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 Features of construction of evaluation algorithms multidimensional random processes

2020 ◽  
pp. 24-32
Author(s):  
A. A. Lobaty ◽  
A. Y. Bumai
Keyword(s):  
Random Process ◽  
Mathematical Description ◽  
A Priori ◽  
Random Processes ◽  
Optimality Criteria ◽  
Posteriori Probability ◽  
A Posteriori ◽  
A Posteriori Probability ◽  
Additional Information

The problem of evaluating the information which is present in random signals from various sources-meters is considered. It is assumed that the random process which is evaluated and the meter output according mathematical description of the problem are vector random processes. In this case, the dimension of the vector of the measurement can be larger than the dimension of the vector of the process being evaluated. The analysis of analytical methods and algorithms of the estimation that based on the determination of the main probabilistic characteristics of a random process by both the a priori and the a posteriori methods with various optimality criteria is carried out. Based on the analysis, the problem of complexing of the meters of the random process is considered according the proposed criterion for the maximum of posterior verisimilitude, combining the criterion of maximum verisimilitude and the criterion of maximum the a posteriori probability, general methodology complexing is developed. Proposed example of the complexing shows the efficiency of the proposed method. This approach to the construction of the algorithms of the evaluation for multidimensional random processes allows to increase the accuracy of estimation, since it takes into account additional information and its complex processing.

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.

Using a Priori Information in Energy-Dispersive X-Ray Fluorescence Analysis of Complex Samples

1991 ◽  
Vol 35 (B) ◽  
pp. 1205-1209
Author(s):  
I. A. Kondurov ◽  
P. A. Sushkov ◽  
T. M. Tjukavina ◽  
G. I. Shulyak
Keyword(s):  
High Temperature Superconductors ◽  
A Priori ◽  
Fluorescence Analysis ◽  
A Priori Information ◽  
Complex Samples ◽  
X Ray ◽  
Edxrf Analysis ◽  
The Matrix ◽  
Priori Information

In multielement EDXRF analysis of very complex unknowns, some problems in data evaluation may be simplified if one can take into account a priori information on the properties of the incident and detected radiations, and also available data on the matrix of the sample. The number of variables can be drastically shortened in the LSM procedures in this case. One of the best examples of complex unknowns is the determination of the rare earth element content of ores, and most recently in samples of high temperature superconductors (HiTc).

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.  

Defect Structure Analysis in Semiconductors by HREM and New Compatible Techniques

1984 ◽  
Vol 42 ◽  
pp. 364-367
Author(s):  
J.C.H. Spence
Keyword(s):  
A Priori ◽  
Heavy Atom ◽  
A Priori Information ◽  
Atomic Column ◽  
Structure Information ◽  
Semiconductor Defects ◽  
Semiconductor Interfaces ◽  
Priori Information ◽  
Similar Unit

The determination of atomic co-ordinates from HREM images has greatly improved our understanding of semiconductor defects, but chemical and electronic structure information are also needed. Thus suitable HREM compatible techniques must be developed and this article reviews some of these.The intimate relationship between resolution and noise has been exploited for many years in biological HREM. Since the centre of a very broad gaussion peak can be found with an accuracy which depends mainly on noise, heavy atom positions in inorganic crystals can be determined from HREM images with an accuracy of ±0.1Å (well beyond the information and point resolution limits of an HREM image) by the addition of similar unit cell images. This method makes extensive use of a-priori information (that there is only one atomic column rather than an unresolved pair, other atom co-ordinates, symmetry) and fails for isolated defects, but may be useful for semiconductor interfaces and surfaces.

METHOD OF COMPENSATION OF IONOSPHERE ERRORS OF SPACE OBJECTS COORDINATES DEFINITION BY MEANS OF TWO POSITION RADAR OBSERVATION

2018 ◽  
pp. 45-49
Author(s):  
P. S. Galkin ◽  
V. N. Lagutkin
Keyword(s):  
Probability Density ◽  
A Priori ◽  
Position Estimation ◽  
Estimation Accuracy ◽  
Posteriori Probability ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
Space Object ◽  
A Posteriori Probability ◽  
Space Objects

