Partitioned likelihood support and the evaluation of data set conflict

In simultaneous analyses of multiple data partitions, the trees relevant when measuring support for a clade are the optimal tree, and the best tree lacking the clade (i.e., the most reasonable alternative). The parsimony-based method of partitioned branch support (PBS) forces each data set to arbitrate between the two relevant trees. This value is the amount each data set contributes to clade support in the combined analysis, and can be very different to support apparent in separate analyses. The approach used in PBS can also be employed in likelihood: a simultaneous analysis of all data retrieves the maximum likelihood tree, and the best tree without the clade of interest is also found. Each data set is fitted to the two trees and the log-likelihood difference calculated, giving partitioned likelihood support (PLS) for each data set. These calculations can be performed regardless of the complexity of the ML model adopted. The significance of PLS can be evaluated using a variety of resampling methods, such as the Kishino-Hasegawa test, the Shimodiara-Hasegawa test, or likelihood weights, although the appropriateness and assumptions of these tests remains debated.

A genetic estimation algorithm for parameters of stochastic ordinary differential equations

A generic method for the estimation of parameters for Stochastic Ordinary Differential Equations (SODEs) is introduced and developed. This algorithm, called the GePERs method, utilises a genetic optimisation algorithm to minimise a stochastic objective function based on the Kolmogorov-Smirnov statistic. Numerical simulations are utilised to form the KS statistic. Further, the examination of some of the factors that improve the precision of the estimates is conducted. This method is used to estimate parameters of diffusion equations and jump-diffusion equations. It is also applied to the problem of model selection for the Queensland electricity market. (C) 2003 Elsevier B.V. All rights reserved.

Phylogeny and biogeography of the freshwater crayfish Euastacus (Decapoda : Parastacidae) based on nuclear and mitochondrial DNA

Euastacus crayfish are endemic to freshwater ecosystems of the eastern coast of Australia. While recent evolutionary studies have focused on a few of these species, here we provide a comprehensive phylogenetic estimate of relationships among the species within the genus. We sequenced three mitochondrial gene regions (COI, 16S, and 12S) and one nuclear region (28S) from 40 species of the genus Euastacus, as well as one undescribed species. Using these data, we estimated the phylogenetic relationships within the genus using maximum-likelihood, parsimony, and Bayesian Markov Chain Monte Carlo analyses. Using Bayes factors to test different model hypotheses, we found that the best phylogeny supports monophyletic groupings of all but two recognized species and suggests a widespread ancestor that diverged by vicariance. We also show that Eitastacus and Astacopsis are most likely monophyletic sister genera. We use the resulting phylogeny as a framework to test biogeographic hypotheses relating to the diversification of the genus. (c) 2005 Elsevier Inc. All rights reserved.

Re-admission to intensive care: Identification of risk factors

Background and Purpose. The re-admission of patients to intensive care is associated with increased morbidity, mortality, loss of morale for patients and family, and increased health costs. The aim of the present study was to identify factors which place patients at a higher risk of re-admission to intensive care. Method. A prospective study of patients who were re-admitted to a 22-bed tertiary level intensive care facility within a 12-month period. Data were kept on every patient re-admitted to intensive care, including standard demographic data, initial admission diagnosis, co-morbidities, re-admission diagnosis, mobility on discharge, secretions, airway, chest X-ray, PaCO2, PaO2, PaO2/FiO2and time of discharge. Subjects included 74 patients who had been re-admitted to intensive care in a 12-month period and a comparison group of patients who were not re-admitted to intensive care. A cross-tabs procedure was initially used to estimate maximum likelihood. Significant factors with an value of 65 years (p

Responses in carcass lean pH at 24 hours post-mortem in lines of Large White pigs selected for growth rate on a fixed ration over a set time

A restricted maximum likelihood analysis applied to an animal model showed no significant differences (P > 0.05) in pH value of the longissimus dorsi measured at 24 h post-mortem (pH24) between high and low lines of Large White pigs selected over 4 years for post-weaning growth rate on restricted feeding. Genetic and phenotypic correlations between pH24 and production and carcass traits were estimated using all performance testing records combined with the pH24 measurements (5.05–7.02) on slaughtered animals. The estimate of heritability for pH24 was moderate (0.29 ± 0.18). Genetic correlations between pH24 and production or carcass composition traits, except for ultrasonic backfat (UBF), were not significantly different from zero. UBF had a moderate, positive genetic correlation with pH24 (0.24 ± 0.33). These estimates of genetic correlations affirmed that selection for increased growth rate on restricted feeding is likely to result in limited changes in pH24 and pork quality since the selection does not put a high emphasis on reduced fatness.

