapse?” Design / Research methods: Brief discussions are given of separate yet interconnected, causally related and overlapping natural and social research domains, illustrating the need for qualified multidisciplinary spokesmen able to separate facts from “alternative facts.”Conclusions / findings:  Making the simple anthropological observation that people can choose policies that are self-destructive does not make social science politicized or value-biased. A society that considers global warming, depletion and pollution caused by fossil fuels as mere externalities makes a demonstrable erratic choice. Because one of the major goals of science is to establish (in)validity of “common sense,” it is duty of academics to tell our students that societies, including entire scientific departments, can make consistent erratic choices.Originality / value of the article: This essay may help scholars and practitioners to start to look at their research domain in a (much) wider global context.

scholarly journals Mathematical Modeling of Biofilm Structures Using COMSTAT Data

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Davide Verotta ◽  
Janus Haagensen ◽  
Alfred M. Spormann ◽  
Katherine Yang
Keyword(s):  
Mathematical Modeling ◽  
Dead Cell ◽  
Mathematical Framework ◽  
Complex Data ◽  
Biofilm Growth ◽  
Statistical Framework ◽  
Cell Accumulation ◽  
Microscopy Data ◽  
Kinetics Of

Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data in terms of few parameters and the capability to (i) compare different experiments and exposures to different agents, (ii) test different hypotheses regarding biofilm growth and interaction with different agents, and (iii) simulate arbitrary administrations of agents. The mathematical framework is divided to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We demonstrate the application of (some of) the models using confocal microscopy data obtained using the computer program COMSTAT.

scholarly journals Meta Research: Replication of Significant Results --- Modeling the Effects of p-Hacking

2020 ◽  
Author(s):  
Rolf Ulrich ◽  
Jeff Miller
Keyword(s):  
Base Rate ◽  
Replication Rate ◽  
Research Practices ◽  
Questionable Research Practices ◽  
Statistical Framework ◽  
Scientific Results ◽  
General Statistical ◽  
Effective Drugs ◽  
Research Domains

This article examines why many studies fail to replicate statistically significant published results. We address this issue within a general statistical framework that also allows usto include various questionable research practices that are thought to reduce replicability. The analyses indicate that the base rate of true effects is the major factor that determines the replication rate of scientific results. Specifically, for purely statistical reasons, replicability is low in research domains where true effects are rare (e.g., search for effective drugs in pharmacology). This point is under-appreciated in current scientific and media discussions of replicability.

scholarly journals Emergent evolutionary forces in spatial models of luminal growth in the human gut microbiota

2021 ◽  
Author(s):  
Olivia M Ghosh ◽  
Benjamin H Good
Keyword(s):  
Growth Rate ◽  
Fluid Flow ◽  
Gut Microbiota ◽  
Intestinal Lumen ◽  
Mathematical Framework ◽  
Average Growth ◽  
Evolutionary Forces ◽  
Generation Times ◽  
Starting Point ◽  
Effective Generation

The genetic composition of the gut microbiota is constantly reshaped by ecological and evolutionary forces. These strain-level dynamics can be challenging to understand because they emerge from complex spatial growth processes that take place within a host. Here we introduce a mathematical framework to predict how stochastic evolutionary forces emerge from simple models of microbial growth in the intestinal lumen. Our framework shows how fluid flow and longitudinal variation in growth rate combine to shape the frequencies of genetic variants in sequenced fecal samples, yielding analytical expressions for the effective generation times, selection coefficients, and rates of genetic drift. We find that the emergent evolutionary dynamics can often be captured by well-mixed models that lack explicit spatial structure, even when there is substantial spatial variation in species-level composition. By applying these results to the human colon, we find that continuous fluid flow is unlikely to create sufficient bottlenecks to allow large fluctuations in mutant frequencies within a host, while the effective generation times may be significantly shorter than expected from traditional average growth rate estimates. Our results provide a starting point for quantifying genetic turnover in the gut microbiota, and may be relevant for other microbial ecosystems where unidirectional fluid flow plays an important role.

scholarly journals What health systems do? Functions as a starting point to assess health systems performance

2021 ◽  
Vol 31 (Supplement_3) ◽  
Author(s):  
Irini Papanicolas
Keyword(s):  
Health System ◽  
Performance Assessment ◽  
Health Systems ◽  
Building Blocks ◽  
Performance Outcomes ◽  
Starting Point ◽  
Common Framework ◽  
System Assessment ◽  
Health Systems Performance ◽  
Health System Building Blocks

Abstract Health system assessment (HSA) tools are often built around static health system building blocks, which lead to largely descriptive narrative and lack of linkages to health system outcomes. The development of a common framework that would also focus on performance outcomes is long overdue. We analysed the key HSA frameworks and tools based on them, with the purpose of identifying a common approach that would allow to link health system components to specific outcomes. The presentation will focus on using the health system functions as the basis of conducting the performance assessment. In a second step, the presentation will elaborate on the intermediate and final health system goals as part of the HSPA framework. It will explain their links to the four functions and thus, discuss their relevance for performance assessment.

