scholarly journals Practical Challenges and Methodological Flexibility in Prior Elicitation

2019 ◽  
Author(s):  
Angelika Stefan ◽  
Nathan J. Evans ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Degrees Of Freedom ◽  
Expert Knowledge ◽  
Bayesian Analyses ◽  
Prior Distributions ◽  
Prior Elicitation ◽  
Statistical Framework ◽  
Elicitation Process ◽  
Parameter Values ◽  
Structured Approach ◽  
Decision Paths

The Bayesian statistical framework requires the specification of prior distributions, which reflect pre-data knowledge about the relative plausibility of different parameter values. As prior distributions influence the results of Bayesian analyses, it is important to specify them with care. Prior elicitation has frequently been proposed as a principled method for deriving prior distributions based on expert knowledge. Although prior elicitation provides a theoretically satisfactory method of specifying prior distributions, there are several implicit decisions that researchers need to make at different stages of the elicitation process, each of them constituting important researcher degrees of freedom. Here, we discuss some of these decisions and group them into three categories: decisions about (1) the setup of the prior elicitation; (2) the core elicitation process; and (3) combination of elicited prior distributions from different experts. Importantly, different decision paths could result in greatly varying priors elicited from the same experts. Hence, researchers who wish to perform prior elicitation are advised to carefully consider each of the practical decisions before, during, and after the elicitation process. By explicitly outlining the consequences of these practical decisions, we hope to raise awareness for methodological flexibility in prior elicitation and provide researchers with a more structured approach to navigate the decision paths in prior elicitation. Making the decisions explicit also provides the foundation for further research that can identify evidence-based best practices that may eventually reduce the methodologically flexibility in prior elicitation.

scholarly journals Expert Agreement in Prior Elicitation and its Effects on Bayesian Inference

2021 ◽  
Author(s):  
Angelika Stefan ◽  
Dimitris Katsimpokis ◽  
Quentin Frederik Gronau ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Bayesian Inference ◽  
Bayes Factor ◽  
Hypothesis Test ◽  
Data Uncertainty ◽  
Sensitivity Analyses ◽  
Prior Distributions ◽  
Prior Elicitation ◽  
Measures Of Concordance ◽  
Multiple Experts ◽  
Parameter Values

Bayesian inference requires the specification of prior distributions that quantify the pre-data uncertainty about parameter values. One way to specify prior distributions is through prior elicitation, an interview method guiding field experts through the process of expressing their knowledge in the form of a probability distribution. However, prior distributions elicited from experts can be subject to idiosyncrasies of experts and elicitation procedures, raising the spectre of subjectivity and prejudice. Here, we investigate the effect of interpersonal variation in elicited prior distributions on the Bayes factor hypothesis test. We elicited prior distributions from six academic experts with a background in different fields of psychology and applied the elicited prior distributions as well as commonly used default priors in a re-analysis of 1710 studies in psychology. The degree to which the Bayes factors vary as a function of the different prior distributions is quantified by three measures of concordance of evidence: We assess whether the prior distributions change the Bayes factor direction, whether they cause a switch in the category of evidence strength, and how much influence they have on the value of the Bayes factor. Our results show that although the Bayes factor is sensitive to changes in the prior distribution, these changes rarely affect the qualitative conclusions of a hypothesis test. We hope that these results help researchers gauge the influence of interpersonal variation in elicited prior distributions in future psychological studies. Additionally, our sensitivity analyses can be used as a template for Bayesian robustness analyses that involves prior elicitation from multiple experts.

Design calculation model of oil fluid property parameter knowledge database for production logging

2020 ◽  
Vol 20 (3) ◽  
pp. 951-958
Author(s):  
Wenguang Song ◽  
Qiongqin Jiang
Keyword(s):  
Crude Oil ◽  
Expert Knowledge ◽  
Calculation Model ◽  
Physical Parameters ◽  
Base System ◽  
Design Calculation ◽  
Calculation Methods ◽  
Fluid Property ◽  
Knowledge Base System ◽  
Parameter Values

The fluid property parameter calculation affects the accuracy of the interpretation the accuracy, in the interpretation of the liquid production profile. Therefore, it is particularly important to accurately calculate the physical property parameter values, in the establishment of the fluid property parameter expert knowledge base system. The main physical parameters include the following calculation methods of the oil. The oil property parameter conversion formula mainly studies the formulas such as bubble point pressure, dissolved gas-oil ratio, crude oil volume coefficient, crude oil density, crude oil viscosity, and crude oil compression coefficient. Design expert knowledge base system, it is based on the calculation methods of these physical parameters. A computational fluid property parameter model is constructed by training production log sample data. Finally, the interactive and friendly product interpretation software model was developed in 9 wells’ data. The design calculation model can increase the accuracy to achieve 95% of oil fluid property parameter. Accurately calculate fluid property parameter values.

