scholarly journals Application of Bayesian Approach to Reduce the Uncertainty in Expert Judgments by Using a Posteriori Mean Function

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2455
Author(s):  
Irina Vinogradova-Zinkevič
Keyword(s):  
Bayesian Method ◽  
A Priori ◽  
Expert Judgment ◽  
A Posteriori ◽  
Personal Qualities ◽  
Data Source ◽  
Priori Information ◽  
Mean Function ◽  
Long Term Experience

Much applied research uses expert judgment as a primary or additional data source, thus the problem solved in this publication is relevant. Despite the expert’s experience and competence, the evaluation is subjective and has uncertainty in it. There are various reasons for this uncertainty, including the expert’s incomplete competence, the expert’s character and personal qualities, the expert’s attachment to the opinion of other experts, and the field of the task to be solved. This paper presents a new way to use the Bayesian method to reduce the uncertainty of an expert judgment by correcting the expert’s evaluation by the a posteriori mean function. The Bayesian method corrects the expert’s evaluation, taking into account the expert’s competence and accumulated long-term experience. Since the paper uses a continuous case of the Bayesian formula, perceived as a continuous approximation of experts’ evaluations, this is not only the novelty of this work, but also a new result in the theory of the Bayesian method and its application. The paper investigates various combinations of the probability density functions of a priori information and expert error. The results are illustrated by the example of the evaluation of distance learning courses.

scholarly journals Ozone profile smoothness as a priori information in the inversion of limb measurements

2004 ◽  
Vol 22 (10) ◽  
pp. 3411-3420 ◽  
Author(s):  
V. F. Sofieva ◽  
J. Tamminen ◽  
H. Haario ◽  
E. Kyrölä ◽  
M. Lehtinen
Keyword(s):  
A Priori ◽  
Optimal Estimation ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
A Priori Information ◽  
Ozone Profile ◽  
Stellar Occultation ◽  
Atmospheric Profiles ◽  
Priori Information ◽  
Typical Measurement

Abstract. In this work we discuss inclusion of a priori information about the smoothness of atmospheric profiles in inversion algorithms. The smoothness requirement can be formulated in the form of Tikhonov-type regularization, where the smoothness of atmospheric profiles is considered as a constraint or in the form of Bayesian optimal estimation (maximum a posteriori method, MAP), where the smoothness of profiles can be included as a priori information. We develop further two recently proposed retrieval methods. One of them - Tikhonov-type regularization according to the target resolution - develops the classical Tikhonov regularization. The second method - maximum a posteriori method with smoothness a priori - effectively combines the ideas of the classical MAP method and Tikhonov-type regularization. We discuss a grid-independent formulation for the proposed inversion methods, thus isolating the choice of calculation grid from the question of how strong the smoothing should be. The discussed approaches are applied to the problem of ozone profile retrieval from stellar occultation measurements by the GOMOS instrument on board the Envisat satellite. Realistic simulations for the typical measurement conditions with smoothness a priori information created from 10-years analysis of ozone sounding at Sodankylä and analysis of the total retrieval error illustrate the advantages of the proposed methods. The proposed methods are equally applicable to other profile retrieval problems from remote sensing measurements.

scholarly journals Design of an Analysis Model for Strategic Behavior in the Digital Economy

2020 ◽  
Vol 8 (2) ◽  
pp. p1
Author(s):  
Miguel Martin-Valmayor ◽  
Luis A. Gil-Alana
Keyword(s):  
Strategic Behavior ◽  
A Priori ◽  
Business Plan ◽  
A Posteriori ◽  
Analysis Model ◽  
Strategic Decisions ◽  
The Sustainable Development ◽  
Conflicting Objectives ◽  
Potential Impact

Nowadays, multi-criteria decision-making techniques are highly developed, and are widely applied in multiple fields. They model and solve decisional problems by optimising multiple conflicting objectives. These techniques are very useful because they simultaneously analyse all the different criteria, and select the best alternatives according to the decision-maker’s objectives and preferences. An important issue in this context is the adequacy of the structure of corporate long-term financing and its potential impact on the sustainable development of the long-term business plan. The purpose of this study is to advance the analysis of these strategic decisions, measuring the a posteriori results and analysing their coherence with the strategies followed a priori. To do this, sustainable strategic decisions will be mathematically modelled and parametrised, creating a system to study the preferences followed and to describe the corporate behaviour. This system is applied as a case example for two leading companies in the digital sector, and the corresponding results over the last few years are evaluated.

scholarly journals Effects of <i>a priori</i> profile shape assumptions oncomparisons between satellite NO<sub>2</sub> columns and model simulations

