Search results for: Likelihood

Authors: Yilun Shang

Abstract:

We consider a heterogeneously mixing SIR stochastic epidemic process in populations described by a general graph. Likelihood theory is developed to facilitate statistic inference for the parameters of the model under complete observation. We show that these estimators are asymptotically Gaussian unbiased estimates by using a martingale central limit theorem.

Keywords: statistic inference, maximum likelihood, epidemicmodel, heterogeneous mixing.

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Authors: Naushad Mamode Khan

Abstract:

The Com-Poisson (CMP) model is one of the most popular discrete generalized linear models (GLMS) that handles both equi-, over- and under-dispersed data. In longitudinal context, an integer-valued autoregressive (INAR(1)) process that incorporates covariate specification has been developed to model longitudinal CMP counts. However, the joint likelihood CMP function is difficult to specify and thus restricts the likelihood-based estimating methodology. The joint generalized quasi-likelihood approach (GQL-I) was instead considered but is rather computationally intensive and may not even estimate the regression effects due to a complex and frequently ill-conditioned covariance structure. This paper proposes a new GQL approach for estimating the regression parameters (GQL-III) that is based on a single score vector representation. The performance of GQL-III is compared with GQL-I and separate marginal GQLs (GQL-II) through some simulation experiments and is proved to yield equally efficient estimates as GQL-I and is far more computationally stable.

Keywords: Longitudinal, Com-Poisson, Ill-conditioned, INAR(1), GLMS, GQL.

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Authors: M. Tridi, N. Nacereddine, N. Oucief

Abstract:

This paper describes a novel method for automatic estimation of the contours of weld defect in radiography images. Generally, the contour detection is the first operation which we apply in the visual recognition system. Our approach can be described as a region based maximum likelihood formulation of parametric deformable contours. This formulation provides robustness against the poor image quality, and allows simultaneous estimation of the contour parameters together with other parameters of the model. Implementation is performed by a deterministic iterative algorithm with minimal user intervention. Results testify for the very good performance of the approach especially in synthetic weld defect images.

Keywords: Contour, gaussian, likelihood, rayleigh.

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Authors: Ing-Jr Ding

Abstract:

This paper presents a technical speaker adaptation method called WMLLR, which is based on maximum likelihood linear regression (MLLR). In MLLR, a linear regression-based transform which adapted the HMM mean vectors was calculated to maximize the likelihood of adaptation data. In this paper, the prior knowledge of the initial model is adequately incorporated into the adaptation. A series of speaker adaptation experiments are carried out at a 30 famous city names database to investigate the efficiency of the proposed method. Experimental results show that the WMLLR method outperforms the conventional MLLR method, especially when only few utterances from a new speaker are available for adaptation.

Keywords: hidden Markov model, maximum likelihood linearregression, speech recognition, speaker adaptation.

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Authors: N. Feroze, M. Aslam

Abstract:

The paper deals with the maximum likelihood estimation of the parameters of the Burr type V distribution based on left censored samples. The maximum likelihood estimators (MLE) of the parameters have been derived and the Fisher information matrix for the parameters of the said distribution has been obtained explicitly. The confidence intervals for the parameters have also been discussed. A simulation study has been conducted to investigate the performance of the point and interval estimates.

Keywords: Fisher information matrix, confidence intervals, censoring.

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Authors: Chie Obayashi, Hidekazu Tanaka, Yoshiji Takagi

Abstract:

In multi-parameter family of distributions, conditions for a modified maximum likelihood estimator to be second order admissible are given. Applying these results to the multi-parameter logistic regression model, it is shown that the maximum likelihood estimator is always second order inadmissible. Also, conditions for the Berkson estimator to be second order admissible are given.

Keywords: Berkson estimator, modified maximum likelihood estimator, Multi-parameter logistic regression model, second order admissibility.

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Authors: N. Mamode Khan, V. Jowaheer

Abstract:

In this paper, we apply and compare two generalized estimating equation approaches to the analysis of car breakdowns data in Mauritius. Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observation as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use the two types of quasi-likelihood estimation approaches to estimate the parameters of the model: marginal and joint generalized quasi-likelihood estimating equation approaches. Under-dispersion parameter is estimated to be around 2.14 justifying the appropriateness of Com-Poisson distribution in modelling underdispersed count responses recorded in this study.

