23,304 research outputs found
Recursive Parameter Estimation: Convergence
We consider estimation procedures which are recursive in the sense that each
successive estimator is obtained from the previous one by a simple adjustment.
We propose a wide class of recursive estimation procedures for the general
statistical model and study convergence.Comment: 25 pages with 1 postscript figur
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Dual state-parameter estimation of hydrological models using ensemble Kalman filter
Hydrologic models are twofold: models for understanding physical processes and models for prediction. This study addresses the latter, which modelers use to predict, for example, streamflow at some future time given knowledge of the current state of the system and model parameters. In this respect, good estimates of the parameters and state variables are needed to enable the model to generate accurate forecasts. In this paper, a dual state-parameter estimation approach is presented based on the Ensemble Kalman Filter (EnKF) for sequential estimation of both parameters and state variables of a hydrologic model. A systematic approach for identification of the perturbation factors used for ensemble generation and for selection of ensemble size is discussed. The dual EnKF methodology introduces a number of novel features: (1) both model states and parameters can be estimated simultaneously; (2) the algorithm is recursive and therefore does not require storage of all past information, as is the case in the batch calibration procedures; and (3) the various sources of uncertainties can be properly addressed, including input, output, and parameter uncertainties. The applicability and usefulness of the dual EnKF approach for ensemble streamflow forecasting is demonstrated using a conceptual rainfall-runoff model. © 2004 Elsevier Ltd. All rights reserved
A Penalty Approach to Differential Item Functioning in Rasch Models
A new diagnostic tool for the identification of differential item functioning (DIF) is proposed. Classical approaches to DIF allow to consider only few subpopulations like ethnic groups when investigating if the solution of items depends on the membership to a subpopulation. We propose an explicit model for differential item functioning that includes a set of variables, containing metric as well as categorical components, as potential candidates for inducing DIF. The ability to include a set of covariates entails that the model contains a large number of parameters. Regularized estimators, in particular penalized maximum likelihood estimators, are used
to solve the estimation problem and to identify the items that induce DIF. It is shown that the method is able to detect items with DIF. Simulations and two applications demonstrate the applicability of the method
A fast and recursive algorithm for clustering large datasets with -medians
Clustering with fast algorithms large samples of high dimensional data is an
important challenge in computational statistics. Borrowing ideas from MacQueen
(1967) who introduced a sequential version of the -means algorithm, a new
class of recursive stochastic gradient algorithms designed for the -medians
loss criterion is proposed. By their recursive nature, these algorithms are
very fast and are well adapted to deal with large samples of data that are
allowed to arrive sequentially. It is proved that the stochastic gradient
algorithm converges almost surely to the set of stationary points of the
underlying loss criterion. A particular attention is paid to the averaged
versions, which are known to have better performances, and a data-driven
procedure that allows automatic selection of the value of the descent step is
proposed.
The performance of the averaged sequential estimator is compared on a
simulation study, both in terms of computation speed and accuracy of the
estimations, with more classical partitioning techniques such as -means,
trimmed -means and PAM (partitioning around medoids). Finally, this new
online clustering technique is illustrated on determining television audience
profiles with a sample of more than 5000 individual television audiences
measured every minute over a period of 24 hours.Comment: Under revision for Computational Statistics and Data Analysi
Polynomial tuning of multiparametric combinatorial samplers
Boltzmann samplers and the recursive method are prominent algorithmic
frameworks for the approximate-size and exact-size random generation of large
combinatorial structures, such as maps, tilings, RNA sequences or various
tree-like structures. In their multiparametric variants, these samplers allow
to control the profile of expected values corresponding to multiple
combinatorial parameters. One can control, for instance, the number of leaves,
profile of node degrees in trees or the number of certain subpatterns in
strings. However, such a flexible control requires an additional non-trivial
tuning procedure. In this paper, we propose an efficient polynomial-time, with
respect to the number of tuned parameters, tuning algorithm based on convex
optimisation techniques. Finally, we illustrate the efficiency of our approach
using several applications of rational, algebraic and P\'olya structures
including polyomino tilings with prescribed tile frequencies, planar trees with
a given specific node degree distribution, and weighted partitions.Comment: Extended abstract, accepted to ANALCO2018. 20 pages, 6 figures,
colours. Implementation and examples are available at [1]
https://github.com/maciej-bendkowski/boltzmann-brain [2]
https://github.com/maciej-bendkowski/multiparametric-combinatorial-sampler
How well can we guess theoretical uncertainties?
The problem of estimating the effect of missing higher orders in perturbation
theory is analyzed with emphasis in the application to Higgs production in
gluon-gluon fusion. Well-known mathematical methods for an approximated
completion of the perturbative series are applied with the goal to not truncate
the series, but complete it in a well-defined way, so as to increase the
accuracy - if not the precision - of theoretical predictions. The uncertainty
arising from the use of the completion procedure is discussed and a recipe for
constructing a corresponding probability distribution function is proposed
Control of flexible joint robotic manipulator using tuning functions design
The goal of this thesis is to design the controller for a single arm manipulator having a flexible joint for the tracking problem in two different cases. A controller is designed for a deterministic case wherein the plant parameters are assumed to be known while another is designed for an adaptive case where all the plant parameters are assumed to be unknown. In general the tracking problem is; given a smooth reference trajectory, the end effector has to track the reference while maintaining the stability. It is assumed that only the output of the manipulator, which is the link angle, is available for measurement. Also without loss of generality, the fast dynamics, that is the dynamics of the driver side of the system are neglected for the sake of simplicity; In the first case, the design procedure adopted is called observer backstepping. Since the states of the system are unavailable for measurement, an observer is designed that estimates the system states. These estimates are fed to the controller which in turn produces the control input to the system; The second case employs a design procedure called tuning functions design. In this case, since the plant parameters are unknown, the observer designed in case one cannot be used for determining the state estimates. For this purpose, parameter update laws and filters are designed for estimation of plant parameters. The filters employed are k-filters. The k-filters and the parameter update laws are given as input to the controller, which generates the control input to the system; For both cases, the mathematical models are simulated using Matlab/Simulink, and the results are verified
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