Bias, precision and heritability of self-reported and clinically measured height in Australian twins

Many studies of quantitative and disease traits in human genetics rely upon self-reported measures. Such measures are based on questionnaires or interviews and are often cheaper and more readily available than alternatives. However, the precision and potential bias cannot usually be assessed. Here we report a detailed quantitative genetic analysis of stature. We characterise the degree of measurement error by utilising a large sample of Australian twin pairs (857 MZ, 815 DZ) with both clinical and self-reported measures of height. Self-report height measurements are shown to be more variable than clinical measures. This has led to lowered estimates of heritability in many previous studies of stature. In our twin sample the heritability estimate for clinical height exceeded 90%. Repeated measures analysis shows that 2-3 times as many self-report measures are required to recover heritability estimates similar to those obtained from clinical measures. Bivariate genetic repeated measures analysis of self-report and clinical height measures showed an additive genetic correlation > 0.98. We show that the accuracy of self-report height is upwardly biased in older individuals and in individuals of short stature. By comparing clinical and self-report measures we also showed that there was a genetic component to females systematically reporting their height incorrectly; this phenomenon appeared to not be present in males. The results from the measurement error analysis were subsequently used to assess the effects of error on the power to detect linkage in a genome scan. Moderate reduction in error (through the use of accurate clinical or multiple self-report measures) increased the effective sample size by 22%; elimination of measurement error led to increases in effective sample size of 41%.

Monitoring Infants By Automatic Video Processing

This work has, as its objective, the development of non-invasive and low-cost systems for monitoring and automatic diagnosing specific neonatal diseases by means of the analysis of suitable video signals. We focus on monitoring infants potentially at risk of diseases characterized by the presence or absence of rhythmic movements of one or more body parts. Seizures and respiratory diseases are specifically considered, but the approach is general. Seizures are defined as sudden neurological and behavioural alterations. They are age-dependent phenomena and the most common sign of central nervous system dysfunction. Neonatal seizures have onset within the 28th day of life in newborns at term and within the 44th week of conceptional age in preterm infants. Their main causes are hypoxic-ischaemic encephalopathy, intracranial haemorrhage, and sepsis. Studies indicate an incidence rate of neonatal seizures of 0.2% live births, 1.1% for preterm neonates, and 1.3% for infants weighing less than 2500 g at birth. Neonatal seizures can be classified into four main categories: clonic, tonic, myoclonic, and subtle. Seizures in newborns have to be promptly and accurately recognized in order to establish timely treatments that could avoid an increase of the underlying brain damage. Respiratory diseases related to the occurrence of apnoea episodes may be caused by cerebrovascular events. Among the wide range of causes of apnoea, besides seizures, a relevant one is Congenital Central Hypoventilation Syndrome (CCHS) \cite{Healy}. With a reported prevalence of 1 in 200,000 live births, CCHS, formerly known as Ondine's curse, is a rare life-threatening disorder characterized by a failure of the automatic control of breathing, caused by mutations in a gene classified as PHOX2B. CCHS manifests itself, in the neonatal period, with episodes of cyanosis or apnoea, especially during quiet sleep. The reported mortality rates range from 8% to 38% of newborn with genetically confirmed CCHS. Nowadays, CCHS is considered a disorder of autonomic regulation, with related risk of sudden infant death syndrome (SIDS). Currently, the standard method of diagnosis, for both diseases, is based on polysomnography, a set of sensors such as ElectroEncephaloGram (EEG) sensors, ElectroMyoGraphy (EMG) sensors, ElectroCardioGraphy (ECG) sensors, elastic belt sensors, pulse-oximeter and nasal flow-meters. This monitoring system is very expensive, time-consuming, moderately invasive and requires particularly skilled medical personnel, not always available in a Neonatal Intensive Care Unit (NICU). Therefore, automatic, real-time and non-invasive monitoring equipments able to reliably recognize these diseases would be of significant value in the NICU. A very appealing monitoring tool to automatically detect neonatal seizures or breathing disorders may be based on acquiring, through a network of sensors, e.g., a set of video cameras, the movements of the newborn's body (e.g., limbs, chest) and properly processing the relevant signals. An automatic multi-sensor system could be used to permanently monitor every patient in the NICU or specific patients at home. Furthermore, a wire-free technique may be more user-friendly and highly desirable when used with infants, in particular with newborns. This work has focused on a reliable method to estimate the periodicity in pathological movements based on the use of the Maximum Likelihood (ML) criterion. In particular, average differential luminance signals from multiple Red, Green and Blue (RGB) cameras or depth-sensor devices are extracted and the presence or absence of a significant periodicity is analysed in order to detect possible pathological conditions. The efficacy of this monitoring system has been measured on the basis of video recordings provided by the Department of Neurosciences of the University of Parma. Concerning clonic seizures, a kinematic analysis was performed to establish a relationship between neonatal seizures and human inborn pattern of quadrupedal locomotion. Moreover, we have decided to realize simulators able to replicate the symptomatic movements characteristic of the diseases under consideration. The reasons is, essentially, the opportunity to have, at any time, a 'subject' on which to test the continuously evolving detection algorithms. Finally, we have developed a smartphone App, called 'Smartphone based contactless epilepsy detector' (SmartCED), able to detect neonatal clonic seizures and warn the user about the occurrence in real-time.

