• Corpus ID: 61664940

Nonparametric Bayesian Approaches to Non-homogeneous Hidden Markov Models

  title={Nonparametric Bayesian Approaches to Non-homogeneous Hidden Markov Models},
  author={Abhra Sarkar and Anindya Bhadra and Bani K. Mallick},
  journal={arXiv: Methodology},
In this article a flexible Bayesian non-parametric model is proposed for non-homogeneous hidden Markov models. The model is developed through the amalgamation of the ideas of hidden Markov models and predictor dependent stick-breaking processes. Computation is carried out using auxiliary variable representation of the model which enable us to perform exact MCMC sampling from the posterior. Furthermore, the model is extended to the situation when the predictors can simultaneously in influence… 

Figures and Tables from this paper

Infinite hidden markov models for multiple multivariate time series with missing data.

An infinite hidden Markov model for multiple asynchronous multivariate time series with missing data is developed designed to include covariates that can inform transitions among hidden states and improves imputations for data that are missing at random compared to existing approaches.



Bayesian non‐parametric hidden Markov models with applications in genomics

A flexible non‐parametric specification of the emission distribution in hidden Markov models is proposed and a novel methodology for carrying out the computations is introduced and an efficient Gibbs sampler for learning Dirichlet process hierarchical models is introduced.

Order-Based Dependent Dirichlet Processes

This article allows the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick-breaking representation and derives the correlation between distributions at different covariate values.

Calculating posterior distributions and modal estimates in Markov mixture models

This paper is concerned with finite mixture models in which the populations from one observation to the next are selected according to an unobserved Markov process. A new, full Bayesian approach

Bayesian Methods for Hidden Markov Models

It is shown how recursive computing allows the statistically efficient use of MCMC output when estimating the hidden states, and the use of log-likelihood for assessing MCMC convergence is illustrated.

Beam sampling for the infinite hidden Markov model

This paper introduces a new inference algorithm for the infinite Hidden Markov model called beam sampling, which typically outperforms the Gibbs sampler and is more robust.

Nonparametric Bayes Conditional Distribution Modeling With Variable Selection

A methodology for flexibly characterizing the relationship between a response and multiple predictors and to identify important predictors for the response distribution change both within local regions and globally is considered.

Monitoring epidemiologic surveillance data using hidden Markov models.

The model characterizes the sequence of measurements by assuming that its probability density function depends on the state of an underlying Markov chain, and the parameter vector includes distribution parameters and transition probabilities between the states.

An HDP-HMM for systems with state persistence

A sampling algorithm is developed that employs a truncated approximation of the DP to jointly resample the full state sequence, greatly improving mixing rates and demonstrating the advantages of the sticky extension, and the utility of the HDP-HMM in real-world applications.

A non‐homogeneous hidden Markov model for precipitation occurrence

A non‐homogeneous hidden Markov model is proposed for relating precipitation occurrences at multiple rain‐gauge stations to broad scale atmospheric circulation patterns (the so‐called ‘downscaling

Bayesian analysis of binary and polychotomous response data

Abstract A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response