Статті в журналах: "Random observations"

1

Jaynes, E. T. "Some random observations." Synthese 63, no. 1 (April 1985): 115–38. http://dx.doi.org/10.1007/bf00485957.

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2

Andrea, Montanari. "Estimating random variables from random sparse observations." European Transactions on Telecommunications 19, no. 4 (2008): 385–403. http://dx.doi.org/10.1002/ett.1289.

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3

Sanandaji, Borhan M., Michael B. Wakin, and Tyrone L. Vincent. "Observability With Random Observations." IEEE Transactions on Automatic Control 59, no. 11 (November 2014): 3002–7. http://dx.doi.org/10.1109/tac.2014.2351693.

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4

O’Neill, Cecily. "Seal Wife – random observations." NJ 41, no. 1 (January 2, 2017): 27–29. http://dx.doi.org/10.1080/14452294.2017.1329687.

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5

Schmidt, Marius, and Rainer Schwabe. "Optimal cutpoints for random observations." Statistics 49, no. 6 (February 17, 2015): 1366–81. http://dx.doi.org/10.1080/02331888.2015.1006225.

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6

WILLIAMS, J. "Random observations on reading research." Issues in Education 5, no. 1 (1999): 161–64. http://dx.doi.org/10.1016/s1080-9724(99)00013-0.

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7

Zirbel, Craig L. "Lagrangian observations of homogeneous random environments." Advances in Applied Probability 33, no. 4 (December 2001): 810–35. http://dx.doi.org/10.1239/aap/1011994031.

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This article deals with the distribution of the view of a random environment as seen by an observer whose location at each moment is determined by the environment. The main application is in statistical fluid mechanics, where the environment consists of a random velocity field and the observer is a particle moving in the velocity field, possibly subject to molecular diffusion. Several results on such Lagrangian observations of the environment have appeared in the literature, beginning with the 1957 dissertation of J. L. Lumley. This article unites these results into a simple unified framework and rounds out the theory with new results in several directions. When the environment is homogeneous, the problem can be re-cast in terms of certain random mappings on the physical space that are based on the random location of the observer. If these mappings preserve the invariant measure on the physical space, then the view from the random location has the same distribution as the view from the origin. If these mappings satisfy the flow property and the environment is stationary, then the succession of Lagrangian observations over time forms a strictly stationary process. In particular, for motion in a homogeneous, stationary, and nondivergent velocity field, the Lagrangian velocity (the velocity of the particle) is strictly stationary, which was first observed by Lumley. In the compressible case, the distribution of a Lagrangian observation has a density with respect to the distribution of the view from the origin, and in some cases convergence in distribution of the Lagrangian observations as time tends to infinity can be shown.

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8

Zirbel, Craig L. "Lagrangian observations of homogeneous random environments." Advances in Applied Probability 33, no. 04 (December 2001): 810–35. http://dx.doi.org/10.1017/s0001867800011216.

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This article deals with the distribution of the view of a random environment as seen by an observer whose location at each moment is determined by the environment. The main application is in statistical fluid mechanics, where the environment consists of a random velocity field and the observer is a particle moving in the velocity field, possibly subject to molecular diffusion. Several results on such Lagrangian observations of the environment have appeared in the literature, beginning with the 1957 dissertation of J. L. Lumley. This article unites these results into a simple unified framework and rounds out the theory with new results in several directions. When the environment is homogeneous, the problem can be re-cast in terms of certain random mappings on the physical space that are based on the random location of the observer. If these mappings preserve the invariant measure on the physical space, then the view from the random location has the same distribution as the view from the origin. If these mappings satisfy the flow property and the environment is stationary, then the succession of Lagrangian observations over time forms a strictly stationary process. In particular, for motion in a homogeneous, stationary, and nondivergent velocity field, the Lagrangian velocity (the velocity of the particle) is strictly stationary, which was first observed by Lumley. In the compressible case, the distribution of a Lagrangian observation has a density with respect to the distribution of the view from the origin, and in some cases convergence in distribution of the Lagrangian observations as time tends to infinity can be shown.