scholarly journals An FDA-Based Approach for Clustering Elicited Expert Knowledge

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 184-204
Author(s):  
Carlos Barrera-Causil ◽  
Juan Carlos Correa ◽  
Andrew Zamecnik ◽  
Francisco Torres-Avilés ◽  
Fernando Marmolejo-Ramos
Keyword(s):  
Functional Data ◽  
Expert Knowledge ◽  
Probability Distributions ◽  
Knowledge Elicitation ◽  
Parallel Analysis ◽  
Data Sets ◽  
Dimensional Problem ◽  
Prior Distributions ◽  
Infinite Dimensional ◽  
Finite Dimensional

Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile discrepant elicited prior distributions. This paper proposes the parallel analysis of clusters of prior distributions through a hierarchical method for clustering distributions and that can be readily extended to functional data. The proposed method consists of (i) transforming the infinite-dimensional problem into a finite-dimensional one, (ii) using the Hellinger distance to compute the distances between curves and thus (iii) obtaining a hierarchical clustering structure. In a simulation study the proposed method was compared to k-means and agglomerative nesting algorithms and the results showed that the proposed method outperformed those algorithms. Finally, the proposed method is illustrated through an EKE experiment and other functional data sets.

scholarly journals Response (minimum clinically relevant change) in ASD symptoms after an intervention according to CARS-2: consensus from an expert elicitation procedure

2021 ◽  
Author(s):  
Lucie Jurek ◽  
Matias Balthazar ◽  
Sheffali Gulati ◽  
Neda Novakovic ◽  
María Núñez ◽  
...  
Keyword(s):  
Autism Spectrum Disorder ◽  
Rating Scale ◽  
Expert Knowledge ◽  
Scientific Evidence ◽  
Autism Spectrum ◽  
Expert Elicitation ◽  
Spectrum Disorder ◽  
Initial Finding ◽  
Elicitation Process ◽  
Core Symptoms

AbstractThe lack of consensual measures to monitor core change in Autism Spectrum Disorder (ASD) or response to interventions leads to difficulty to prove intervention efficacy on ASD core symptoms. There are no universally accepted outcome measures developed for measuring changes in core symptoms. However, the CARS (Childhood Autism Rating Scale) is one of the outcomes recommended in the EMA Guideline on the clinical development of medicinal products for the treatment of ASD. Unfortunately, there is currently no consensus on the response definition for CARS among individuals with ASD. The aim of this elicitation process was to determine an appropriate definition of a response on the CARS2 scale for interventions in patients with Autism Spectrum Disorder (ASD). An elicitation process was conducted following the Sheffield Elicitation Framework (SHELF). Five experts in the field of ASD and two experts in expert knowledge elicitation participated in an 1-day elicitation workshop. Experts in ASD were previously trained in the SHELF elicitation process and received a dossier of scientific evidence concerning the topic. The response definition was set as the mean clinically relevant improvement averaged over all patients, levels of functioning, age groups ***and clinicians. Based on the scientific evidence and expert judgment, a normal probability distribution was agreed to represent the state of knowledge of this response with expected value 4.03 and standard deviation 0.664. Considering the remaining uncertainty of the estimation and the available literature, a CARS-2 improvement of 4.5 points has been defined as a threshold to conclude to a response after an intervention. A CARS-2 improvement of 4.5 points could be used to evaluate interventions' meaningfulness in indivudals. This initial finding represents an important new benchmark and may aid decision makers in evaluating the efficacy of interventions in ASD.

Effect of a Planetary Gearbox on the Dynamics of a Rotor System

2018 ◽  
Author(s):  
Ali Tatar ◽  
Christoph W. Schwingshackl
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Rotor System ◽  
Mode Shapes ◽  
Rotating System ◽  
Planetary Gearbox ◽  
Finite Element Software ◽  
Gyroscopic Effects ◽  
The Masses ◽  
Parameter Values

