scholarly journals Confidence Intervals for the Mixture Transition Distribution (MTD) Model and Other Markovian Models

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 351
Author(s):  
André Berchtold
Keyword(s):  
Markov Chains ◽  
Markov Model ◽  
Em Algorithm ◽  
Hidden Markov Model ◽  
Confidence Intervals ◽  
Hidden Markov ◽  
Simple Calculation ◽  
Standard Methods ◽  
Transition Distribution ◽  
Simulation Results

The Mixture Transition Distribution (MTD) model used for the approximation of high-order Markov chains does not allow a simple calculation of confidence intervals, and computationnally intensive methods based on bootstrap are generally used. We show here how standard methods can be extended to the MTD model as well as other models such as the Hidden Markov Model. Starting from existing methods used for multinomial distributions, we describe how the quantities required for their application can be obtained directly from the data or from one run of the E-step of an EM algorithm. Simulation results indicate that when the MTD model is estimated reliably, the resulting confidence intervals are comparable to those obtained from more demanding methods.

Confidence intervals for hidden Markov model parameters

2000 ◽  
Vol 53 (2) ◽  
pp. 317-327 ◽  
Author(s):  
Ingmar Visser ◽  
Maartje E. J. Raijmakers ◽  
Peter C. M. Molenaar
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Confidence Intervals ◽  
Hidden Markov ◽  
Model Parameters

scholarly journals Wideband Spectrum Sensing Method Based on Channels Clustering and Hidden Markov Model Prediction

Information ◽  
2019 ◽  
Vol 10 (11) ◽  
pp. 331 ◽  
Author(s):  
Wang ◽  
Wu ◽  
Yao ◽  
Qin
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Spectrum Sensing ◽  
Clustering Algorithm ◽  
Hidden Markov ◽  
Wideband Spectrum Sensing ◽  
Density Based Clustering ◽  
Radio Technology ◽  
Simulation Results ◽  
Cognitive Radio Technology

Spectrum sensing is the necessary premise for implementing cognitive radio technology. The conventional wideband spectrum sensing methods mainly work with sweeping frequency and still face major challenges in performance and efficiency. This paper introduces a new wideband spectrum sensing method based on channels clustering and prediction. This method counts on the division of the wideband spectrum into uniform sub-channels, and employs a density-based clustering algorithm called Ordering Points to Identify Clustering Structure (OPTICS) to cluster the channels in view of the correlation between the channels. The detection channel (DC) is selected and detected for each cluster, and states of other channels (estimated channels, ECs) in the cluster are then predicted with Hidden Markov Model (HMM), so that all channels states of the wideband spectrum are finally obtained. The simulation results show that the proposed method could effectively improve the wideband spectrum sensing performance.

EM algorithm for Markov chains observed via Gaussian noise and point process information: Theory and case studies

2018 ◽  
Vol 35 (1-2) ◽  
pp. 51-72 ◽  
Author(s):  
Camilla Damian ◽  
Zehra Eksi ◽  
Rüdiger Frey
Keyword(s):  
Markov Model ◽  
Em Algorithm ◽  
Credit Risk ◽  
Hidden Markov Model ◽  
Point Process ◽  
Gaussian Noise ◽  
Goodness Of Fit ◽  
Markov Models ◽  
Hidden Markov ◽  
Process Observation

AbstractIn this paper we study parameter estimation via the Expectation Maximization (EM) algorithm for a continuous-time hidden Markov model with diffusion and point process observation. Inference problems of this type arise for instance in credit risk modelling. A key step in the application of the EM algorithm is the derivation of finite-dimensional filters for the quantities that are needed in the E-Step of the algorithm. In this context we obtain exact, unnormalized and robust filters, and we discuss their numerical implementation. Moreover, we propose several goodness-of-fit tests for hidden Markov models with Gaussian noise and point process observation. We run an extensive simulation study to test speed and accuracy of our methodology. The paper closes with an application to credit risk: we estimate the parameters of a hidden Markov model for credit quality where the observations consist of rating transitions and credit spreads for US corporations.

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