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9

Cohen, Joel E., and Thomas M. Liggett. "Random arithmetic-geometric means and random pi: observations and conjectures." Stochastic Processes and their Applications 41, no. 2 (June 1992): 261–71. http://dx.doi.org/10.1016/0304-4149(92)90126-b.

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10

Eather, Wolfgang, and Matthias Albbecht. "Linear Eegression with Random Fuzzy Observations." Statistics 21, no. 4 (January 1990): 521–31. http://dx.doi.org/10.1080/02331889008802262.

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11

Hofmann, Glenn, та H. N. Nagaraja. "Random and Poisson paced record models in the Fα setup". Journal of Applied Probability 37, № 2 (червень 2000): 374–88. http://dx.doi.org/10.1239/jap/1014842543.

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We study a random record model where the observation Xi has continuous distribution function Fαi (αi > 0) and the number of available observations is random and independent of the observations. We obtain the joint distribution of the record values and inter-record times for our model. We investigate the distribution of the number of records when the number of observations has one of the common distributions and the α's increase geometrically or linearly. A particularly interesting case arises when the observations arrive at time points paced by a Poisson point process. For this model we obtain distributional results for the inter-arrival times of records for a large class of combinations of α structures and intensity functions.

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12

Hofmann, Glenn, та H. N. Nagaraja. "Random and Poisson paced record models in the F α setup". Journal of Applied Probability 37, № 02 (червень 2000): 374–88. http://dx.doi.org/10.1017/s0021900200015588.

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We study a random record model where the observation X i has continuous distribution function F α i (α i > 0) and the number of available observations is random and independent of the observations. We obtain the joint distribution of the record values and inter-record times for our model. We investigate the distribution of the number of records when the number of observations has one of the common distributions and the α's increase geometrically or linearly. A particularly interesting case arises when the observations arrive at time points paced by a Poisson point process. For this model we obtain distributional results for the inter-arrival times of records for a large class of combinations of α structures and intensity functions.

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13

Boldyrikhin, N. V., and V. V. Khutortsev. "Control of observations over random processes fluxes." Automation and Remote Control 67, no. 12 (December 2006): 1900–1912. http://dx.doi.org/10.1134/s0005117906120046.

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14

Eryilmaz, S. "Random threshold models based on multivariate observations." Journal of Statistical Planning and Inference 113, no. 2 (May 2003): 557–68. http://dx.doi.org/10.1016/s0378-3758(01)00319-6.

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15

Vo, Ba-Tuong, Ba-Ngu Vo, and Antonio Cantoni. "Bayesian Filtering With Random Finite Set Observations." IEEE Transactions on Signal Processing 56, no. 4 (April 2008): 1313–26. http://dx.doi.org/10.1109/tsp.2007.908968.

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16

Konopka, Jörg, and Norbert Schmitz. "Redundant observations at testing i.i.d. random variables." Statistical Papers 44, no. 2 (April 2003): 289. http://dx.doi.org/10.1007/bf03036359.

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17

Stein, Michael L. "Predicting random fields with increasing dense observations." Annals of Applied Probability 9, no. 1 (February 1999): 242–73. http://dx.doi.org/10.1214/aoap/1029962604.

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18

Konopka, Jörg, and Norbert Schmitz. "Redundant observations at testing i.i.d. random variables." Statistical Papers 43, no. 4 (October 2002): 595–602. http://dx.doi.org/10.1007/s00362-002-0127-6.

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19

Hill, Aaron J., Christopher C. Weiss, and Brian C. Ancell. "Factors Influencing Ensemble Sensitivity–Based Targeted Observing Predictions at Convection-Allowing Resolutions." Monthly Weather Review 148, no. 11 (November 2020): 4497–517. http://dx.doi.org/10.1175/mwr-d-20-0015.1.