The dynamic analysis of rotors with bladed disks has been investigated in detail over many decades and is reasonably well understood today. In contrast, the dynamic behaviour of two rotors that are coupled via a planetary gearbox is much less well understood. The planetary gearbox adds inertia, mass, stiffness, damping and gyroscopic moments to the system and can strongly affect the modal properties and the dynamic behaviour of the global rotating system. The main objective of this paper is to create a six degrees of freedom numerical model of a rotor system with a planetary gearbox and to investigate its effect on the coupled rotor system. The analysis is based on the newly developed finite element software “GEAROT” which provides axial, torsional and lateral deflections of the two shafts at different speeds via Timoshenko beam elements and also takes gyroscopic effects into account. The disks are currently considered as rigid and the bearings are modelled with isotropic stiffness elements in the translational and rotational directions. A novel planetary gearbox model has been developed, which takes the translational and rotational stiffness and the damping of the gearbox, as well as the masses and inertias of the sun gear, ring gear, planet gears and carrier into account. A rotating system with a planetary gearbox has been investigated with GEAROT. The gearbox mass and stiffness parameters are identified as having a significant effect on the modal behaviour of the rotor system, affecting its natural frequencies and mode shapes. The higher frequency modes are found to be more sensitive to the parameter changes as well as the modes which have a higher deflection at the location of the gearbox on the rotor system. Compared with a single shaft system, the presence of a gearbox introduces new global modes to the rotor system and decouples the mode shapes of the two shafts. The introduction of a planetary gearbox may also lead to an increase or a reduction of the frequency response of the rotor system based on gear parameter values.

scholarly journals Gravitational theory of cosmology, galaxies and galaxy clusters

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
J. W. Moffat
Keyword(s):  
Power Spectrum ◽  
Galaxy Clusters ◽  
Degrees Of Freedom ◽  
Galaxy Cluster ◽  
Gravitational Theory ◽  
Baryon Density ◽  
Late Time ◽  
Matter Power Spectrum ◽  
The Galaxy ◽  
Parameter Values

AbstractA modified gravitational theory explains early universe and late time cosmology, galaxy and galaxy cluster dynamics. The modified gravity (MOG) theory extends general relativity (GR) by three extra degrees of freedom: a scalar field G, enhancing the strength of the Newtonian gravitational constant $$G_N$$ G N , a gravitational, spin 1 vector graviton field $$\phi _\mu $$ ϕ μ , and the effective mass $$\mu $$ μ of the ultralight spin 1 graviton. For $$t < t_\mathrm{rec}$$ t < t rec , where $$t_\mathrm{rec}$$ t rec denotes the time of recombination and re-ionization, the density of the vector graviton $$\rho _\phi > \rho _b$$ ρ ϕ > ρ b , where $$\rho _b$$ ρ b is the density of baryons, while for $$t > t_\mathrm{rec}$$ t > t rec we have $$\rho _b > \rho _\phi $$ ρ b > ρ ϕ . The matter density is parameterized by $$\Omega _M=\Omega _b+\Omega _\phi +\Omega _r$$ Ω M = Ω b + Ω ϕ + Ω r where $$\Omega _r=\Omega _\gamma +\Omega _\nu $$ Ω r = Ω γ + Ω ν . For the cosmological parameter values obtained by the Planck Collaboration, the CMB acoustical oscillation power spectrum, polarization and lensing data can be fitted as in the $$\Lambda $$ Λ CDM model. When the baryon density $$\rho _b$$ ρ b dominates the late time universe, MOG explains galaxy rotation curves, the dynamics of galaxy clusters, galaxy lensing and the galaxy clusters matter power spectrum without dominant dark matter.

scholarly journals Cardiovascular Modeling With Adapted Parametric Inference

2018 ◽  
Vol 62 ◽  
pp. 91-107 ◽  
Author(s):  
Didier Lucor ◽  
Olivier P. Le Maître
Keyword(s):  
Approximation Error ◽  
Surrogate Models ◽  
Patient Specific ◽  
System Response ◽  
Cardiovascular Parameter ◽  
Monte Carlo Algorithms ◽  
Statistical Framework ◽  
Posterior Sampling ◽  
Powerful Approach ◽  
Parameter Values

Computational modeling of the cardiovascular system, promoted by the advance of fluid-structure interaction numerical methods, has made great progress towards the development of patient-specific numerical aids to diagnosis, risk prediction, intervention and clinical treatment. Nevertheless, the reliability of these models is inevitably impacted by rough modeling assumptions. A strong in-tegration of patient-specific data into numerical modeling is therefore needed in order to improve the accuracy of the predictions through the calibration of important physiological parameters. The Bayesian statistical framework to inverse problems is a powerful approach that relies on posterior sampling techniques, such as Markov chain Monte Carlo algorithms. The generation of samples re-quires many evaluations of the cardiovascular parameter-to-observable model. In practice, the use of a full cardiovascular numerical model is prohibitively expensive and a computational strategy based on approximations of the system response, or surrogate models, is needed to perform the data as-similation. As the support of the parameters distribution typically concentrates on a small fraction of the initial prior distribution, a worthy improvement consists in gradually adapting the surrogate model to minimize the approximation error for parameter values corresponding to high posterior den-sity. We introduce a novel numerical pathway to construct a series of polynomial surrogate models, by regression, using samples drawn from a sequence of distributions likely to converge to the posterior distribution. The approach yields substantial gains in efficiency and accuracy over direct prior-based surrogate models, as demonstrated via application to pulse wave velocities identification in a human lower limb arterial network.