Keywords: Breakdowns, under-dispersion, com-poisson, generalized linear model, marginal quasi-likelihood estimation, joint quasi-likelihood estimation.

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Authors: I. V. Pinto, M. R. Sooriyarachchi

Abstract:

It can be frequently observed that the data arising in our environment have a hierarchical or a nested structure attached with the data. Multilevel modelling is a modern approach to handle this kind of data. When multilevel modelling is combined with a binary response, the estimation methods get complex in nature and the usual techniques are derived from quasi-likelihood method. The estimation methods which are compared in this study are, marginal quasi-likelihood (order 1 & order 2) (MQL1, MQL2) and penalized quasi-likelihood (order 1 & order 2) (PQL1, PQL2). A statistical model is of no use if it does not reflect the given dataset. Therefore, checking the adequacy of the fitted model through a goodness-of-fit (GOF) test is an essential stage in any modelling procedure. However, prior to usage, it is also equally important to confirm that the GOF test performs well and is suitable for the given model. This study assesses the suitability of the GOF test developed for binary response multilevel models with respect to the method used in model estimation. An extensive set of simulations was conducted using MLwiN (v 2.19) with varying number of clusters, cluster sizes and intra cluster correlations. The test maintained the desirable Type-I error for models estimated using PQL2 and it failed for almost all the combinations of MQL. Power of the test was adequate for most of the combinations in all estimation methods except MQL1. Moreover, models were fitted using the four methods to a real-life dataset and performance of the test was compared for each model.

Keywords: Goodness-of-fit test, marginal quasi-likelihood, multilevel modelling, type-I error, penalized quasi-likelihood, power, quasi-likelihood.

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Authors: Yohei Saika, Yuji Haraguchi

Abstract:

We constructed a method of noise reduction for JPEG-compressed image based on Bayesian inference using the maximizer of the posterior marginal (MPM) estimate. In this method, we tried the MPM estimate using two kinds of likelihood, both of which enhance grayscale images converted into the JPEG-compressed image through the lossy JPEG image compression. One is the deterministic model of the likelihood and the other is the probabilistic one expressed by the Gaussian distribution. Then, using the Monte Carlo simulation for grayscale images, such as the 256-grayscale standard image “Lena" with 256 × 256 pixels, we examined the performance of the MPM estimate based on the performance measure using the mean square error. We clarified that the MPM estimate via the Gaussian probabilistic model of the likelihood is effective for reducing noises, such as the blocking artifacts and the mosquito noise, if we set parameters appropriately. On the other hand, we found that the MPM estimate via the deterministic model of the likelihood is not effective for noise reduction due to the low acceptance ratio of the Metropolis algorithm.

Keywords: Noise reduction, JPEG-compressed image, Bayesian inference, the maximizer of the posterior marginal estimate

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Authors: Rakesh Kumar, A. K. Ghosh

Abstract:

The paper presents the modeling of nonlinear longitudinal aerodynamics using flight data of Hansa-3 aircraft at high angles of attack near stall. The Kirchhoff-s quasi-steady stall model has been used to incorporate nonlinear aerodynamic effects in the aerodynamic model used to estimate the parameters, thereby, making the aerodynamic model nonlinear. The Maximum Likelihood method has been applied to the flight data (at high angles of attack) for the estimation of parameters (aerodynamic and stall characteristics) using the nonlinear aerodynamic model. To improve the accuracy level of the estimates, an approach of fixing the strong parameters has also been presented.

Keywords: Maximum Likelihood, nonlinear, parameters, stall.

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Authors: Young-Hwan Song, Doo-Heon Kyun, Jong-Kuk Kim, Myung-Jin Bae

Abstract:

People have the habitual pitch level which is used when people say something generally. However this pitch should be changed irregularly in the presence of noise. So it is useful to estimate SNR of speech signal by pitch. In this paper, we obtain the energy of input speech signal and then we detect a stationary region on voiced speech. And we get the pitch period by NAMDF for the stationary region that is not varied pitch rapidly. After getting pitch, each frame is divided by pitch period and the likelihood of closed pitch is estimated. In this paper, we proposed new parameter, NLF, to estimate the SNR of received speech signal. The NLF is derived from the correlation of near pitch periods. The NLF is obtained for each stationary region in voiced speech. Finally we confirmed good performance of the estimation of the SNR of received input speech in the presence of noise.

Keywords: Likelihood, pitch, SNR, speech.