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AbstractEnsemble sensitivity analysis (ESA) is applied to select types of observations, in various locations and in advance of forecast convection, to systematically evaluate the effectiveness of ESA-based observation targeting for 10 convection forecasts. To facilitate the analysis, observing system simulation experiments and perfect models are utilized to generate synthetic targeted observations of temperature and pressure for future assimilation with an ensemble prediction system. Various observation assimilation experiments are carried out to assess the impacts of nonlinearity, covariance localization, and numerical noise on ESA-based observation-impact predictions. It is discovered that localization applied during data assimilation restricts targeted-observation increments onto the forecast responses of composite reflectivity and 3-hourly accumulated precipitation, making impact predictions poor. In addition, numerical noise introduced by nonlinear perturbation evolution tends to reduce the correlations between observed and predicted impacts; small, random-perturbation experiments often yielded similar impacts on forecasts as targeted observations. Nonlinearity also manifests in the observation impacts when comparing targeted observations with nontargeted, randomly chosen observations; random observations have seemingly the same impact on forecasts as targeted observations. The results, under idealized conditions and simplified ensemble configurations, demonstrate that ESA-based targeting for nonlinear convection forecasts may be most applicable at short time scales. Important implications for ESA-based targeting methods employed with real-time ensemble systems are also discussed.

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20

Demers, Matthew, Herb Kunze, and Davide La Torre. "ON RANDOM ITERATED FUNCTION SYSTEMS WITH GREYSCALE MAPS." Image Analysis & Stereology 31, no. 2 (May 17, 2012): 109. http://dx.doi.org/10.5566/ias.v31.p109-120.

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In the theory of Iterated Function Systems (IFSs) it is known that one can find an IFS with greyscale maps (IFSM) to approximate any target signal or image with arbitrary precision, and a systematic approach for doing so was described. In this paper, we extend these ideas to the framework of random IFSM operators. We consider the situation where one has many noisy observations of a particular target signal and show that the greyscale map parameters for each individual observation inherit the noise distribution of the observation. We provide illustrative examples.

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21

Ying, Zu-guang, Rong-chun Hu, and Rong-hua Huan. "Stochastic Minimax Vibration Control for Uncertain Nonlinear Quasi-Hamiltonian Systems with Noisy Observations." International Journal of Acoustics and Vibration 24, no. 4 (December 31, 2019): 707–16. http://dx.doi.org/10.20855/ijav.2019.24.41446.

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A stochastic minimax control strategy for uncertain nonlinear quasi-Hamiltonian systems with noisy observations under random excitations is proposed based on the extended Kalman filter and minimax stochastic dynamical programming principle. A structure system with smart sensors and actuators is modeled as a controlled, excited and dissipative Hamiltonian system with noisy observations. The differential equations for the uncertain nonlinear quasi-Hamiltonian system with control and observation under random excitation are given first. The estimated nonlinear stochastic control system with uncertain parameters is obtained from the uncertain quasi-Hamiltonian system with noisy observation. In this case, the optimally estimated state is determined by the observation based on the extended Kalman filter. The dual dynamical programming equation for the estimated uncertain system is then obtained based on the minimax stochastic dynamical programming principle. The worst-case disturbances are determined for bounded uncertain parameters and the optimal control law is determined for the worst case by the programming equation. The proposed minimax control strategy is applied to two uncertain nonlinear stochastic systems with controls and noisy observations. The control effectiveness for the stochastic vibration response reductions of the systems is illustrated with numerical results. The proposed minimax control strategy is applicable to general uncertain nonlinear multi-degree-of-freedom structure systems with noisy observations under random excitations.

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22

Bosov, Alexey. "Tracking a Maneuvering Object by Indirect Observations with Random Delays." Drones 7, no. 7 (July 13, 2023): 468. http://dx.doi.org/10.3390/drones7070468.

