15,438 research outputs found
Recommended from our members
Bayesian extreme quantile regression for hidden Markov models
This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel UniversityThe main contribution of this thesis is the introduction of Bayesian quantile regression for hidden
Markov models, especially when we have to deal with extreme quantile regression analysis, as there is a limited research to inference conditional quantiles for hidden Markov models, under a Bayesian approach.
The first objective is to compare Bayesian extreme quantile regression and the classical extreme
quantile regression, with the help of simulated data generated by three specific models, which only differ in the error termâs distribution. It is also investigated if and how the error termâs distribution affects Bayesian extreme quantile regression, in terms of parameter and confidence intervals estimation. Bayesian extreme quantile regression is performed by implementing a Metropolis-Hastings algorithm to update our parameters, while the classical extreme quantile regression is performed by using linear programming.
Moreover, the same analysis and comparison is performed on a real data set. The results provide strong evidence that our method can be improved, by combining MCMC algorithms and linear programming, in order to obtain better parameter and confidence intervals estimation.
After improving our method for Bayesian extreme quantile regression, we extend it by including hidden Markov models. First, we assume a discrete time finite state-space hidden Markov model, where the distribution associated with each hidden state is a) a Normal distribution and b) an asymmetric Laplace distribution. Our aim is to explore the number of hidden states that describe the extreme quantiles of our data sets and check whether a different distribution associated with each hidden state can affect our estimation. Additionally, we also explore whether there are structural changes (breakpoints), by using break-point hidden Markov models. In order to perform this analysis we implement two new MCMC algorithms. The first one updates the parameters and the hidden states by using a Forward-Backward algorithm and Gibbs sampling (when a Normal distribution is assumed), and the second one uses a Forward-Backward algorithm and a mixture of Gibbs and Metropolis-Hastings sampling (when an asymmetric Laplace distribution is assumed).
Finally, we consider hidden Markov models, where the hidden state (latent variables) are continuous. For this case of the discrete-time continuous state-space hidden Markov model we implement a method that uses linear programming and the Kalman filter (and Kalman smoother).
Our methods are used in order to analyze real interest rates by assuming hidden states, which represent different financial regimes. We show that our methods work very well in terms of parameter estimation and also in hidden state and break-point estimation, which is very useful for the real life applications of those methods
Combining vocal tract length normalization with hierarchial linear transformations
Recent research has demonstrated the effectiveness of vocal tract length normalization (VTLN) as a rapid adaptation technique for statistical parametric speech synthesis. VTLN produces speech with naturalness preferable to that of MLLR-based adaptation techniques, being much closer in quality to that generated by the original av-erage voice model. However with only a single parameter, VTLN captures very few speaker specific characteristics when compared to linear transform based adaptation techniques. This paper pro-poses that the merits of VTLN can be combined with those of linear transform based adaptation in a hierarchial Bayesian frame-work, where VTLN is used as the prior information. A novel tech-nique for propagating the gender information from the VTLN prior through constrained structural maximum a posteriori linear regres-sion (CSMAPLR) adaptation is presented. Experiments show that the resulting transformation has improved speech quality with better naturalness, intelligibility and improved speaker similarity. Index Terms â Statistical parametric speech synthesis, hidden Markov models, speaker adaptation, vocal tract length normaliza-tion, constrained structural maximum a posteriori linear regression 1
Causal Discovery with Continuous Additive Noise Models
We consider the problem of learning causal directed acyclic graphs from an
observational joint distribution. One can use these graphs to predict the
outcome of interventional experiments, from which data are often not available.
We show that if the observational distribution follows a structural equation
model with an additive noise structure, the directed acyclic graph becomes
identifiable from the distribution under mild conditions. This constitutes an
interesting alternative to traditional methods that assume faithfulness and
identify only the Markov equivalence class of the graph, thus leaving some
edges undirected. We provide practical algorithms for finitely many samples,
RESIT (Regression with Subsequent Independence Test) and two methods based on
an independence score. We prove that RESIT is correct in the population setting
and provide an empirical evaluation
Measuring the Influence of Observations in HMMs through the Kullback-Leibler Distance
We measure the influence of individual observations on the sequence of the
hidden states of the Hidden Markov Model (HMM) by means of the Kullback-Leibler
distance (KLD). Namely, we consider the KLD between the conditional
distribution of the hidden states' chain given the complete sequence of
observations and the conditional distribution of the hidden chain given all the
observations but the one under consideration. We introduce a linear complexity
algorithm for computing the influence of all the observations. As an
illustration, we investigate the application of our algorithm to the problem of
detecting outliers in HMM data series
Forecasting Time Series Subject to Multiple Structural Breaks
This paper provides a novel approach to forecasting time series subject to discrete structural breaks. We propose a Bayesian estimation and prediction procedure that allows for the possibility of new breaks over the forecast horizon, taking account of the size and duration of past breaks (if any) by means of a hierarchical hidden Markov chain model. Predictions are formed by integrating over the hyper parameters from the meta distributions that characterize the stochastic break point process. In an application to US Treasury bill rates, we find that the method leads to better out-of-sample forecasts than alternative methods that ignore breaks, particularly at long horizons.structural breaks, forecasting, hierarchical hidden Markov chain model, Bayesian model averaging.
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
Switching Regression Models and Causal Inference in the Presence of Discrete Latent Variables
Given a response and a vector of predictors,
we investigate the problem of inferring direct causes of among the vector
. Models for that use all of its causal covariates as predictors enjoy
the property of being invariant across different environments or interventional
settings. Given data from such environments, this property has been exploited
for causal discovery. Here, we extend this inference principle to situations in
which some (discrete-valued) direct causes of are unobserved. Such cases
naturally give rise to switching regression models. We provide sufficient
conditions for the existence, consistency and asymptotic normality of the MLE
in linear switching regression models with Gaussian noise, and construct a test
for the equality of such models. These results allow us to prove that the
proposed causal discovery method obtains asymptotic false discovery control
under mild conditions. We provide an algorithm, make available code, and test
our method on simulated data. It is robust against model violations and
outperforms state-of-the-art approaches. We further apply our method to a real
data set, where we show that it does not only output causal predictors, but
also a process-based clustering of data points, which could be of additional
interest to practitioners.Comment: 46 pages, 14 figures; real-world application added in Section 5.2;
additional numerical experiments added in the Appendix
- âŠ