Ex Libris                        Wanted                           
blank

       
blank

blank
blank
blank
blank
Cappe O., Ryden T., Moulines E. Inference in Hidden Markov Models
Cappe O., Ryden T., Moulines E.  Inference in Hidden Markov Models







?
Ctrl+Enter


: Inference in Hidden Markov Models

: Cappe O., Ryden T., Moulines E.

:

Hidden Markov models have become a widely used class of statistical models with applications in diverse areas such as communications engineering, bioinformatics, finance and many more. This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states.

In a unified way the book covers both models with finite state spaces, which allow for exact algorithms for filtering, estimation etc. and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Simulation in hidden Markov models is addressed in five different chapters that cover both Markov chain Monte Carlo and sequential Monte Carlo approaches. Many examples illustrate the algorithms and theory. The book also carefully treats Gaussian linear state-space models and their extensions and it contains a chapter on general Markov chain theory and probabilistic aspects of hidden Markov models.


: en

: /

:

ed2k: ed2k stats

: 1st edition

: 2005

: 654

: 02.07.2008

: | | ID
blank
Absorbing state      12
Accept-reject algorithm      166169 173
Accept-reject algorithm in sequential Monte Carlo      224 261
Acceptance probability in accept-reject      169
Acceptance probability in Metropolis-Hastings      171
Acceptance ratio in Metropolis-Hastings      171
Acceptance ratio in reversible jump MCMC      486
Accessible set      517
AEP      see Asymptotic equipartition property
Asymptotic equipartition property      568 see
Asymptotically tight      see Bounded in probability
atom      518
Auxiliary variable      260
Auxiliary variable in sequential Monte Carlo      256264
Averaging in MCEM      403 424
Averaging in SAEM      411
Averaging in stochastic approximation      409 429
Backward smoothing, decomposition      70
Backward smoothing, kernels      7071 125 130
Bahadur efficiency      559
Balance equations, detailed      41
Balance equations, global      41
Balance equations, local      41
Baum Welch      see Forward-backward
Bayes, formula      71
Bayes, operator      102
Bayes, rule      64 157
Bayes, theorem      172
Bayesian information criterion      560 563 568
Bayesian, decision procedure      466
Bayesian, estimation      358 465
Bayesian, model      71 466
Bayesian, network      see Graphical model
Bayesian, posterior      see Posterior
Bayesian, prior      see Prior
BCJR algorithm      74
Bearings-only tracking      2324
Bennett inequality      584
Bernoulli Gaussian model      196
BIC      see Bayesian information criterion
Binary deconvolution model      373
Binary deconvolution model, estimation using EM      374
Binary deconvolution model, estimation using quasi-Newton      374
Binary deconvolution model, estimation using SAME      500
Binary symmetric channel      7 8
Bootstrap filter      238 254256 259
Bounded in probability      334
Bryson Frazier      see Smoothing
Burn-in      395 491
Canonical space      38
Capture-recapture model      12 479
Cauchy sequence      600
CGLSSM      see State-space model
Chapman Kolmogorov equations      36
Coding probability      565 568
Coding probability, mixture      567
Coding probability, normalized maximum likelihood      566
Coding probability, universal      566
Communicating states      507
Companion matrix      16 30
Computable bounds      185
Conditional likelihood function      218
Conditional likelihood function, log-concave      225
Contrast function      436
Coordinate process      38
Coupling inequality      536
Coupling of Markov chains      536539
Coupling set      537
Critical region      564
Darroch model      12
Data augmentation      476
Dirichlet distribution      470 567
Disturbance noise      127
Dobrushin coefficient      96
Doeblin condition      97
Doeblin condition for hidden Markov model      555
Drift conditions for hidden Markov model      555
Drift conditions for Markov chain      531534 542545
Drift conditions, Foster Lyapunov      542
ECM      see Expectation-maximization
Effective sample size      235
Efficiency      574
Efficiency, Bahadur      575
Efficiency, Pitman      574
Efficient score test      461
EKF      see Kalman extended
em      see Expectation-maximization