scholarly journals Penalized complexity priors for degrees of freedom in Bayesian P-splines

2016 ◽  
Vol 16 (6) ◽  
pp. 429-453 ◽  
Author(s):  
Massimo Ventrucci ◽  
Håvard Rue
Keyword(s):  
Random Field ◽  
Markov Random Field ◽  
Smooth Function ◽  
Degrees Of Freedom ◽  
Penalized Splines ◽  
Prior Elicitation ◽  
Gaussian Markov Random Field ◽  
Markov Random ◽  
Gaussian Data

Bayesian penalized splines (P-splines) assume an intrinsic Gaussian Markov random field prior on the spline coefficients, conditional on a precision hyper-parameter [Formula: see text]. Prior elicitation of [Formula: see text] is difficult. To overcome this issue, we aim to building priors on an interpretable property of the model, indicating the complexity of the smooth function to be estimated. Following this idea, we propose penalized complexity (PC) priors for the number of effective degrees of freedom. We present the general ideas behind the construction of these new PC priors, describe their properties and show how to implement them in P-splines for Gaussian data.

A sequential method for selecting parameter values in the Barcelona basic model

2010 ◽  
Vol 47 (11) ◽  
pp. 1175-1186 ◽  
Author(s):  
Domenico Gallipoli ◽  
Francesca D’Onza ◽  
Simon J. Wheeler
Keyword(s):  
Laboratory Tests ◽  
Degrees Of Freedom ◽  
Sequential Method ◽  
Multiple Parameters ◽  
Basic Model ◽  
Specific Order ◽  
Iterative Procedures ◽  
Key Aspects ◽  
Soil Behaviour ◽  
Parameter Values

The popularity of the Barcelona basic model (BBM) has grown steadily since its publication in 1990, due to its ability to capture key aspects of unsaturated soil behaviour. Nevertheless, the BBM is still rarely employed by practitioners, partly because of the absence of simple and objective methods for selecting parameter values from laboratory tests. One difficulty is that, in the BBM, individual aspects of the isotropic virgin behaviour are controlled by multiple parameters, while at the same time a single parameter controls more than one aspect of soil behaviour. This has led to iterative procedures where parameter values are adjusted in turn to match experiments, which requires significant experience and can lead to the selection of widely varying parameter values depending on the user. The proposed method streamlines parameter selection with a view to increasing the appeal of the BBM for practitioners. The method adopts a “sequential” procedure where the five parameters governing isotropic virgin behaviour are matched to degrees of freedom in the BBM, which are then fixed one at a time, in a specific order, without any assumption about other parameters. The simplicity and reduced subjectivity of the method in comparison with iterative procedures is demonstrated by selecting parameter values from laboratory tests.

Ergonomic Level Improving of Armoured Fighting Vehicle Crew

2017 ◽  
Vol 68 (1) ◽  
pp. 33
Author(s):  
N. V. Ramamurthy ◽  
B. K. Vinayagam ◽  
Roopchand J.
Keyword(s):  
Degrees Of Freedom ◽  
Ride Comfort ◽  
Equations Of Motion ◽  
Research Work ◽  
Composite Model ◽  
Seat Suspension ◽  
Lumped Parameter ◽  
Vibration Responses ◽  
Suspension Model ◽  
Parameter Values

<p class="p1">The armoured fighting vehicle (AFV)-occupant composite system is modelled as a lumped parameter system, in this paper, wherein the 4 degrees of freedom (dof) biodynamic occupant model is integrated with 10 dof in-plane AFV model including the crew seat, thus leading to the 14 dof vehicle-occupant composite model and the governing equations of motion are obtained. The composite model is subjected to idealised road input simulating the ground reaction forces. Natural frequencies and the frequency domain vibration responses of various masses of model are obtained. The natural frequency of chassis thus obtained is compared with the result established by an earlier research work, to validate the model. The study is focused on crew seat location. A 2 dof occupant-seat suspension model is formulated and validated through case study. The optimised values of seat suspension parameters for ride comfort are obtained using the said model, through two methods of Invariant points theory and genetic algorithm toolbox of Matlab 2014a software. Acceleration responses of body for the current and optimised parameter values obtained illustrate that comfort of crew is improved with optimised values through minimization in the acceleration responses.</p>

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