John Moriarty

Phylogenetic inference for function-valued traits : speech sound evolution

Phylogenetic models have recently been proposed for data that are best represented as a mathematical function (i.e. function valued). Such methods can be used to model the change over time in function-based descriptions of various data of interest to evolutionary biologists, including the sound of speech. This approach to phylogenetic inference and analysis is challenging, both in terms of modeling the phylogenetics of functions and in engaging with previously existing evidence for character-state change. Nevertheless, it is both a real and exciting prospect. Our approach could provide those interested in investigating a greater range of evolutionary processes with the ability to use statistical hypothesis-testing procedures and to create estimates of the states of function-valued characteristics (e.g. speech sounds) at earlier historical times.

The expected lifetime of an extraction project

When a mining company begins extraction from a finite resource, it does so in the presence of numerous uncertainties. One key uncertainty is the future price of the commodity being extracted, since a large enough drop in price can make a resource no longer cost-effective to extract, resulting in the mine being closed down. By specifying a stochastic price process, and implementing a financial-type model which leads to the use of partial differential equations, this paper creates the framework for efficiently capturing the probability of a mine remaining open throughout its planned extraction period, and derives the associated expected lifetime of extraction. An approximation to the abandonment price is described, which enables a closed-form solution to be derived for the probability of operational success and expected lifetime. This approximation compares well with the full solution obtained using a semi-Lagrangian numerical technique.

Evolutionary inference for function-valued traits: Gaussian process regression on phylogenies

Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated owing to phylogenetic relationships. In this paper, we give a flexible statistical model for such data, by combining assumptions from phylogenetics with Gaussian processes. We describe its use as a non-parametric Bayesian prior distribution, both for prediction (placing posterior distributions on ancestral functions) and model selection (comparing rates of evolution across a phylogeny, or identifying the most likely phylogenies consistent with the observed data). Our work is integrative, extending the popular phylogenetic Brownian motion and Ornstein–Uhlenbeck models to functional data and Bayesian inference, and extending Gaussian process regression to phylogenies. We provide a brief illustration of the application of our method.

Function-valued traits in evolution

Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Given a dataset of function-valued traits generated by evolution, we develop a practical, statistical approach to infer ancestral function-valued traits, and estimate the generative evolutionary process. We do this by combining dimension reduction and phylogenetic Gaussian process regression, a non-parametric procedure that explicitly accounts for known phylogenetic relationships. We test the performance of methods on simulated, function-valued data generated from a stochastic evolutionary model. The methods are applied assuming that only the phylogeny, and the function-valued traits of taxa at its tips are known. Our method is robust and applicable to a wide range of function-valued data, and also offers a phylogenetically aware method for estimating the autocorrelation of function-valued traits.

Exit problems associated with affine reflection groups

We obtain a formula for the distribution of the first exit time of Brownian motion from the alcove of an affine Weyl group. In most cases the formula is expressed compactly, in terms of Pfaffians. Expected exit times are derived in the type

Analysis of spike train data: A multivariate mixed effects model for phase and amplitude

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Risk-sensitive optimal switching and applications to district energy systems

case. The results extend to other Markov processes. We also give formulas for the real eigenfunctions of the Dirichlet and Neumann Laplacians on alcoves, observing that the ‘Hot Spots’ conjecture of J. Rauch is true for alcoves.

Stochastic control and real options valuation of thermal storage-enabled demand response from flexible district energy systems

The aim of this paper, which is framed within the research activities of the EC FP7 IREEN Project, is to quantify the value of operational flexibility (with applications to planning) in ICT-enabled district energy systems. In particular, our work offers an integrated approach to the optimal operation and planning of flexible systems composed of high efficiency combined heat and power (CHP) and heat storage resources that can provide optimal demand response (DR) to real-time external signals (such as energy prices) and considering measurements and forecasts of different variables (weather, energy loads, and so on). The methodological approach, borrowed from finance theory, is based on a mixed operational and planning model using stochastic control techniques (for operational optimization, closely related to the pricing of swing options) which is in turn used for long-term (planning) real options evaluation. Numerical applications to exemplify the model developed refer to realistic UK applications. The model is a first step towards quantifying the operational and planning value of smart technologies and thus enabling the development of business cases for ICT-enabled energy efficient neighborhoods.