2020 ◽  
Author(s):  
Matthew J. Cooper ◽  
Randall V. Martin ◽  
Daven K. Henze ◽  
Dylan B. A. Jones
Keyword(s):  
Shape Factor ◽  
A Priori ◽  
Trace Gas ◽  
A Posteriori ◽  
A Priori Information ◽  
Profile Shape ◽  
Satellite Retrievals ◽  
Mass Factor ◽  
The Difference ◽  
Priori Information

Abstract. A critical step in satellite retrievals of trace gas columns is the calculation of the air mass factor (AMF) used to convert observed slant columns to vertical columns. This calculation requires a priori information on the shape of the vertical profile. As a result, comparisons between satellite-retrieved and model-simulated column abundances are influenced by the a priori profile shape. We examine how differences between the shape of the simulated and a priori profile can impact the interpretation of satellite retrievals by performing an adjoint-based 4D-Var assimilation of synthetic NO2 observations for constraining NOx emissions. We use the GEOS-Chem Adjoint model to perform assimilations using a variety of AMFs to examine how a posteriori emission estimates are affected if the AMF is calculated using an a priori shape factor that is inconsistent with the simulated profile. In these tests, an inconsistent a priori shape factor increased errors in a posteriori emissions estimates by up to 80 % over polluted regions. As the difference between the simulated profile shape and the a priori profile shape increases, so do the corresponding assimilated emission errors. This reveals the importance of using simulated profile information for AMF calculations when comparing that simulated output to satellite retrieved columns.

scholarly journals Detection of Jumps Parameters in Economic Processes(the Case of Modelling Profitability)

2018 ◽  
Vol 7 (4.3) ◽  
pp. 488 ◽  
Author(s):  
O. V. Poliarus ◽  
Y. O. Poliakov ◽  
I. L. Nazarenko ◽  
Y. T. Borovyk ◽  
M. V. Kondratiuk
Keyword(s):  
A Priori ◽  
Machine Building ◽  
Building Industry ◽  
A Posteriori ◽  
A Priori Information ◽  
Parameter Change ◽  
Economic Process ◽  
Intense Noise ◽  
Priori Information ◽  
Economic Nature

A new method of parameters jumps detection in economic processes is presented. A jump of the economic process parameter must be understood as a rapid parameter change for a time that does not exceed the period of process registration.  A system of stochastic differential equations for a posteriori density probability of a jump is synthesized. The solution of the system is the probability of a parameter jump, the estimation and variance of the jump in the presence of a priori information under conditions of noise influence. The simulation results are conducted for profitability of machine building industry of Kharkiv region, Ukraine. The system provides detection of jump parameters, even in conditions of intense noise of economic nature. To increase the probability of finding jumps it is necessary to have a priori information.  

scholarly journals Getting a risk-free trial during COVID: Accidental and deliberate home educators, responsibilisation and the growing population of children being educated outside of school

2021 ◽  
Vol 12 (1) ◽  
pp. 77-98
Author(s):  
Rebecca English
Keyword(s):  
Coming Out ◽  
A Priori ◽  
Department Of Education ◽  
Home Education ◽  
A Posteriori ◽  
School Closures ◽  
Negative Experiences ◽  
Free Trial ◽  
Home Educators

Abstract Numbers coming out of education departments in Australia suggest that, even though most Australian schools are open, and families are able to send their children to them, increasing numbers of parents are deciding to keep their children at home for their education (Queensland Government: Department of Education, 2020). It may be that, as the president of Australia’s home education representative body stated during the pandemic, Covid school closures offered a “risk-free trial” of home education (Lever, 2020) by providing an a-posteriori experience of education outside of schools. Building on the Covid experiences, this paper suggests that ‘accidentally falling into’ home education may be significant in understanding parents’ home education choices. Using numbers of home educators from Australia, and the associated data on their location and ages, this paper argues responsibilisation (see Doherty & Dooley, 2018) provides a suitable lens to examine how parents may decide, after an a-posteriori experience such as Covid school closures and previous, often negative, experiences of schooling, to home educate in the medium to long term. This paper proposes that increasing numbers of home educators will be seen in various jurisdictions where families perceive themselves responsibilised to home educate due to Covid as an a-posteriori experiences of home education. The paper proposes these families are ‘accidental’ home educators (English, 2021). By contrast, much more stable is the ‘deliberate’ home education population, those whose choices are based in a-priori beliefs about schooling. The paper proposes that the accidental home education category may be better able to explain the growing numbers of home educators in Australia and across the world, providing a means for governments to respond to the needs of this cohort, and the policies required to manage this population.