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A mathematical model for the target tracking problem is proposed. The model makes it possible to describe conditions when the time for an observer to receive the results of indirect observations of a moving object depends not only on the state of the observation environment but also on the state of the object itself. The source of such a model is the observation process, by stationary means, of an autonomous underwater vehicle, in which the time for obtaining up-to-date data depends on the unknown distance between the object and the observer. As part of the study of the problem, the equations of the optimal Bayesian filter are obtained. But this filter is not possible to implement. For practical purposes, it is proposed to use the conditionally minimax nonlinear filter, which has shown promising results in other complex tracking models. The conditions for the filter’s evaluation and its accuracy characteristics are given. A large-scale numerical experiment illustrating the filter’s operation and the observation system’s features with random delays are described.

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23

Boguslavsky, I. A. "A Bayes Estimator of Parameters of Nonlinear Dynamic Systems." Mathematical Problems in Engineering 2009 (2009): 1–21. http://dx.doi.org/10.1155/2009/801475.

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A new multipolynomial approximations algorithm (the MPA algorithm) is proposed for estimating the state vectorθof virtually any dynamical (evolutionary) system. The input of the algorithm consists of discrete-time observationsY. An adjustment of the algorithm is required to the generation of arrays of random sequences of state vectors and observations scalars corresponding to a given sequence of time instants. The distributions of the random factors (vectors of the initial states and random perturbations of the system, scalars of random observational errors) can be arbitrary but have to be prescribed beforehand. The output of the algorithm is a vector polynomial series with respect to products of nonnegative integer powers of the results of real observations or some functions of these results. The sum of the powers does not exceed some given integerd. The series is a vector polynomial approximation of the vectorE(θ∣Y), which is the conditional expectation of the vector under evaluation (or given functions of the components of that vector). The vector coefficients of the polynomial series are constructed in such a way that the approximation errors uniformly tend to zero as the integerdincreases. These coefficients are found by the Monte-Carlo method and a process of recurrent calculations that do not require matrix inversion.

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24

Lacaze, Bernard, and Corinne Mailhes. "Random process reconstruction from multiple noisy source observations." Sampling Theory in Signal and Image Processing 3, no. 3 (September 2004): 257–77. http://dx.doi.org/10.1007/bf03549417.

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25

Sedlacek, William E. "Quasi-Random Observations of a Relatively New Editor." Measurement and Evaluation in Counseling and Development 18, no. 2 (July 1985): 50. http://dx.doi.org/10.1080/07481756.1985.12022789.

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26

Aidara Diouf, Alioune, Souleymane Sene, and Bassirou Lo. "New Magnetics Observations with a Random Exchange Interaction." American Journal of Electromagnetics and Applications 7, no. 2 (2019): 19. http://dx.doi.org/10.11648/j.ajea.20190702.12.

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27

Porosiński, Z. "Full-information best choice problems with imperfect observation and a random number of observations." Applicationes Mathematicae 21, no. 2 (1991): 179–92. http://dx.doi.org/10.4064/am-21-2-179-192.

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28

Mazalov, Vladimir, and Evgeny Ivashko. "Bayes' Model of the Best-Choice Problem with Disorder." International Journal of Stochastic Analysis 2012 (August 3, 2012): 1–8. http://dx.doi.org/10.1155/2012/697458.

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We consider the best-choice problem with disorder and imperfect observation. The decision-maker observes sequentially a known number of i.i.d random variables from a known distribution with the object of choosing the largest. At the random time the distribution law of observations is changed. The random variables cannot be perfectly observed. Each time a random variable is sampled the decision-maker is informed only whether it is greater than or less than some level specified by him. The decision-maker can choose at most one of the observation. The optimal rule is derived in the class of Bayes' strategies.

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29

Tian, Yongge. "A matrix handling of predictions of new observations under a general random-effects model." Electronic Journal of Linear Algebra 29 (September 20, 2015): 30–45. http://dx.doi.org/10.13001/1081-3810.2895.

