39,826 research outputs found
Autoregressive hidden Markov model with application in an El Niño study
Hidden Markov models are extensions of Markov models where each observation is the result of a stochastic process in one of several unobserved states. Though favored by many scientists because of its unique and applicable mathematical structure, its independence assumption between the consecutive observations hampered further application. Autoregressive hidden Markov model is a combination of autoregressive time series and hidden Markov chains. Observations are generated by a few autoregressive time series while the switches between each autoregressive time series are controlled by a hidden Markov chain. In this thesis, we present the basic concepts, theory and associated approaches and algorithms for hidden Markov models, time series and autoregressive hidden Markov models. We have also built a bivariate autoregressive hidden Markov model on the temperature data from the Pacific Ocean to understand the mechanism of El
Nino. The parameters and the state path of the model are estimated through the Segmental K-mean algorithm and the state estimations of the autoregressive hidden Markov model have been compared with the estimations from a conventional hidden Markov model. Overall, the results confirm the strength of the autoregressive hidden Markov models in the El Nino study and the research sets an example of ARHMM's application in the meteorology
Evaluating the CDMA System Using Hidden Markov and Semi Hidden Markov Models
CDMA is an important and basic part of today’s communications technologies. This technology can be analyzed efficiently by reducing the time, computation burden, and cost by characterizing the physical layer with a Markov Model. Waveform level simulation is generally used for simulating different parts of a digital communication system. In this paper, we introduce two different mathematical methods to model digital communication channels. Hidden Markov and Semi Hidden Markov models’ applications have been investigated for evaluating the DS-CDMA link performance with different parameters. Hidden Markov Models have been a powerful mathematical tool that can be applied as models of discrete-time series in many fields successfully. A semi-hidden Markov model as a stochastic process is a modification of hidden Markov models with states that are no longer unobservable and less hidden. A principal characteristic of this mathematical model is statistical inertia, which admits the generation, and analysis of observation symbol contains frequent runs. The SHMMs cause a substantial reduction in the model parameter set. Therefore in most cases, these models are computationally more efficient models compared to HMMs. After 30 iterations for different Number of Interferers, all parameters have been estimated as the likelihood become constant by the Baum Welch algorithm. It has been demonstrated that by employing these two models for different Numbers of Interferers and Number of symbols, Error sequences can be generated, which are statistically the same as the sequences derived from the CDMA simulation. An excellent match confirms both models’ reliability to those of the underlying CDMA-based physical layer
Formalized Quantum Stochastic Processes and Hidden Quantum Models with Applications to Neuron Ion Channel Kinetics
A new class of formal latent-variable stochastic processes called hidden
quantum models (HQM's) is defined in order to clarify the theoretical
foundations of ion channel signal processing. HQM's are based on quantum
stochastic processes which formalize time-dependent observation. They allow the
calculation of autocovariance functions which are essential for
frequency-domain signal processing. HQM's based on a particular type of
observation protocol called independent activated measurements are shown to to
be distributionally equivalent to hidden Markov models yet without an
underlying physical Markov process. Since the formal Markov processes are
non-physical, the theory of activated measurement allows merging energy-based
Eyring rate theories of ion channel behavior with the more common
phenomenological Markov kinetic schemes to form energy-modulated quantum
channels. Using the simplest quantum channel model consistent with neuronal
membrane voltage-clamp experiments, activation eigenenergies are calculated for
the Hodgkin-Huxley K+ and Na+ ion channels. It is also shown that maximizing
entropy under constrained activation energy yields noise spectral densities
approximating , thus offering a biophysical explanation
for the ubiquitous -type in neurological signals.Comment: Several proofs were found to be incomplete or in error including the
proof that quantum rotations can induce arbitrary noise weights. A fully
corrected version of this paper is published as: A. Paris, G. Atia, A.
Vosoughi, and S. Berman, "Hidden quantum processes, quantum ion channels, and
1/f-type noise", Neural Computation, vol. 30, num. 7, pp. 1830-1929 (2018),
doi:10.1162/neco_a_0106
Robust filtering and propagation of uncertainty in hidden Markov models
We consider the filtering of continuous-time finite-state hidden Markov models, where the rate and observation matrices depend on unknown time-dependent parameters, for which no prior or stochastic model is available. We quantify and analyze how the induced uncertainty may be propagated through time as we collect new observations, and used to simultaneously provide robust estimates of the hidden signal and to learn the unknown parameters, via techniques based on pathwise filtering and new results on the optimal control of rough differential equations
Pattern Recognition for Command and Control Data Systems
To analyze real-world events, researchers collect observation data from an underlying process and construct models to represent the observed situation. In this work, we consider issues that affect the construction and usage of a specific type of model. Markov models are commonly used because their combination of discrete states and stochastic transitions is suited to applications with both deterministic and stochastic components. Hidden Markov Models (HMMs) are a class of Markov model commonly used in pattern recognition. We first demonstrate how to construct HMMs using only the observation data, and no a priori information, by extending a previously developed approach from J.P. Crutchfield and C.R. Shalizi. We also show how to determine with a level of statistical confidence whether or not the model fully encapsulates the underlying process. Once models are constructed from observation data, the models are used to identify other types of observations. Traditional approaches consider the maximum likelihood that the model matches the observation, solving a classification problem. We present a new method using confidence intervals and receiver operating characteristic curves. Our method solves a detection problem by determining if observation data matches zero, one, or more than one model. To detect the occurrence of a behavior in observation data, one must consider the amount of data required. We consider behaviors to be \u27serial Markovian,\u27 when the behavior can change from one model to another at any time. When analyzing observation data, considering too much data induces high delay and could lead to confusion in the system if multiple behaviors are observed in the data stream. If too little data is used, the system has a high false positive rate and is unable to correctly detect behaviors. We demonstrate the effectiveness of all methods using illustrative examples and consumer behavior data
Stochastic modelling with randomized Markov bridges
We consider the filtering problem of estimating a hidden random variable X by noisy observations. The noisy observation process is constructed by a randomized Markov bridge (RMB) (Zt)t∈[0,T] of which terminal value is set to ZT=X. That is, at the terminal time T, the noise of the bridge process vanishes and the hidden random variable X is revealed. We derive the explicit filtering formula, governing the dynamics of the conditional probability process, for a general RMB. It turns out that the conditional probability is given by a function of current time t, the current observation Zt, the initial observation Z0, and the a priori distribution ν of X at t = 0. As an example for an RMB, we explicitly construct the skew-normal randomized diffusion bridge and show how it can be utilized to extend well-known commodity pricing models and how one may propose novel stochastic price models for financial instruments linked to greenhouse gas emissions
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