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About 10,000 papers for “Bayesian parameter estimation”

Outline • Bayesian parameter estimation • Hierarchical Bayesian models

2012

– A more general approach to MCMCCoin flipping • Comparing two simple hypotheses – P(H) = 0.5 vs. P(H) = 1.0 • Comparing simple and complex hypotheses – P(H) = 0.5 vs. P(H) = θ • Comparing infinitely many hypotheses – P(H) = θ: Infer θComparing infinitely many hypotheses • Assume data are generated from a model: θ d 1 d 2 d 3 d 4 P(H) = θ • What is the value of θ? – each value of θ is a hypothesis H – requires inference over infinitely many hypothesesComparing infinitely many hypotheses • Flip a coin 10 times and see 5 heads, 5 tails. • P(H) on next flip? 50% • Why? 50 % = 5 / (5+5) = 5/10. • “Future will be like the past.” • Suppose we had seen 4 heads and 6 tails. • P(H) on next flip? Closer to 50 % than to 40%. • Why? Prior knowledge. Integrating prior knowledge and data P ( H | D)

Cited by 0

Bayesian Estimation Based Parameter Estimation for Composite Load

Chang Fu, Zhe Yu, Di Shi et al. · arXiv (Cornell University) · 2019

Accurate identification of parameters of load models is essential in power system computations, including simulation, prediction, and stability and reliability analysis. Conventional point estimation based composite load modeling approaches suffer from disturbances and noises and provide limited information of the system dynamics. In this work, a statistic (Bayesian Estimation) based distribution estimation approach is proposed for both static (ZIP) and dynamic (Induction Motor) load modeling. When dealing with multiple parameters, Gibbs sampling method is employed. In each iteration, the proposal samples each parameter while keeps others fixed. The proposed method provides a distribution estimation of load models coefficients and is robust to measurement errors.

Cited by 0Open access

P T-Enhanced Bayesian Parameter Estimation

Yaroslav Balytskyi, Manohar Raavi, Sang‐Yoon Chang · 2021

The frequentist (local) quantum parameter estimation based on the Cramer-Rao bound is an asymptotic theory and therefore requires an infinite number of samples for the measurements. On the other hand, by introducing the prior probability distribution, Bayesian parameter estimation approach relaxes this requirement and can be successfully applied under realistic assumption of possessing a limited prior information about the parameter value under investigation. Meanwhile, recent advances in ${{{\mathcal{P}}}}{{{\mathcal{T}}}}$-symmetric quantum mechanics, both theoretically and experimentally, provide an opportunity to significantly enhance the parameter estimation precision by manipulating the Hilbert space of the system. Taking advantage of these, we develop the Bayesian parameter estimation approach for the two-level system possessing ${{{\mathcal{P}}}}{{{\mathcal{T}}}}$ symmetry. We consider both options available in ${{{\mathcal{P}}}}{{{\mathcal{T}}}}$-symmetric quantum mechanics, namely the ${{{\mathcal{C}}}}{{{\mathcal{P}}}}{{{\mathfrak{T}}}}$ and Hermitian measurements, for encoding the probe state and manipulation of the quantum Fisher information of the system and take into account possible decoherence effects inherent for the practical implementations. Our approach should be particularly relevant for applications where the accuracy of quantum parameter estimation is crucial, such as quantum randomness sources and the quantum key distribution. Finally, to bridge the gap with the practical implementations, we consider the relation of our scheme with the current implementation of ${{{\mathcal{P}}}}{{{\mathcal{T}}}}$ symmetry on the IBM quantum processor and formulate our approach as Bayesian parameter estimation employing an ancilla qubit.

Cited by 2

Bayesian Parameter Estimation on velocity data.