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Assume that a general linear random-effects model $\by = \bX\bbe + \bve$ is given, and new observations in the future follow the linear model $\by_{\!f} = \bX_{\!f}\bbe + \bve_{\!f}$. This paper shows how to establish all possible best linear unbiased predictors (BLUPs) under the general linear random-effects model with original and new observations from the original observation vector $\by$ under a most general assumption on the covariance matrix among the random vectors $\bbe$, $\bve$ and $\bve_{\!f}$. It utilizes a standard method of solving optimization problem in the L\"owner partial ordering on a constrained quadratic matrix-valued function, and obtains analytical expressions of the BLUPs, including those for $\by_{\!f}$, $\bX_{\!f}\bbe$ and $\bve_{\!f}$. In particular, some fundamental equalities for the BLUPs are established under the linear random-effects model.

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30

Cho, Byungwoo, and Myungjin Cho. "Three-Dimensional Single Random Phase Encryption." Sensors 24, no. 6 (March 19, 2024): 1952. http://dx.doi.org/10.3390/s24061952.

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In this paper, we propose a new optical encryption technique that uses the single random phase mask. In conventional optical encryptions such as double random phase encryption (DRPE), two different random phase masks are required to encrypt the primary data. For decryption, DRPE requires taking the absolute value of the decrypted data because it is complex-valued. In addition, when key information is revealed, the primary data may be reconstructed by attackers. To reduce the number of random phase masks and enhance the security level, in this paper, we propose single random phase encryption (SRPE) with additive white Gaussian noise (AWGN) and volumetric computational reconstruction (VCR) of integral imaging. In our method, even if key information is known, the primary data may not be reconstructed. To enhance the visual quality of the decrypted data by SRPE, multiple observation is utilized. To reconstruct the primary data, we use VCR of integral imaging because it can remove AWGN by average effect. Thus, since the reconstruction depth can be another key piece of information of SRPE, the security level can be enhanced. In addition, it does not require taking the absolute value of the decrypted data for decryption. To verify the validity of our method, we implement the simulation and calculate performance metrics such as peak sidelobe ratio (PSR) and structural similarity (SSIM). In increasing the number of observations, SSIM for the decrypted data can be improved dramatically. Moreover, even if the number of observations is not enough, three-dimensional (3D) data can be decrypted by SRPE at the correct reconstruction depth.

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31

Nakonechnyi, O. G., and P. M. Zinko. "Estimates of matrix solutions of operator equations with random parameters under uncertainties." Matematychni Studii 60, no. 2 (December 18, 2023): 208–22. http://dx.doi.org/10.30970/ms.60.2.208-222.

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We investigate problems of estimating solutions of linear operator equations with random parameters under conditions of uncertainty. We establish that the guaranteed rms estimates of the matrices are found as solutions of special optimization problems under certain observations of the system state. As the output signals of the system, we have observations that are described by linear functions from the solutions of such equations with random right-hand sides, which have unknown second moments. Under the condition that the observation second moments of the right-hand parts and errors belong to certain sets, it is proved that the guaranteed estimates are expressed through solutions of operator equation systems. When the linear operator is given by the scalar product of rectangular matrices, a quasi-minimax estimate and its error are constructed. It is shown that the quasi-minimax estimation error tends to zero when the number of observations tends to infinity. An example of calculating the guaranteed rms estimate of the matrix's trace, which is a solution of a matrix equation with a random parameter, is given.

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32

Harbitz, Alf, and Michaela Aschan. "A two-dimensional geostatistic method to simulate the precision of abundance estimates." Canadian Journal of Fisheries and Aquatic Sciences 60, no. 12 (December 1, 2003): 1539–51. http://dx.doi.org/10.1139/f03-134.