Equivalent parameters      445
Error, exponent      575
Error, overestimation      562
Error, underestimation      562
Exchangeable distribution      472
Expectation-Maximization      347351
Expectation-maximization, convergence of      387392
Expectation-maximization, ECM      391
Expectation-maximization, for MAP estimation      358
Expectation-maximization, for missing data models      357
Expectation-maximization, in exponential family      350
Expectation-maximization, intermediate quantity of      347
Expectation-maximization, SAGE      392
Exponential family      350
Exponential family natural parameterization      467
Exponential family natural parameterization of the Normal      149
Exponential forgetting      see Forgetting
Filtered space      37
Filtering      54
Filtration      37
Filtration natural      38
Fisher identity      352 360 452
Forgetting      100120
Forgetting exponential, of time-reversed chain      455
Forgetting, exponential      109 440
Forgetting, strong mixing condition      105 108
Forgetting, uniform      100 105110
Forward smoothing, decomposition      66
Forward smoothing, kernels      66 101 327
Forward-backward      5666
Forward-backward, $\alpha$      see Forward variable
Forward-backward, $\beta$      see Backward variable
Forward-backward, backward variable      57
Forward-backward, Baum Welch denomination      74
Forward-backward, decomposition      57
Forward-backward, forward variable      57
Forward-backward, in finite state space HMM      123124
Forward-backward, in state-space model      154
Forward-backward, scaling      61 74
Gaussian linear model      128 149
Generalized likelihood ratio test      see Likelihood ratio test
Gibbs sampler      180182
Gibbs sampler in CGLSSM      194
Gibbs sampler in hidden Markov model      475480
Gibbs sampler, random scan      181
Gibbs sampler, sweep of      180 397 478
Gibbs sampler, systematic scan      181
Gilbert Elliott channel      6
Global sampling      see Resampling global
Global updating      see Updating of hidden chain
Gram Schmidt orthogonalization      135
Graphical model      1 4
Growth model, comparison of SIS kernels      230231
Growth model, performance of bootstrap filter      240242
Hahn Jordan decomposition      91
Harris recurrent chain      see Markov chain Harris
Harris recurrent set      526
Hidden Markov model      15 4244
Hidden Markov model, aperiodic      553
Hidden Markov model, discrete      43
Hidden Markov model, ergodic      33
Hidden Markov model, finite      612
Hidden Markov model, fully dominated      43
Hidden Markov model, hierarchical      4647
Hidden Markov model, in biology      10
Hidden Markov model, in ion channel modelling      13
Hidden Markov model, in speech recognition      13
Hidden Markov model, left-to-right      33
Hidden Markov model, likelihood      53
Hidden Markov model, log-likelihood      53
Hidden Markov model, normal      see Normal hidden Markov Hidden Markov model model
Hidden Markov model, partially dominated      43
Hidden Markov model, phi-irreducible      553
Hidden Markov model, positive      553
Hidden Markov model, recurrent      553
Hidden Markov model, transient      553
Hidden Markov model, with finite state space      121126
Hilbert space      612
Hitting time      507 515
HMM      see Hidden Markov model
Hoeffding inequality      292
Homogeneous      see Markov chain
HPD (highest posterior density) region      240
Hybrid MCMC algorithms      179
Hyperparameter      see Prior
Hypothesis testing, composite      559 561 563 575
Hypothesis testing, simple      564
Ideal codeword length      565
Identifiability      444451 462 472 559 562
Identifiability in Gaussian linear state-space model      382
Identifiability of finite mixtures      448
Identifiability of mixtures      448449
Implicit conditioning convention      58
Importance kernel      see Instrumental kernel
Importance sampling      173 210211 287295
Importance sampling, self-normalized      211 293295
Importance sampling, self-normalized, asympotic normality      293
Importance sampling, self-normalized, consistency      293
Importance sampling, self-normalized, deviation bound      294
Importance sampling, sequential      see Sequential Monte Carlo
Importance sampling, unnormalized      210 287292
Importance sampling, unnormalized, asymptotic normality      288
Importance sampling, unnormalized, consistency      288