The ILRS Contribution to ITRF2020

2021 ◽  
Author(s):  
Vincenza Luceri ◽  
Erricos C. Pavlis ◽  
Antonio Basoni ◽  
David Sarrocco ◽  
Magdalena Kuzmicz-Cieslak ◽  
...  
Keyword(s):  
Time Series ◽  
Tracking System ◽  
A Priori ◽  
Systematic Errors ◽  
Novel Approach ◽  
Priori Information ◽  
The Stability ◽  
The Individual ◽  
Stability And Consistency

&lt;p&gt;The International Laser Ranging Service (ILRS) contribution to ITRF2020 has been prepared after the re-analysis of the data from 1993 to 2020, based on an improved modeling of the data and a novel approach that ensures the results are free of systematic errors in the underlying data. This reanalysis incorporates an improved &amp;#8220;target signature&amp;#8221; model (CoM) that allows better separation of true systematic error of each tracking system from the errors in the model describing the target&amp;#8217;s signature. The new approach was developed after the completion of ITRF2014, the ILRS Analysis Standing Committee (ASC) devoting almost entirely its efforts on this task. The robust estimation of persistent systematic errors at the millimeter level permitted the adoption of a consistent set of long-term mean corrections for data collected in past years, which are now applied a priori (information provided by the stations from their own engineering investigations are still taken into consideration). The reanalysis used these corrections, leading to improved results for the TRF attributes, reflected in the resulting new time series of the TRF origin and especially in the scale. Seven official ILRS Analysis Centers computed time series of weekly solutions, according to the guidelines defined by the ILRS ASC. These series were combined by the ILRS Combination Center to obtain the official ILRS product contribution to ITRF2020.&lt;/p&gt;&lt;p&gt;The presentation will provide an overview of the analysis procedures and models, and it will demonstrate the level of improvement with respect to the previous ILRS product series; the stability and consistency of the solution are discussed for the individual AC contributions and the combined SLR time series.&lt;/p&gt;

scholarly journals Atmospheric composition and thermodynamic retrievals from the ARIES airborne FTS system – Part 1: Technical aspects and simulated capability

2014 ◽  
Vol 7 (4) ◽  
pp. 1133-1150 ◽  
Author(s):  
S. M. Illingworth ◽  
G. Allen ◽  
S. Newman ◽  
A. Vance ◽  
F. Marenco ◽  
...  
Keyword(s):  
Evaluation System ◽  
Degrees Of Freedom ◽  
Retrieval System ◽  
A Priori ◽  
Atmospheric Composition ◽  
A Posteriori ◽  
Technical Aspects ◽  
System Part ◽  
Priori Information ◽  
The Uk

Abstract. In this study we present an assessment of the retrieval capability of the Airborne Research Interferometer Evaluation System (ARIES): an airborne remote-sensing Fourier transform spectrometer (FTS) operated on the UK Facility for Airborne Atmospheric Measurement (FAAM) aircraft. Simulated maximum a posteriori retrievals of partial column trace gas concentrations, and thermodynamic vertical profiles throughout the troposphere and planetary boundary layer have been performed here for simulated infrared spectra representative of the ARIES system operating in the nadir-viewing geometry. We also describe the operational and technical aspects of the pre-processing necessary for routine retrieval from the FAAM platform and the selection and construction of a priori information. As exemplars of the capability of the ARIES retrieval system, simulated retrievals of temperature, water vapour (H2O), carbon monoxide (CO), ozone (O3), and methane (CH4), and their corresponding sources of error and potential vertical sensitivity, are discussed for ARIES scenes across typical global environments. The maximum Degrees of Freedom for Signal (DOFS) for the retrievals, assuming a flight altitude of 7 km, were 3.99, 2.97, 0.85, 0.96, and 1.45 for temperature, H2O, CO, O3, and CH4, respectively, for the a priori constraints specified. Retrievals of temperature display significant vertical sensitivity (DOFS in the range 2.6 to 4.0 across the altitude range) as well as excellent simulated accuracy, with the vertical sensitivity for H2O also extending to lower altitudes (DOFS ranging from 1.6 to 3.0). It was found that the maximum sensitivity for CO, O3, and CH4 was approximately 1–2 km below the simulated altitudes in all scenarios. Comparisons of retrieved and simulated-truth partial atmospheric columns are used to assess the capability of the ARIES measurement system. Maximum mean biases (and bias standard deviations) in partial columns (i.e. below aircraft total columns) were found to be +0.06 (±0.02 at 1σ)%, +3.95 (±3.11)%, +3.74 (±2.97)%, −8.26 (±4.64)%, and +3.01 (±2.61)% for temperature, H2O, CO, O3, and CH4, respectively, illustrating that the retrieval system performs well compared to an optimal scheme. The maximum total a posteriori retrieval errors across the partial columns were also calculated, and were found to be 0.20, 22.57, 18.22, 17.61, and 16.42% for temperature, H2O, CO, O3, and CH4, respectively.