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In this paper, we outline a geostatistic method to simulate the relative precision (coefficient of variation, CV) of total abundance estimates of one species in a predetermined, stratified area when it is appropriate to treat the observations within each stratum as realizations of a second-order homogenous and ergodic random process. To model the spatial correlations, a variogram is fitted to normal-transformed values of the original observations. Based on the variogram and its corresponding covariance matrix, extensive simulations on a fine grid that includes the sample locations provide random realizations of the process. The normal values are back-transformed to original observation space by nonparametric reversed bootstrap, as well as by a parametric Weibull approach. The method is applied to a total of 1069 shrimp (Pandalus borealis) abundance observations from 11 annual surveys in the Barents Sea (1992–2002) where a 20 nautical mile sampling grid has been applied. On average, the CV was estimated to be 6.4% for the applied regular grid when the simulations were conditional on the observations, compared with 8.1% when the sampling locations within each of the six strata were random.

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33

Zamo, Michaël, Liliane Bel, Olivier Mestre, and Joël Stein. "Improved Gridded Wind Speed Forecasts by Statistical Postprocessing of Numerical Models with Block Regression." Weather and Forecasting 31, no. 6 (December 1, 2016): 1929–45. http://dx.doi.org/10.1175/waf-d-16-0052.1.

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Abstract Numerical weather forecast errors are routinely corrected through statistical postprocessing by several national weather services. These statistical postprocessing methods build a regression function called model output statistics (MOS) between observations and forecasts that is based on an archive of past forecasts and associated observations. Because of limited spatial coverage of most near-surface parameter measurements, MOS have been historically produced only at meteorological station locations. Nevertheless, forecasters and forecast users increasingly ask for improved gridded forecasts. The present work aims at building improved hourly wind speed forecasts over the grid of a numerical weather prediction model. First, a new observational analysis, which performs better in terms of statistical scores than those operationally used at Météo-France, is described as gridded pseudo-observations. This analysis, which is obtained by using an interpolation strategy that was selected among other alternative strategies after an intercomparison study conducted internally at Météo-France, is very parsimonious since it requires only two additive components, and it requires little computational resources. Then, several scalar regression methods are built and compared, using the new analysis as the observation. The most efficient MOS is based on random forests trained on blocks of nearby grid points. This method greatly improves forecasts compared with raw output of numerical weather prediction models. Furthermore, building each random forest on blocks and limiting those forests to shallow trees does not impair performance compared with unpruned and pointwise random forests. This alleviates the storage burden of the objects and speeds up operations.

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34

Loskot, Pavel. "Polynomial Representations of High-Dimensional Observations of Random Processes." Mathematics 9, no. 2 (January 7, 2021): 123. http://dx.doi.org/10.3390/math9020123.

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The paper investigates the problem of performing a correlation analysis when the number of observations is large. In such a case, it is often necessary to combine random observations to achieve dimensionality reduction of the problem. A novel class of statistical measures is obtained by approximating the Taylor expansion of a general multivariate scalar symmetric function by a univariate polynomial in the variable given as a simple sum of the original random variables. The mean value of the polynomial is then a weighted sum of statistical central sum-moments with the weights being application dependent. Computing the sum-moments is computationally efficient and amenable to mathematical analysis, provided that the distribution of the sum of random variables can be obtained. Among several auxiliary results also obtained, the first order sum-moments corresponding to sample means are used to reduce the numerical complexity of linear regression by partitioning the data into disjoint subsets. Illustrative examples provided assume the first and the second order Markov processes.

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35

Loskot, Pavel. "Polynomial Representations of High-Dimensional Observations of Random Processes." Mathematics 9, no. 2 (January 7, 2021): 123. http://dx.doi.org/10.3390/math9020123.

