Search results for " likelihood"

showing 10 items of 115 documents

Segmented mixed models with random changepoints: a maximum likelihood approach with application to treatment for depression study

2014

We present a simple and effective iterative procedure to estimate segmented mixed models in a likelihood based framework. Random effects and covariates are allowed for each model parameter, including the changepoint. The method is practical and avoids the computational burdens related to estimation of nonlinear mixed effects models. A conventional linear mixed model with proper covariates that account for the changepoints is the key to our estimating algorithm. We illustrate the method via simulations and using data from a randomized clinical trial focused on change in depressive symptoms over time which characteristically show two separate phases of change.

Statistics and ProbabilityMixed modelMaximum likelihoodrandom changepointRandom effects modelpsychiatric longitudinal dataGeneralized linear mixed modelNonlinear systemchangepointmixed segmented regressionStatisticsCovariateMixed effectsStatistics Probability and Uncertaintynonlinear mixed modelSettore SECS-S/01 - StatisticaAlgorithmDepressive symptomsMathematics
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Windowed Etas Models With Application To The Chilean Seismic Catalogs

2015

Abstract The seismicity in Chile is estimated using an ETAS (Epidemic Type Aftershock sequences) space–time point process through a semi-parametric technique to account for the estimation of parametric and nonparametric components simultaneously. The two components account for triggered and background seismicity respectively, and are estimated by alternating a ML estimation for the parametric part and a forward predictive likelihood technique for the nonparametric one. Given the geographic and seismological characteristics of Chile, the sensitivity of the technique with respect to different geographical areas is examined in overlapping successive windows with varying latitude. A different b…

Statistics and ProbabilityNonparametric statisticsManagement Monitoring Policy and LawInduced seismicityGeodesyPoint processPhysics::GeophysicsLatitudeSpace-time point processes ETAS model etasFLP R packagePredictive likelihoodStatisticsSensitivity (control systems)Computers in Earth SciencesAftershockGeologyParametric statistics
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An approximation to maximum likelihood estimates in reduced models

1990

SUMMARY An approximation to the maximum likelihood estimates of the parameters in a model can be obtained from the corresponding estimates and information matrices in an extended model, i.e. a model with additional parameters. The approximation is close provided that the data are consistent with the first model. Applications are described to log linear models for discrete data, to models for multivariate normal distributions with special covariance matrices and to mixed discrete-continuous models.

Statistics and ProbabilityRestricted maximum likelihoodApplied MathematicsGeneral MathematicsMaximum likelihoodMultivariate normal distributionMaximum likelihood sequence estimationCovarianceAgricultural and Biological Sciences (miscellaneous)Extended modelStatisticsExpectation–maximization algorithmLog-linear modelStatistics Probability and UncertaintyGeneral Agricultural and Biological SciencesMathematicsBiometrika
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Inferential tools in penalized logistic regression for small and sparse data: A comparative study.

2016

This paper focuses on inferential tools in the logistic regression model fitted by the Firth penalized likelihood. In this context, the Likelihood Ratio statistic is often reported to be the preferred choice as compared to the ‘traditional’ Wald statistic. In this work, we consider and discuss a wider range of test statistics, including the robust Wald, the Score, and the recently proposed Gradient statistic. We compare all these asymptotically equivalent statistics in terms of interval estimation and hypothesis testing via simulation experiments and analyses of two real datasets. We find out that the Likelihood Ratio statistic does not appear the best inferential device in the Firth penal…

Statistics and ProbabilityScore testPRESS statisticEpidemiologyStatistics as TopicScoreWald testLogistic regression01 natural sciences010104 statistics & probability03 medical and health sciences0302 clinical medicineHealth Information ManagementStatisticsEconometricsHumans030212 general & internal medicine0101 mathematicsStatisticMathematicsLikelihood FunctionsModels StatisticalLogistic regression firth penalized likelihood sandwich formula score statistic gradient statisticLogistic ModelsLikelihood-ratio testData Interpretation StatisticalSample SizeAncillary statisticSettore SECS-S/01 - StatisticaStatistical methods in medical research
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The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing

2016

Abstract This paper refers to the problem stated by Balakrishnan et al. (2002). They proved that maximum likelihood estimator (MLE) of the exponential mean obtained from grouped samples is stochastically ordered provided that the sequence of the successive distances between inspection times is decreasing. In this paper we show that the assumption of monotonicity of the sequence of distances can be dropped.

Statistics and ProbabilitySequenceExponential distributionMaximum likelihood010102 general mathematicsFixed-point theoremMonotonic function01 natural sciencesExponential functionGrouped data010104 statistics & probabilityStatisticsApplied mathematics0101 mathematicsStatistics Probability and UncertaintyMathematicsStatistics & Probability Letters
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Likelihood Inference for Gibbs Processes in the Analysis of Spatial Point Patterns

2001

Plusieurs auteurs ont propose des approximations stochastiques et non-stochastiques au MLE pour les processus de Gibbs utilises pour decrire les interactions entre deux points dans une distribution spatiale de points. Cettes approximations sont necessaires a cause de la difficulte en l'evaluation de la constante qui normalise la f.d.p., Cet article present une comparaison, parmi d'un model de Strauss, des methodes qui utilisent des approximations directes aux MLE et des methodes qui utilisent techniques de Monte Carlo de chaine de Markov. Les techniques de simulation utilisees sont le Gibbs sampler et l'algorithm de Metropolis-Hastings.