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Authors: Vandna Jowaheer, Naushad A. Mamode Khan

Abstract:

Com Poisson distribution is capable of modeling the count responses irrespective of their mean variance relation and the parameters of this distribution when fitted to a simple cross sectional data can be efficiently estimated using maximum likelihood (ML) method. In the regression setup, however, ML estimation of the parameters of the Com Poisson based generalized linear model is computationally intensive. In this paper, we propose to use quasilikelihood (QL) approach to estimate the effect of the covariates on the Com Poisson counts and investigate the performance of this method with respect to the ML method. QL estimates are consistent and almost as efficient as ML estimates. The simulation studies show that the efficiency loss in the estimation of all the parameters using QL approach as compared to ML approach is quite negligible, whereas QL approach is lesser involving than ML approach.

Keywords: Com Poisson, Cross-sectional, Maximum Likelihood, Quasi likelihood

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Authors: D. A. Farinde

Abstract:

In this paper, two-sided uniformly normal distribution techniques were used in the derivation of monotone likelihood ratio. The approach mainly employed the parameters of the distribution for a class of all size a. The derivation technique is fast, direct and less burdensome when compared to some existing methods.

Keywords: Neyman-Pearson Lemma, Normal distribution

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Authors: Hadeel Salim Alkutubi

Abstract:

The objective of this study is to introduce estimators to the parameters and survival function for Weibull distribution using three different methods, Maximum Likelihood estimation, Standard Bayes estimation and Modified Bayes estimation. We will then compared the three methods using simulation study to find the best one base on MPE and MSE.

Keywords: Maximum Likelihood estimation , Bayes estimation, Jeffery prior information, Simulation study

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Authors: Autcha Araveeporn

Abstract:

The Random Coefficient Dynamic Regression (RCDR) model is to developed from Random Coefficient Autoregressive (RCA) model and Autoregressive (AR) model. The RCDR model is considered by adding exogenous variables to RCA model. In this paper, the concept of the Maximum Likelihood (ML) method is used to estimate the parameter of RCDR(1,1) model. Simulation results have shown the AIC and BIC criterion to compare the performance of the the RCDR(1,1) model. The variables as the stationary and weakly stationary data are good estimates where the exogenous variables are weakly stationary. However, the model selection indicated that variables are nonstationarity data based on the stationary data of the exogenous variables.

Keywords: Autoregressive, Maximum Likelihood Method, Nonstationarity, Random Coefficient Dynamic Regression, Stationary.

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Authors: Sunusi N., Kresna A. J., Islamiyati A., Raupong

Abstract:

Hazard rate estimation is one of the important topics in forecasting earthquake occurrence. Forecasting earthquake occurrence is a part of the statistical seismology where the main subject is the point process. Generally, earthquake hazard rate is estimated based on the point process likelihood equation called the Hazard Rate Likelihood of Point Process (HRLPP). In this research, we have developed estimation method, that is hazard rate single decrement HRSD. This method was adapted from estimation method in actuarial studies. Here, one individual associated with an earthquake with inter event time is exponentially distributed. The information of epicenter and time of earthquake occurrence are used to estimate hazard rate. At the end, a case study of earthquake hazard rate will be given. Furthermore, we compare the hazard rate between HRLPP and HRSD method.

Keywords: Earthquake forecast, Hazard Rate, Likelihood point process, Point process.

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Authors: Ilaria Lucrezia Amerise

Abstract:

The statistical modelling of precipitation data for a given portion of territory is fundamental for the monitoring of climatic conditions and for Hydrogeological Management Plans (HMP). This modelling is rendered particularly complex by the changes taking place in the frequency and intensity of precipitation, presumably to be attributed to the global climate change. This paper applies the Wakeby distribution (with 5 parameters) as a theoretical reference model. The number and the quality of the parameters indicate that this distribution may be the appropriate choice for the interpolations of the hydrological variables and, moreover, the Wakeby is particularly suitable for describing phenomena producing heavy tails. The proposed estimation methods for determining the value of the Wakeby parameters are the same as those used for density functions with heavy tails. The commonly used procedure is the classic method of moments weighed with probabilities (probability weighted moments, PWM) although this has often shown difficulty of convergence, or rather, convergence to a configuration of inappropriate parameters. In this paper, we analyze the problem of the likelihood estimation of a random variable expressed through its quantile function. The method of maximum likelihood, in this case, is more demanding than in the situations of more usual estimation. The reasons for this lie, in the sampling and asymptotic properties of the estimators of maximum likelihood which improve the estimates obtained with indications of their variability and, therefore, their accuracy and reliability. These features are highly appreciated in contexts where poor decisions, attributable to an inefficient or incomplete information base, can cause serious damages.