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Анотація:

The paper investigates the problem of performing a correlation analysis when the number of observations is large. In such a case, it is often necessary to combine random observations to achieve dimensionality reduction of the problem. A novel class of statistical measures is obtained by approximating the Taylor expansion of a general multivariate scalar symmetric function by a univariate polynomial in the variable given as a simple sum of the original random variables. The mean value of the polynomial is then a weighted sum of statistical central sum-moments with the weights being application dependent. Computing the sum-moments is computationally efficient and amenable to mathematical analysis, provided that the distribution of the sum of random variables can be obtained. Among several auxiliary results also obtained, the first order sum-moments corresponding to sample means are used to reduce the numerical complexity of linear regression by partitioning the data into disjoint subsets. Illustrative examples provided assume the first and the second order Markov processes.

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36

Matamoros, Javier, and Carles Anton-Haro. "Estimation of Spatially-Correlated Random Fields With Compressed Observations." IEEE Transactions on Wireless Communications 13, no. 12 (December 2014): 6542–56. http://dx.doi.org/10.1109/twc.2014.2362750.

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37

Fowler, K. "From the editor's bench - Some "random" observations and comments." IEEE Instrumentation & Measurement Magazine 8, no. 5 (December 2005): 4–6. http://dx.doi.org/10.1109/mim.2005.1578605.

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38

Šaltyte, J., and K. Dučinskas. "STATISTICAL CLASSIFICATION BASED ON OBSERVATIONS OF RANDOM GAUSSIAN FIELDS." Mathematical Modelling and Analysis 4, no. 1 (December 15, 1999): 153–62. http://dx.doi.org/10.3846/13926292.1999.9637120.

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The problem of classification of objects located in domain D ⊂ R2 based on observations of random Gaussian fields with a factorized covariance function is considered. The first‐order asymptotic expansion for the expected error regret is presented. Obtained numerical results allow us to compare suggested expansion for some widely applicable models of spatial covariance function.

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39

Gouet, Raúl, F. Javier López, and Gerardo Sanz. "Records from stationary observations subject to a random trend." Advances in Applied Probability 47, no. 4 (December 2015): 1175–89. http://dx.doi.org/10.1239/aap/1449859805.

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Анотація:

We prove strong convergence and asymptotic normality for the record and the weak record rate of observations of the form Yn = Xn + Tn, n ≥ 1, where (Xn)n ∈ Z is a stationary ergodic sequence of random variables and (Tn)n ≥ 1 is a stochastic trend process with stationary ergodic increments. The strong convergence result follows from the Dubins-Freedman law of large numbers and Birkhoff's ergodic theorem. For the asymptotic normality we rely on the approach of Ballerini and Resnick (1987), coupled with a moment bound for stationary sequences, which is used to deal with the random trend process. Examples of applications are provided. In particular, we obtain strong convergence and asymptotic normality for the number of ladder epochs in a random walk with stationary ergodic increments.

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40

Kimble, Gerald W. "Observations on the generation of permutations from random sequences." International Journal of Computer Mathematics 29, no. 1 (January 1989): 11–19. http://dx.doi.org/10.1080/00207168908803745.

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41

Barsotti, Flavia, Anne Philippe, and Paul Rochet. "Hypothesis testing for Markovian models with random time observations." Journal of Statistical Planning and Inference 173 (June 2016): 87–98. http://dx.doi.org/10.1016/j.jspi.2015.12.009.

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42

Chaikin, P. M., Aleksandar Donev, Weining Man, Frank H. Stillinger, and Salvatore Torquato. "Some Observations on the Random Packing of Hard Ellipsoids." Industrial & Engineering Chemistry Research 45, no. 21 (October 2006): 6960–65. http://dx.doi.org/10.1021/ie060032g.

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43

Gouet, Raúl, F. Javier López, and Gerardo Sanz. "Records from stationary observations subject to a random trend." Advances in Applied Probability 47, no. 04 (December 2015): 1175–89. http://dx.doi.org/10.1017/s0001867800049065.