scholarly journals Statistical Ranging of Orbits for Trans-Neptunian Objects

2002 ◽  
Vol 12 ◽  
pp. 255-256 ◽  
Author(s):  
J. Virtanen ◽  
K. Muinonen ◽  
E. Bowell
Keyword(s):  
Phase Space ◽  
A Priori ◽  
Posteriori Probability ◽  
A Posteriori ◽  
A Priori Information ◽  
A Posteriori Probability ◽  
Uncertainty Prediction ◽  
Absolute Magnitudes ◽  
Priori Information

AbstractWe consider initial determination of orbits for trans-neptunian objects (TNOs), a topical theme because of the rapidly growing TNO population and the challenges in recovering lost TNOs. We apply the method of initial phase-space ranging of orbits to the poorly observed TNOs. The rigorous a posteriori probability density of the TNO orbital elements is examined using a Monte Carlo technique by varying the TNO topocentric ranges corresponding to the observation dates. We can optionally adopt a Bayesian approach to select the region of phase space containing the most plausible orbits. This is accomplished by incorporating semimajor axes, eccentricities, inclinations, and absolute magnitudes of multi-apparition TNOs as a priori information. The resulting a posteriori distributions permit ephemeris and ephemeris uncertainty prediction for TNO recovery observations.

Joint interpretation and uncertainty analysis of petrophysical properties in unconventional shale reservoirs

2015 ◽  
Vol 3 (1) ◽  
pp. SA33-SA49 ◽  
Author(s):  
Qinshan Yang ◽  
Carlos Torres-Verdín
Keyword(s):  
Joint Inversion ◽  
A Priori ◽  
Estimation Method ◽  
Monte Carlo Algorithm ◽  
Posteriori Probability ◽  
Inversion Method ◽  
A Posteriori ◽  
A Priori Information ◽  
Core Data ◽  
Priori Information

Interpretation of hydrocarbon-bearing shale is subject to great uncertainty because of pervasive heterogeneity, thin beds, and incomplete and uncertain knowledge of saturation-porosity-resistivity models. We developed a stochastic joint-inversion method specifically developed to address the quantitative petrophysical interpretation of hydrocarbon-bearing shale. The method was based on the rapid and interactive numerical simulation of resistivity and nuclear logs. Instead of property values themselves, the estimation method delivered the a posteriori probability of each property. The Markov-chain Monte Carlo algorithm was used to sample the model space to quantify the a posteriori distribution of formation properties. Additionally, the new interpretation method allows the use of fit-for-purpose statistical correlations between water saturation, salt concentration, porosity, and electrical resistivity to implement uncertain, non-Archie resistivity models derived from core data, including those affected by total organic carbon (TOC). In the case of underdetermined estimation problems, i.e., when the number of measurements was lower than the number of unknowns, the use of a priori information enabled plausible results within prespecified petrophysical and compositional bounds. The developed stochastic interpretation technique was successfully verified with data acquired in the Barnett and Haynesville Shales. Core data (including X-ray diffraction data) were combined into a priori information for interpretation of nuclear and resistivity logs. Results consisted of mineral concentrations, TOC, and porosity together with their uncertainty. Eighty percent of the core data was located within the 95% credible interval of estimated mineral/fluid concentrations.

scholarly journals Effects of a priori profile shape assumptions on comparisons between satellite NO<sub>2</sub> columns and model simulations

2020 ◽  
Vol 20 (12) ◽  
pp. 7231-7241
Author(s):  
Matthew J. Cooper ◽  
Randall V. Martin ◽  
Daven K. Henze ◽  
Dylan B. A. Jones
Keyword(s):  
Shape Factor ◽  
A Priori ◽  
Trace Gas ◽  
A Posteriori ◽  
Profile Shape ◽  
Satellite Retrievals ◽  
Mass Factor ◽  
The Difference ◽  
Priori Information ◽  
Mean Square Errors

Abstract. A critical step in satellite retrievals of trace gas columns is the calculation of the air mass factor (AMF) used to convert observed slant columns to vertical columns. This calculation requires a priori information on the shape of the vertical profile. As a result, comparisons between satellite-retrieved and model-simulated column abundances are influenced by the a priori profile shape. We examine how differences between the shape of the simulated and a priori profiles can impact the interpretation of satellite retrievals by performing an adjoint-based four-dimensional variational (4D-Var) assimilation of synthetic NO2 observations for constraining NOx emissions. We use the GEOS-Chem adjoint model to perform assimilations using a variety of AMFs to examine how a posteriori emission estimates are affected if the AMF is calculated using an a priori shape factor that is inconsistent with the simulated profile. In these tests, an inconsistent a priori shape factor increased root mean square errors in a posteriori emission estimates by up to 30 % for realistic conditions over polluted regions. As the difference between the simulated profile shape and the a priori profile shape increases, so do the corresponding assimilated emission errors. This reveals the importance of using simulated profile information for AMF calculations when comparing that simulated output to satellite-retrieved columns.

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