Laura Barca (324939), Giovanni Pezzulo (324940) · Figshare · 2015

<p>Summaries of posterior distributions for the derived parameters: difference in means (muDiff), difference in standard deviation (sigmaDiff) and effect size (effSz). Probabilities that the difference in means (probDiffmu>0) and standard deviation (probDiffsigma>0) are greater than zero are also reported.</p><p>Bayesian Parameter Estimation on velocity data.</p>

Cited by 0Open access

Service - Bayesian parameter estimation Web Service

Universitat Pompeu Fabra (UPF) · The COCOON platform (University of Paris) · 2012

Given a training set encoded as vectors of cue (or feature) occurrences, this web service estimates the parameters P(cuei|class): the probability of seeing each cue as a member or non-member of the class. This estimation is performed using Bayesian inference, which combines prior knowledge with observed data. The parameters estimated with this web service can be used, for example, to classify new instances using a Naive Bayes \nclassifier. The output format is the one needed as input for the naive_bayes_classifier webservice.

Cited by 0

Bayesian Parameter Estimation on acceleration data.

Laura Barca (324939), Giovanni Pezzulo (324940) · Figshare · 2015

<p>Summaries of posterior distributions for the derived parameters: difference in means (muDiff), difference in standard deviation (sigma Diff) and effect size (effSz). Probabilities that the difference in means (probDiffmu>0) and standard deviation (probDiffsigma>0) are greater than zero are also reported.</p><p>Bayesian Parameter Estimation on acceleration data.</p>

Cited by 0Open access

Bayesian Parameter Estimation for Nonlinear Dynamics

Chou, Yi · CU Scholar (University of Colorado Boulder) · 2021

We investigate approximate Bayesian inference techniques for nonlinear systems under noisy observations. The systems can be modeled by ordinary differential equations and difference equations. These models are often described by parameters that are not directly measurable and have an impact on the system behaviors. Often, noisy measurement data serve as the means for finding appropriate values of these parameters. Our approaches operate under a Bayesian framework, given prior distribution over the parameter space and noisy observations. Unlike standard Monte-Carlo approaches by sampling, our approaches are based on set-valued reachability analysis to approximate models for the posterior distribution. First, we use interval analysis and reachability analysis to explore subsets of the space of model parameters, computing bounds on the likelihood for each subset, which is also called imprecise approximation. However, the curse of dimensionality problem appears in the subdivision. To alleviate the curse of dimensionality, we investigate a variational inference approach for approximating the posterior distribution. Reachability analysis using polynomial expansion of state variables as a function of time allows us to represent the log-likelihood function as a polynomial over the model parameters. We show how polynomial expansions of the log-likelihood function can be used in variational inference with various distribution families. Polynomial expansions help us cast the variational inference problem directly as a gradient descent optimization with the ability to calculate derivatives quite easily. We demonstrate our approach on interesting nonlinear dynamics models, comparing our approach against other Monte-Carlo approaches. Finally, we show one of these applications to runtime monitoring of unmanned aerial vehicles.

Cited by 0

Bayesian Parameter Estimation Via Variational Methods

Tommi S. Jaakkola, Michael I. Jordan · 1999

We consider a logistic regression model with a Gaussian prior distribution over the parameters. We show that an accurate variational transformation can be used to obtain a closed form approximation to the posterior distribution of the parameters thereby yielding an approximate posterior predictive model. This approach is readily extended to binary graphical model with complete observations. For graphical models with incomplete observations we utilize an additional variational transformation and again obtain a closed form approximation to the posterior. Finally, we show that the dual of the regression problem gives a latent variable density model, the variational formulation of which leads to exactly solvable EM updates. 1 Introduction Bayesian methods have a number of virtues, particularly their uniform treatment of uncertainty at all levels of the modeling process. The formalism also allows ready incorporation of prior knowledge and the seamless combination of such knowledg...

Cited by 0

Bayesian parameter estimation via variational methods

1998

We consider a logistic regression model with a Gaussian prior distribution over the parameters. We show that an accurate variational transformation can be used to obtain a closed form approximation to the posterior distribution of the parameters thereby yielding an approximate posterior predictive model. This approach is readily extended to binary graphical model with complete observations. For graphical models with incomplete observations we utilize an additional variational transformation and again obtain a closed form approximation to the posterior. Finally, we show that the dual of the regression problem gives a latent variable density model, the variational formulation of which leads to exactly solvable EM updates.

Cited by 0