Statistics and ProbabilitySequential methodMaximum likelihoodCalculusPattern analysisApplied mathematicsInferenceStatistics Probability and UncertaintyMathematicsInternational Statistical Review
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Selecting the tuning parameter in penalized Gaussian graphical models

2019

Penalized inference of Gaussian graphical models is a way to assess the conditional independence structure in multivariate problems. In this setting, the conditional independence structure, corresponding to a graph, is related to the choice of the tuning parameter, which determines the model complexity or degrees of freedom. There has been little research on the degrees of freedom for penalized Gaussian graphical models. In this paper, we propose an estimator of the degrees of freedom in $$\ell _1$$ -penalized Gaussian graphical models. Specifically, we derive an estimator inspired by the generalized information criterion and propose to use this estimator as the bias term for two informatio…

Statistics and ProbabilityStatistics::TheoryKullback–Leibler divergenceKullback-Leibler divergenceComputer scienceGaussianInformation Criteria010103 numerical & computational mathematicsModel complexityModel selection01 natural sciencesTheoretical Computer Science010104 statistics & probabilitysymbols.namesakeStatistics::Machine LearningGeneralized information criterionEntropy (information theory)Statistics::MethodologyGraphical model0101 mathematicsPenalized Likelihood Kullback-Leibler Divergence Model Complexity Model Selection Generalized Information Criterion.Model selectionEstimatorStatistics::ComputationComputational Theory and MathematicsConditional independencesymbolsPenalized likelihoodStatistics Probability and UncertaintySettore SECS-S/01 - StatisticaAlgorithmStatistics and Computing
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Stochastic ordering of classical discrete distributions

2010

For several pairs $(P,Q)$ of classical distributions on $\N_0$, we show that their stochastic ordering $P\leq_{st} Q$ can be characterized by their extreme tail ordering equivalent to $ P(\{k_\ast \})/Q(\{k_\ast\}) \le 1 \le \lim_{k\to k^\ast} P(\{k\})/Q(\{k\})$, with $k_\ast$ and $k^\ast$ denoting the minimum and the supremum of the support of $P+Q$, and with the limit to be read as $P(\{k^\ast\})/Q(\{k^\ast\})$ for $k^\ast$ finite. This includes in particular all pairs where $P$ and $Q$ are both binomial ($b_{n_1,p_1} \leq_{st} b_{n_2,p_2}$ if and only if $n_1\le n_2$ and $(1-p_1)^{n_1}\ge(1-p_2)^{n_2}$, or $p_1=0$), both negative binomial ($b^-_{r_1,p_1}\leq_{st} b^-_{r_2,p_2}$ if and on…

Statistics and ProbabilityWaiting timeApplied MathematicsProbability (math.PR)010102 general mathematicsCoupling (probability)Poisson distribution01 natural sciencesStochastic orderingInfimum and supremumHypergeometric distributionCombinatorics010104 statistics & probabilitysymbols.namesakeFOS: MathematicsMonotone likelihood ratiosymbolsLimit (mathematics)60E150101 mathematicsMathematics - ProbabilityMathematicsAdvances in Applied Probability
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An extended continuous mapping theorem for outer almost sure weak convergence

2019

International audience; We prove an extended continuous mapping theorem for outer almost sure weak convergence in a metric space, a notion that is used in bootstrap empirical processes theory. Then we make use of those results to establish the consistency of several bootstrap procedures in empirical likelihood theory for functional parameters.

Statistics and ProbabilityWeak convergence010102 general mathematicsContinuous mapping theorem16. Peace & justiceEmpirical measure01 natural sciences010104 statistics & probabilityMetric spaceEmpirical likelihoodConsistency (statistics)[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]Applied mathematicsStatistics::Methodology0101 mathematicsStatistics Probability and UncertaintyMathematics
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Urban runoff modelling uncertainty: Comparison among Bayesian and pseudo-Bayesian methods

2009

Urban stormwater quality modelling plays a central role in evaluation of the quality of the receiving water body. However, the complexity of the physical processes that must be simulated and the limited amount of data available for calibration may lead to high uncertainty in the model results. This study was conducted to assess modelling uncertainty associated with catchment surface pollution evaluation. Eight models were compared based on the results of a case study in which there was limited data available for calibration. Uncertainty analysis was then conducted using three different methods: the Bayesian Monte Carlo method, the GLUE pseudo-Bayesian method and the GLUE method revised by m…

Urban stormwater modellingEnvironmental EngineeringSettore ICAR/03 - Ingegneria Sanitaria-AmbientaleCalibration (statistics)Computer scienceEcological ModelingSettore ICAR/02 - Costruzioni Idrauliche E Marittime E IdrologiaBayesian probabilityMonte Carlo methodBayesian methodGeneralised Likelihood Uncertainty EstimationStatisticsUncertainty assessmentSensitivity analysisSurface runoffGLUESoftwareReliability (statistics)Uncertainty analysisEnvironmental Modelling & Software
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