Bayesian spatio-temporal modelling of rainfall through non-homogenous hidden Markov models

Multi-site statistical models for daily rainfall should account for spatial and temporal dependence amongst measurements and also allow for the event of no rain. Recent research into climate change and variability has sparked interest in the relationship between rainfall and climate, stimulating the development of statistical models that relate large-scale atmospheric variables to local precipitation. Although modelling daily rainfall presents a challenging and topical problem, there have been few attempts taking a subjective Bayesian approach. This thesis is concerned with developing hidden Markov models (HMMs) for the spatio-temporal analysis of rainfall data, within a Bayesian framework. In these models, daily rainfall patterns are driven by a finite number of unobserved states, interpreted as weather states, that evolve in time as a first order Markov chain. The weather states explain space time structure in the data so that reasonably simple models can be adopted within states. Throughout this thesis, the models and procedures are illustrated using data from a small dense network of six sites situated in Yorkshire, UK. First we study a simple (homogeneous) HMM in which rainfall occurrences and amounts, given occurrences, are conditionally independent in space and time, given the weather state, and have Bernoulli and gamma distributions, respectively. We compare methods for approximating the posterior distribution for the number of weather states. This simple model does not incorporate atmospheric information and appears not to capture the observed spatio-temporal structure. We therefore investigate two non-homogeneous hidden Markov models (NHMMs) in which we allow the transition probabilities between weather states to depend on time-varying atmospheric variables and successively relax the conditional independence assumptions. The first NHMM retains the simple conditional model for non-zero rainfall amounts but allows occurrences to form a Markov chain of autologistic models, given the weather state. The second introduces latent multivariate normal random variables to form a hierarchical NHMM in which neither rainfall occurrences nor non-zero amounts are conditionally spatially or temporally independent, given the weather state. Throughout this thesis, we emphasise the elicitation of prior distributions that convey genuine initial beliefs. For each hidden Markov model studied we demonstrate techniques to assist in this task.EThOS - Electronic Theses Online ServiceEngineering and Physical Sciences Research CouncilGBUnited Kingdo

Time as a guide to cause

How do people learn causal structure? In two studies we investigated the interplay between temporal order, intervention and covariational cues. In Study 1 temporal order overrode covariation information, leading to spurious causal inferences when the temporal cues were misleading. In Study 2 both temporal order and intervention contributed to accurate causal inference, well beyond that achievable through covariational data alone. Together the studies show that people use both temporal order and interventional cues to infer causal structure, and that these cues dominate the available statistical information. We endorse a hypothesis-driven account of learning, whereby people use cues such as temporal order to generate initial models, and then test these models against the incoming covariational data

A Framework for Bioacoustic Vocalization Analysis Using Hidden Markov Models

Using Hidden Markov Models (HMMs) as a recognition framework for automatic classification of animal vocalizations has a number of benefits, including the ability to handle duration variability through nonlinear time alignment, the ability to incorporate complex language or recognition constraints, and easy extendibility to continuous recognition and detection domains. In this work, we apply HMMs to several different species and bioacoustic tasks using generalized spectral features that can be easily adjusted across species and HMM network topologies suited to each task. This experimental work includes a simple call type classification task using one HMM per vocalization for repertoire analysis of Asian elephants, a language-constrained song recognition task using syllable models as base units for ortolan bunting vocalizations, and a stress stimulus differentiation task in poultry vocalizations using a non-sequential model via a one-state HMM with Gaussian mixtures. Results show strong performance across all tasks and illustrate the flexibility of the HMM framework for a variety of species, vocalization types, and analysis tasks

A hidden spatial-temporal Markov random field model for network-based analysis of time course gene expression data

Microarray time course (MTC) gene expression data are commonly collected to study the dynamic nature of biological processes. One important problem is to identify genes that show different expression profiles over time and pathways that are perturbed during a given biological process. While methods are available to identify the genes with differential expression levels over time, there is a lack of methods that can incorporate the pathway information in identifying the pathways being modified/activated during a biological process. In this paper we develop a hidden spatial-temporal Markov random field (hstMRF)-based method for identifying genes and subnetworks that are related to biological processes, where the dependency of the differential expression patterns of genes on the networks are modeled over time and over the network of pathways. Simulation studies indicated that the method is quite effective in identifying genes and modified subnetworks and has higher sensitivity than the commonly used procedures that do not use the pathway structure or time dependency information, with similar false discovery rates. Application to a microarray gene expression study of systemic inflammation in humans identified a core set of genes on the KEGG pathways that show clear differential expression patterns over time. In addition, the method confirmed that the TOLL-like signaling pathway plays an important role in immune response to endotoxins.Comment: Published in at http://dx.doi.org/10.1214/07--AOAS145 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Discrimination of Individual Tigers (\u3cem\u3ePanthera tigris\u3c/em\u3e) from Long Distance Roars

This paper investigates the extent of tiger (Panthera tigris) vocal individuality through both qualitative and quantitative approaches using long distance roars from six individual tigers at Omaha\u27s Henry Doorly Zoo in Omaha, NE. The framework for comparison across individuals includes statistical and discriminant function analysis across whole vocalization measures and statistical pattern classification using a hidden Markov model (HMM) with frame-based spectral features comprised of Greenwood frequency cepstral coefficients. Individual discrimination accuracy is evaluated as a function of spectral model complexity, represented by the number of mixtures in the underlying Gaussian mixture model (GMM), and temporal model complexity, represented by the number of sequential states in the HMM. Results indicate that the temporal pattern of the vocalization is the most significant factor in accurate discrimination. Overall baseline discrimination accuracy for this data set is about 70% using high level features without complex spectral or temporal models. Accuracy increases to about 80% when more complex spectral models (multiple mixture GMMs) are incorporated, and increases to a final accuracy of 90% when more detailed temporal models (10-state HMMs) are used. Classification accuracy is stable across a relatively wide range of configurations in terms of spectral and temporal model resolution

Exploring Cognitive States: Methods for Detecting Physiological Temporal Fingerprints

Cognitive state detection and its relationship to observable physiologically telemetry has been utilized for many human-machine and human-cybernetic applications. This paper aims at understanding and addressing if there are unique psychophysiological patterns over time, a physiological temporal fingerprint, that is associated with specific cognitive states. This preliminary work involves commercial airline pilots completing experimental benchmark task inductions of three cognitive states: 1) Channelized Attention (CA); 2) High Workload (HW); and 3) Low Workload (LW). We approach this objective by modeling these "fingerprints" through the use of Hidden Markov Models and Entropy analysis to evaluate if the transitions over time are complex or rhythmic/predictable by nature. Our results indicate that cognitive states do have unique complexity of physiological sequences that are statistically different from other cognitive states. More specifically, CA has a significantly higher temporal psychophysiological complexity than HW and LW in EEG and ECG telemetry signals. With regards to respiration telemetry, CA has a lower temporal psychophysiological complexity than HW and LW. Through our preliminary work, addressing this unique underpinning can inform whether these underlying dynamics can be utilized to understand how humans transition between cognitive states and for improved detection of cognitive states