Keywords: Generalized extreme values (GEV), likelihood estimation, precipitation data, Wakeby distribution.

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Authors: Cheng-Chieh Chiang, Yi-Chia Chan, Greg C. Lee

Abstract:

This paper proposes a video-based framework for face recognition to identify which faces appear in a video sequence. Our basic idea is like a tracking task - to track a selection of person candidates over time according to the observing visual features of face images in video frames. Hence, we employ the state-space model to formulate video-based face recognition by dividing this problem into two parts: the likelihood and the transition measures. The likelihood measure is to recognize whose face is currently being observed in video frames, for which two-dimensional linear discriminant analysis is employed. The transition measure estimates the probability of changing from an incorrect recognition at the previous stage to the correct person at the current stage. Moreover, extra nodes associated with head nodes are incorporated into our proposed state-space model. The experimental results are also provided to demonstrate the robustness and efficiency of our proposed approach.

Keywords: 2DLDA, face recognition, state-space model, likelihood measure, transition measure.

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Authors: H.Panahi, S.Asadi

Abstract:

In this article, we consider the estimation of P[Y < X], when strength, X and stress, Y are two independent variables of Burr Type XII distribution. The MLE of the R based on one simple iterative procedure is obtained. Assuming that the common parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are discussed. The exact confidence interval of the R is also obtained. Monte Carlo simulations are performed to compare the different proposed methods.

Keywords: Stress-Strength model, Maximum likelihood estimator, Bayes estimator, Burr type XII distribution.

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Authors: Abdullah Y. Al-Hossain

Abstract:

This paper considers inference under progressive type II censoring with a compound Rayleigh failure time distribution. The maximum likelihood (ML), and Bayes methods are used for estimating the unknown parameters as well as some lifetime parameters, namely reliability and hazard functions. We obtained Bayes estimators using the conjugate priors for two shape and scale parameters. When the two parameters are unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We use Lindley.s approximation to compute the Bayes estimates. Another Bayes estimator has been obtained based on continuous-discrete joint prior for the unknown parameters. An example with the real data is discussed to illustrate the proposed method. Finally, we made comparisons between these estimators and the maximum likelihood estimators using a Monte Carlo simulation study.

Keywords: Progressive type II censoring, compound Rayleigh failure time distribution, maximum likelihood estimation, Bayes estimation, Lindley's approximation method, Monte Carlo simulation.

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Authors: Gamze Ozel, Selen Cakmakyapan

Abstract:

We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study. 

Keywords: Marshall-Olkin distribution, Rayleigh distribution, estimation, maximum likelihood.

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Authors: L. Lindsay, S. A. Coleman, D. Kerr, B. J. Taylor, A. Moorhead

Abstract:

Cognitive decline and frailty is apparent in older adults leading to an increased likelihood of the risk of falling. Currently health care professionals have to make professional decisions regarding such risks, and hence make difficult decisions regarding the future welfare of the ageing population. This study uses health data from The Irish Longitudinal Study on Ageing (TILDA), focusing on adults over the age of 50 years, in order to analyse health risk factors and predict the likelihood of falls. This prediction is based on the use of machine learning algorithms whereby health risk factors are used as inputs to predict the likelihood of falling. Initial results show that health risk factors such as long-term health issues contribute to the number of falls. The identification of such health risk factors has the potential to inform health and social care professionals, older people and their family members in order to mitigate daily living risks.

Keywords: Classification, falls, health risk factors, machine learning, older adults.

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Authors: Khunsa Fatima, Umar K. Khattak, Allah Bakhsh Kausar

Abstract:

Satellite images interpretation and analysis assist geologists by providing valuable information about geology and minerals of an area to be surveyed. A test site in Fatejang of district Attock has been studied using Landsat ETM+ and ASTER satellite images for lithological mapping. Five different supervised image classification techniques namely maximum likelihood, parallelepiped, minimum distance to mean, mahalanobis distance and spectral angle mapper have been performed upon both satellite data images to find out the suitable classification technique for lithological mapping in the study area. Results of these five image classification techniques were compared with the geological map produced by Geological Survey of Pakistan. Result of maximum likelihood classification technique applied on ASTER satellite image has highest correlation of 0.66 with the geological map. Field observations and XRD spectra of field samples also verified the results. A lithological map was then prepared based on the maximum likelihood classification of ASTER satellite image.