Leading Anywhere Workers

2017 ◽  
pp. 47-88 ◽  
Author(s):  
Christianne T. Varty ◽  
Thomas A. O'Neill ◽  
Laura A. Hambley
Keyword(s):  
Leadership Effectiveness ◽  
Leadership And Management ◽  
Starting Point ◽  
Common Framework

As organizations continue to adopt anywhere working, it remains critical to address the leadership and management challenges of leading anywhere workers. Through interviews with experienced anywhere leaders from several different organizations, this chapter clarifies how leaders meet and overcome those challenges. Building on existing behaviorally-based models of leadership, the authors propose a hierarchical taxonomy of anywhere leadership effectiveness behaviors. The taxonomy is composed of four metacategories (Relationships, Flexibility, Productivity, Culture) and fourteen subcategories, which detail the behavioral capabilities necessary for anywhere leadership. In doing so, this chapter provides a common framework for understanding anywhere leadership, lays the foundation for the assessment and development of anywhere leaders, and is a starting point for further research.

Magnitude-Based Streamlines Seed Point Selection for 3D Flow Visualization

2020 ◽  
Author(s):  
Yusman Azimi Yusoff ◽  
Farhan Mohamed ◽  
Nor Azrini Jaafar ◽  
Mohd Shahrizal Sunar ◽  
Ali Selamat
Keyword(s):  
Flow Visualization ◽  
Evaluation Method ◽  
3D Visualization ◽  
Point Selection ◽  
Seed Point ◽  
3D Space ◽  
Starting Point ◽  
Research Domains ◽  
Point Placement ◽  
Placement Technique

Seed point placement techniques have been introduced and improved flow visualization research domains since the beginning of the introduction of streamlines visualization. It is a starting point of the streamlines. Thus, it is crucial because the result is directly impacted by the seed point placement. Improved seed point placement has been presented with the objectives to generate uniform streamlines placement, to have longer streamlines, and to highlight important regions in the visualization result. These three objectives need to be balanced because there is a trade-off between them. Most of the available seed point placement techniques only focus on one objective and sacrifices the other two. In this paper, the Magnitude-Based Seed Point placement technique is improved to be used in 3D space. Experts review is conducted to evaluate the result as there is no proper quantitative evaluation method for 3D visualization results. Feedback from experts shows that the proposed technique provides a better result with the same streamlines count.

scholarly journals Questionable research practices may have little effect on replicability

eLife ◽  
2020 ◽  
Vol 9 ◽  
Author(s):  
Rolf Ulrich ◽  
Jeff Miller
Keyword(s):  
Base Rate ◽  
Replication Rate ◽  
Research Practices ◽  
Questionable Research Practices ◽  
Statistical Framework ◽  
Scientific Results ◽  
General Statistical ◽  
Effective Drugs ◽  
Research Domains

This article examines why many studies fail to replicate statistically significant published results. We address this issue within a general statistical framework that also allows us to include various questionable research practices (QRPs) that are thought to reduce replicability. The analyses indicate that the base rate of true effects is the major factor that determines the replication rate of scientific results. Specifically, for purely statistical reasons, replicability is low in research domains where true effects are rare (e.g., search for effective drugs in pharmacology). This point is under-appreciated in current scientific and media discussions of replicability, which often attribute poor replicability mainly to QRPs.

scholarly journals Unbounded generalization of logarithmic representation of infinitesimal generators

2021 ◽  
Author(s):  
Yoritaka Iwata
Keyword(s):  
Nonlinear Analysis ◽  
Integrable Systems ◽  
General Framework ◽  
Evolution Operator ◽  
Mathematical Framework ◽  
Evolution Operators ◽  
Essential Ingredient ◽  
Infinitesimal Generators ◽  
Rigorous Treatment

The logarithmic representation of infinitesimal generators is generalized to the cases when the evolution operator is unbounded. The generalized result is applicable to the representation of infinitesimal generators of unbounded evolution operators, where unboundedness of evolution operator is an essential ingredient of nonlinear analysis. In conclusion a general framework for the identification between the infinitesimal generators with evolution operators is established. A mathematical framework for such an identification is indispensable to the rigorous treatment of nonlinear transforms: e.g., transforms appearing in the theory of integrable systems.

Sign in / Sign up

Export Citation Format

Share Document