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Анотація:

We prove strong convergence and asymptotic normality for the record and the weak record rate of observations of the form Y n = X n + T n , n ≥ 1, where (X n ) n ∈ Z is a stationary ergodic sequence of random variables and (T n ) n ≥ 1 is a stochastic trend process with stationary ergodic increments. The strong convergence result follows from the Dubins-Freedman law of large numbers and Birkhoff's ergodic theorem. For the asymptotic normality we rely on the approach of Ballerini and Resnick (1987), coupled with a moment bound for stationary sequences, which is used to deal with the random trend process. Examples of applications are provided. In particular, we obtain strong convergence and asymptotic normality for the number of ladder epochs in a random walk with stationary ergodic increments.

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44

Basrak, Bojan, and Drago Špoljarić. "On randomly spaced observations and continuous-time random walks." Journal of Applied Probability 53, no. 3 (September 2016): 888–98. http://dx.doi.org/10.1017/jpr.2016.47.

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Анотація:

AbstractWe consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy-tailed steps, the limiting behavior of extreme observations until a given time t tends to be rather involved. We describe the asymptotics and extend several partial results which appeared in this setting. The theory is applied to determine the asymptotic distribution of maximal excursions and sojourn times for continuous-time random walks.

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45

Gajic, Z., and H. Khalil. "Multimodel strategies under random disturbances and imperfect partial observations." Automatica 22, no. 1 (January 1986): 121–25. http://dx.doi.org/10.1016/0005-1098(86)90113-5.

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46

Boyarchenko, Svetlana, and Sergei Levendorskiĭ. "Optimal Stopping Problems in Lévy Models with Random Observations." Acta Applicandae Mathematicae 163, no. 1 (September 19, 2018): 19–48. http://dx.doi.org/10.1007/s10440-018-0212-z.

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47

Pikovsky, A. "Reconstruction of a random phase dynamics network from observations." Physics Letters A 382, no. 4 (January 2018): 147–52. http://dx.doi.org/10.1016/j.physleta.2017.11.012.

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48

Zhang, Yingzhuo, Noa Malem-Shinitski, Stephen A. Allsop, Kay M. Tye, and Demba Ba. "Estimating a Separably Markov Random Field from Binary Observations." Neural Computation 30, no. 4 (April 2018): 1046–79. http://dx.doi.org/10.1162/neco_a_01059.

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Анотація:

A fundamental problem in neuroscience is to characterize the dynamics of spiking from the neurons in a circuit that is involved in learning about a stimulus or a contingency. A key limitation of current methods to analyze neural spiking data is the need to collapse neural activity over time or trials, which may cause the loss of information pertinent to understanding the function of a neuron or circuit. We introduce a new method that can determine not only the trial-to-trial dynamics that accompany the learning of a contingency by a neuron, but also the latency of this learning with respect to the onset of a conditioned stimulus. The backbone of the method is a separable two-dimensional (2D) random field (RF) model of neural spike rasters, in which the joint conditional intensity function of a neuron over time and trials depends on two latent Markovian state sequences that evolve separately but in parallel. Classical tools to estimate state-space models cannot be applied readily to our 2D separable RF model. We develop efficient statistical and computational tools to estimate the parameters of the separable 2D RF model. We apply these to data collected from neurons in the prefrontal cortex in an experiment designed to characterize the neural underpinnings of the associative learning of fear in mice. Overall, the separable 2D RF model provides a detailed, interpretable characterization of the dynamics of neural spiking that accompany the learning of a contingency.

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49

Koskinen, Johan, Peng Wang, Garry Robins, and Philippa Pattison. "Outliers and Influential Observations in Exponential Random Graph Models." Psychometrika 83, no. 4 (September 18, 2018): 809–30. http://dx.doi.org/10.1007/s11336-018-9635-8.

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50

Agarwal, Ravi P., Jewgeni H. Dshalalow, and Donal O'Regan. "Random observations of marked Cox processes. Time insensitive functionals." Journal of Mathematical Analysis and Applications 293, no. 1 (May 2004): 1–13. http://dx.doi.org/10.1016/j.jmaa.2003.12.040.

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