Keywords: ASTER, Landsat-ETM+, Satellite, Image classification.

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Authors: Y. N. Phang, E. F. Loh

Abstract:

Zero inflated Strict Arcsine model is a newly developed model which is found to be appropriate in modeling overdispersed count data. In this study, maximum likelihood estimation method is used in estimating the parameters for zero inflated strict arcsine model. Bootstrapping is then employed to compute the confidence intervals for the estimated parameters.

Keywords: overdispersed count data, maximum likelihood estimation, simulated annealing, BCa confidence intervals.

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Authors: Abd El Hady N. Ebraheim

Abstract:

This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: Exponentiated, Inversion Method, Maximum Likelihood Estimation, Transmutation Map.

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Authors: Mounira RouaÐùnia, Noureddine Doghmane

Abstract:

In this paper we consider the problem of change detection and non stationary signals tracking. Using parametric estimation of signals based on least square lattice adaptive filters we consider for change detection statistical parametric methods using likelihood ratio and hypothesis tests. In order to track signals dynamics, we introduce a compensation procedure in the adaptive estimation. This will improve the adaptive estimation performances and fasten it-s convergence after changes detection.

Keywords: Change detection, Hypothesis test, likelihood ratioleast square lattice adaptive filters.

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Authors: Autcha Araveeporn

Abstract:

This paper is to compare the parameter estimation of the mean in normal distribution by Maximum Likelihood (ML), Bayes, and Markov Chain Monte Carlo (MCMC) methods. The ML estimator is estimated by the average of data, the Bayes method is considered from the prior distribution to estimate Bayes estimator, and MCMC estimator is approximated by Gibbs sampling from posterior distribution. These methods are also to estimate a parameter then the hypothesis testing is used to check a robustness of the estimators. Data are simulated from normal distribution with the true parameter of mean 2, and variance 4, 9, and 16 when the sample sizes is set as 10, 20, 30, and 50. From the results, it can be seen that the estimation of MLE, and MCMC are perceivably different from the true parameter when the sample size is 10 and 20 with variance 16. Furthermore, the Bayes estimator is estimated from the prior distribution when mean is 1, and variance is 12 which showed the significant difference in mean with variance 9 at the sample size 10 and 20.

Keywords: Bayes method, Markov Chain Monte Carlo method, Maximum Likelihood method, normal distribution.

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Authors: Y. N. Phang, E. F. Loh

Abstract:

Zero inflated strict arcsine model is a newly developed model which is found to be appropriate in modeling overdispersed count data. In this study, we extend zero inflated strict arcsine model to zero inflated strict arcsine regression model by taking into consideration the extra variability caused by extra zeros and covariates in count data. Maximum likelihood estimation method is used in estimating the parameters for this zero inflated strict arcsine regression model.

Keywords: Overdispersed count data, maximum likelihood estimation, simulated annealing.

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Authors: Humayun Rashid, Lin Zhao

Abstract:

Retention in the IT profession is critical for organizations to stay competitive and operate reliably in the dynamic business environment. Most organizations rely on compensation and rewards as primary tools to enhance retention of employees. In this quantitative survey-based study conducted at a large global bank, we analyze the perceptions of 575 information technology (IT) software professionals in India and Malaysia and find that fairness of rewards has very little impact on retention likelihood. It is far more important to actively involve employees in organizational activities. In addition, our findings indicate that involvement is far more important than information flow: the typical organizational communication to keep employees informed.

Keywords: fairness of rewards, information flow, informationinvolvement, retention

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Authors: Nikolay Nikolaev, Evgueni Smirnov

Abstract:

This paper develops an unscented grid-based filter and a smoother for accurate nonlinear modeling and analysis of time series. The filter uses unscented deterministic sampling during both the time and measurement updating phases, to approximate directly the distributions of the latent state variable. A complementary grid smoother is also made to enable computing of the likelihood. This helps us to formulate an expectation maximisation algorithm for maximum likelihood estimation of the state noise and the observation noise. Empirical investigations show that the proposed unscented grid filter/smoother compares favourably to other similar filters on nonlinear estimation tasks.

Keywords:

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