Estimating conditional volatility with neural networks

It is well known that one of the obstacles to effective forecasting of exchange rates is heteroscedasticity (non-stationary conditional variance). The autoregressive conditional heteroscedastic (ARCH) model and its variants have been used to estimate a time dependent variance for many financial time series. However, such models are essentially linear in form and we can ask whether a non-linear model for variance can improve results just as non-linear models (such as neural networks) for the mean have done. In this paper we consider two neural network models for variance estimation. Mixture Density Networks (Bishop 1994, Nix and Weigend 1994) combine a Multi-Layer Perceptron (MLP) and a mixture model to estimate the conditional data density. They are trained using a maximum likelihood approach. However, it is known that maximum likelihood estimates are biased and lead to a systematic under-estimate of variance. More recently, a Bayesian approach to parameter estimation has been developed (Bishop and Qazaz 1996) that shows promise in removing the maximum likelihood bias. However, up to now, this model has not been used for time series prediction. Here we compare these algorithms with two other models to provide benchmark results: a linear model (from the ARIMA family), and a conventional neural network trained with a sum-of-squares error function (which estimates the conditional mean of the time series with a constant variance noise model). This comparison is carried out on daily exchange rate data for five currencies.

Delay estimation for multivariate time series

Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models (HMMs) to identify the lag (or delay) between different variables for such data. We first present a method using maximum likelihood estimation and propose a simple algorithm which is capable of identifying associations between variables. We also adopt an information-theoretic approach and develop a novel procedure for training HMMs to maximise the mutual information between delayed time series. Both methods are successfully applied to real data. We model the oil drilling process with HMMs and estimate a crucial parameter, namely the lag for return.

Variational inference for diffusion processes

Diffusion processes are a family of continuous-time continuous-state stochastic processes that are in general only partially observed. The joint estimation of the forcing parameters and the system noise (volatility) in these dynamical systems is a crucial, but non-trivial task, especially when the system is nonlinear and multimodal. We propose a variational treatment of diffusion processes, which allows us to compute type II maximum likelihood estimates of the parameters by simple gradient techniques and which is computationally less demanding than most MCMC approaches. We also show how a cheap estimate of the posterior over the parameters can be constructed based on the variational free energy.

Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes

Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are particles of different types. Usually such a process is not observable in the sense of the whole tree, but only as the “generation” at a given moment in time, which consists of the number of particles of every type. This requires an EM-type algorithm to obtain a maximum likelihood (ML) estimate of the parameters of the branching process. Using a version of the inside-outside algorithm for stochastic context-free grammars (SCFG), such an estimate could be obtained for the offspring distribution of the process.

Study on Robustness of Strehler-Mildvan Model

2000 Mathematics Subject Classi cation: 62F35, 62F15

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

Three essays on asset pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lvy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.

Three Essays on Asset Pricing

In this dissertation, I investigate three related topics on asset pricing: the consumption-based asset pricing under long-run risks and fat tails, the pricing of VIX (CBOE Volatility Index) options and the market price of risk embedded in stock returns and stock options. These three topics are fully explored in Chapter II through IV. Chapter V summarizes the main conclusions. In Chapter II, I explore the effects of fat tails on the equilibrium implications of the long run risks model of asset pricing by introducing innovations with dampened power law to consumption and dividends growth processes. I estimate the structural parameters of the proposed model by maximum likelihood. I find that the stochastic volatility model with fat tails can, without resorting to high risk aversion, generate implied risk premium, expected risk free rate and their volatilities comparable to the magnitudes observed in data. In Chapter III, I examine the pricing performance of VIX option models. The contention that simpler-is-better is supported by the empirical evidence using actual VIX option market data. I find that no model has small pricing errors over the entire range of strike prices and times to expiration. In general, Whaley’s Black-like option model produces the best overall results, supporting the simpler-is-better contention. However, the Whaley model does under/overprice out-of-the-money call/put VIX options, which is contrary to the behavior of stock index option pricing models. In Chapter IV, I explore risk pricing through a model of time-changed Lévy processes based on the joint evidence from individual stock options and underlying stocks. I specify a pricing kernel that prices idiosyncratic and systematic risks. This approach to examining risk premia on stocks deviates from existing studies. The empirical results show that the market pays positive premia for idiosyncratic and market jump-diffusion risk, and idiosyncratic volatility risk. However, there is no consensus on the premium for market volatility risk. It can be positive or negative. The positive premium on idiosyncratic risk runs contrary to the implications of traditional capital asset pricing theory.