Importance sampling, unnormalized, deviation bound      292
Importance weights      173
Importance weights, normalized      211
Importance weights, normalized, coefficient of variation of      235
Importance weights, normalized, Shannon entropy of      235
Incremental weight      216
Information divergence rate      568
Information matrix      458
Information matrix, observed      436
Information matrix, observed, convergence of      459
Information parameterization      148149
Initial distribution      38
Innovation sequence      136
Instrumental distribution      210
Instrumental kernel      215
Instrumental kernel, choice of      218
Instrumental kernel, optimal      220224
Instrumental kernel, optimal, local approximation of      225231
Instrumental kernel, prior kernel      218
Integrated autocorrelation time      191
Invariant measure      511 527
Invariant measure sub-invariant measure      527
Inversion method      242
Irreducibility measure, maximal      516
Irreducibility measure, of hidden Markov model      550
Irreducibility measure, of Markov chain      515
Jacobian      480 486 489490
Kalman, extended filter      228
Kalman, filter      141142
Kalman, filter, gain      141
Kalman, filtering with non-zero means      142
Kalman, predictor      137139
Kalman, predictor, gain      138
Kalman, unscented filter      228
Kernel      see Transition
Kraft McMillan inequality      565
Krichevsky Trofimov mixture      567
Kullback Leibler divergence      348
Label switching      473
Lagrange multiplier test      461
Large deviations      578
Latent variable model      2
Law of iterated logarithm      565
Level      564
Level, asymptotic      564
Likelihood      53 357 437439
Likelihood in state-space model      139
Likelihood ratio test      460462
Likelihood ratio test, generalized      461 559 564 568 578
Likelihood, conditional      65 66 438
Linear prediction      131136
Local asymptotic normality      437
Local updating      see Updating of hidden chain
Log-likelihood      see Likelihood
Log-normal distribution      480
Louis identity      352
Lyapunov function      417
Lyapunov function, differential      426
MAP      see Maximum a posteriori
Marcinkiewicz Zygmund inequality      292
Markov chain Monte Carlo      169186
Markov chain, aperiodic      514 535
Markov chain, canonical version      39
Markov chain, central limit theorem      548 549
Markov chain, ergodic theorem      514 536
Markov chain, geometrically ergodic      542
Markov chain, Harris recurrent      526
Markov chain, homogeneous      2
Markov chain, irreducible      508
Markov chain, law of large numbers      546
Markov chain, non-homogeneous      40 163
Markov chain, null      513 528
Markov chain, on countable space      507514
Markov chain, on general space      514549
Markov chain, phi-irreducible      515
Markov chain, positive      528
Markov chain, positive recurrent      513
Markov chain, recurrent      511
Markov chain, reverse      40
Markov chain, reversible      41
Markov chain, solidarity property      510
Markov chain, strongly aperiodic      535
Markov chain, transient      511
Markov jump system      see Markov switching model
Markov property      39
Markov property, strong      40
Markov-switching model      4
Markov-switching model, maximum likelihood estimation      463
Markov-switching model, smoothing      86
Matrix inversion lemma      149 152
Maximum a posteriori      358 467 495504
Maximum a posteriori, state estimation      125 208
Maximum likelihood estimator      358 435
Maximum likelihood estimator, asymptotic Maximum likelihood estimator, normality      437 459
Maximum likelihood estimator, asymptotics      436437
Maximum likelihood estimator, consistency      436 440444 459
Maximum likelihood estimator, convergence in quotient topology      444
Maximum likelihood estimator, efficiency      437
Maximum marginal posterior estimator      466
Maximum marginal posterior estimator in CGLSSM      208
MCEM      see Monte Carlo EM
MCMC      see Markov chain Monte Carlo
MDL      see Minimum description length
Mean field in stochastic approximation      426
Mean square, convergence      612
Mean square, error      614
Mean square, prediction      614
Measurable function      599
Measurable set      599
Measurable space      599
1 2
blank
blank
blank
HR
@Mail.ru
       © , 2004-2022
   | Valid HTML 4.01! | Valid CSS!