The algorithm of estimation and compensation of ionosphere influence on the measurement of parameters of the motion of space objects in two-position radar system with account of radio physical effects depending on elevation angles and the operating frequency is developed. It is assumed that the observed space object is traсked object, the orbital parameters which are well known, including the dependence of the velocity of the point on the orbit, and the uncertainty of the current coordinates of the object is caused mainly by forecast error of its position of in orbit (longitudinal error). To estimate the true position of space object in the orbit and the parameter, determining the influence of the ionosphere, a joint optimal processing of measurement of ranges to the object, obtained by two separated radars, taking into account the relevant ionospheric propagation delays and available a priori data on observable object trajectory. Estimation of unknown parameters are obtained on the basis of the criterion of maximum a posteriori probability density for these parameters, taking into account the measured and a priori data. The task of searching for maximum a posteriori probability density is reduced to task of searching of minimum weighted sum of squares, for the solution of which the cascade algorithm of iteration through is implemented in the work. Estimation accuracy of the position of space objects in orbit after compensation of ionosphere influence have been studied by Monte-Carlo method. Dependencies of mean square error of the position estimation of space objects upon elevation angles, operation frequency and solar activity have been obtained. It is shown that the effectiveness of the algorithm increases with the spatial base of measurements (for a fixed orbit of the object).

Bayesian Learning on Discrete Systems of Two Classes

2017 ◽  
Vol 32 (01) ◽  
pp. 1860013 ◽  
Author(s):  
J. H. Pacheco-Sánchez ◽  
R. D. Vera-Torres ◽  
R. Alejo
Keyword(s):  
Bayesian Learning ◽  
A Priori ◽  
Discrete Systems ◽  
Posteriori Probability ◽  
Original Sample ◽  
A Posteriori ◽  
Main Interest ◽  
Probability Curve ◽  
A Posteriori Probability ◽  
Probability Field

Bayesian learning is applied on two class systems. Partitioning a big sample made up of many elements of two classes of indistinguishable objects, we indistinctly pursue from 2 to 5 training sets called hypotheses in the probability field, with a plausible rate of object from each hypothesis. Objects are taken one by one from the sample. The basic aim faced is to predict one type of objects in the following occasion in which an agent takes one of them from the original sample to test it. We obtain the graph of a posteriori probability for each hypothesis of one of the objects. A prediction that the following object is specifically one of them is acquired in one probability curve by means of training previously accomplished. This methodology is applied on manufacture of glass bottles of two classes: good or crash. The main interest is to predict which machine produced one detected crash bottle because bottles turn to be indistinguishable when they are reviewed. This is solved by fixing a priori probabilities and taking into account all possible probability distribution combinations in the classes.

scholarly journals Determination of the barycentric velocity of an astrometric satellite using its own observational data

2007 ◽  
Vol 3 (S248) ◽  
pp. 252-255 ◽  
Author(s):  
A. G. Butkevich ◽  
S. A. Klioner
Keyword(s):  
Observational Data ◽  
A Priori ◽  
Translational Motion ◽  
Orbital Velocity ◽  
A Priori Information ◽  
Proposed Model ◽  
Velocity Constraints ◽  
Priori Information ◽  
Astrometric Data

AbstractThe problem of determination of the orbital velocity of an astrometric satellite from its own observational data is studied. It is well known that data processing of microarcsecond-level astrometric observations imposes very stringent requirements on the accuracy of the orbital velocity of satellite (a velocity correction of 1.45 mm/s implies an aberrational correction of 1 μas). Because of a number of degeneracies the orbital velocity cannot be fully restored from observations provided by the satellite. Seven constraints that must be applied on a velocity parameterization are discussed and formulated mathematically. It is shown what part of velocity can be recovered from astrometric data using a combined fit of both velocity parameters and astrometric parameters of the sources. Numerical simulations show that, with the seven constraints applied, the velocity and astrometric parameters can be reliably estimated from observational data. It is also argued that the idea to improve the velocity of an astrometric satellite from its own observational data is only useful if a priori information on orbital velocity justifies the applicability of the velocity constraints. The proposed model takes into account only translational motion of the satellite and ignores any satellite-specific parameters. Therefore, the results of this study are equally applicable to both scanning missions similar to Gaia, and pointing ones like SIM, provided that enough sources were observed sufficiently uniformly.

Sign in / Sign up

Export Citation Format

Share Document