Consistency of Bayesian nonparametric Hidden Markov Models
نویسنده
چکیده
We are interested in Bayesian nonparametric Hidden Markov Models. More precisely, we are going to prove the consistency of these models under appropriate conditions on the prior distribution and when the number of states of the Markov Chain is finite and known. Our approach is based on exponential forgetting and usual Bayesian consistency techniques.
منابع مشابه
Mixed Membership Models for Time Series
20.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 20.1.1 State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 20.1.2 Latent Dirichlet Allocation . . . . . . . . . . . ...
متن کاملBayesian nonparametric hidden semi-Markov models
There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDPHMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM’s strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can exten...
متن کاملBayesian time series models and scalable inference
With large and growing datasets and complex models, there is an increasing need for scalable Bayesian inference. We describe two lines of work to address this need. In the first part, we develop new algorithms for inference in hierarchical Bayesian time series models based on the hidden Markov model (HMM), hidden semi-Markov model (HSMM), and their Bayesian nonparametric extensions. The HMM is ...
متن کاملBayesian Nonparametric Learning with semi-Markovian Dynamics
There is much interest in the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) as a natural Bayesian nonparametric extension of the ubiquitous Hidden Markov Model for learning from sequential and time-series data. However, in many settings the HDP-HMM’s strict Markovian constraints are undesirable, particularly if we wish to learn or encode non-geometric state durations. We can exte...
متن کاملParameter Estimation for Hidden Markov Models with Intractable Likelihoods
Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many fields, there has been little investigation of the theoretical properties of the resulting estimators. In this paper we give a theoretical analysis of the as...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013