Efficient Recursions for General Factorisable Models

Let n S-valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r+1 of the n components in the joint distribution, we term this a lag-r model, whose normalising constant can be computed using a forward recursion in O(Sr+1) computations, as opposed to O(Sn) for the direct computation. We show how a lag-r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed

Driving performance impairments due to hypovigilance on monotonous roads

Drivers' ability to react to unpredictable events deteriorates when exposed to highly predictable and uneventful driving tasks. Highway design reduces the driving task mainly to a lane-keeping manoeuvre. Such a task is monotonous, providing little stimulation and this contributes to crashes due to inattention. Research has shown that driver's hypovigilance can be assessed with EEG measurements and that driving performance is impaired during prolonged monotonous driving tasks. This paper aims to show that two dimensions of monotony - namely road design and road side variability - decrease vigilance and impair driving performance. This is the first study correlating hypovigilance and driver performance in varied monotonous conditions, particularly on a short time scale (a few seconds). We induced vigilance decrement as assessed with an EEG during a monotonous driving simulator experiment. Road monotony was varied through both road design and road side variability. The driver's decrease in vigilance occurred due to both road design and road scenery monotony and almost independently of the driver's sensation seeking level. Such impairment was also correlated to observable measurements from the driver, the car and the environment. During periods of hypovigilance, the driving performance impairment affected lane positioning, time to lane crossing, blink frequency, heart rate variability and non-specific electrodermal response rates. This work lays the foundation for the development of an in-vehicle device preventing hypovigilance crashes on monotonous roads

Variational bayes for estimating the parameters of a hidden Potts model

Hidden Markov random field models provide an appealing representation of images and other spatial problems. The drawback is that inference is not straightforward for these models as the normalisation constant for the likelihood is generally intractable except for very small observation sets. Variational methods are an emerging tool for Bayesian inference and they have already been successfully applied in other contexts. Focusing on the particular case of a hidden Potts model with Gaussian noise, we show how variational Bayesian methods can be applied to hidden Markov random field inference. To tackle the obstacle of the intractable normalising constant for the likelihood, we explore alternative estimation approaches for incorporation into the variational Bayes algorithm. We consider a pseudo-likelihood approach as well as the more recent reduced dependence approximation of the normalisation constant. To illustrate the effectiveness of these approaches we present empirical results from the analysis of simulated datasets. We also analyse a real dataset and compare results with those of previous analyses as well as those obtained from the recently developed auxiliary variable MCMC method and the recursive MCMC method. Our results show that the variational Bayesian analyses can be carried out much faster than the MCMC analyses and produce good estimates of model parameters. We also found that the reduced dependence approximation of the normalisation constant outperformed the pseudo-likelihood approximation in our analysis of real and synthetic datasets

Forecasting negative effects of monotony and sensation seeking on performance during a vigilance task

The driving task requires sustained attention during prolonged periods, and can be performed in highly predictable or repetitive environments. Such conditions could create hypovigilance and impair performance towards critical events. Identifying such impairment in monotonous conditions has been a major subject of research, but no research to date has attempted to predict it in real-time. This pilot study aims to show that performance decrements due to monotonous tasks can be predicted through mathematical modelling taking into account sensation seeking levels. A short vigilance task sensitive to short periods of lapses of vigilance called Sustained Attention to Response Task is used to assess participants‟ performance. The framework for prediction developed on this task could be extended to a monotonous driving task. A Hidden Markov Model (HMM) is proposed to predict participants‟ lapses in alertness. Driver‟s vigilance evolution is modelled as a hidden state and is correlated to a surrogate measure: the participant‟s reactions time. This experiment shows that the monotony of the task can lead to an important decline in performance in less than five minutes. This impairment can be predicted four minutes in advance with an 86% accuracy using HMMs. This experiment showed that mathematical models such as HMM can efficiently predict hypovigilance through surrogate measures. The presented model could result in the development of an in-vehicle device that detects driver hypovigilance in advance and warn the driver accordingly, thus offering the potential to enhance road safety and prevent road crashes

Real-time performance modelling of a sustained attention to response task

Vigilance declines when exposed to highly predictable and uneventful tasks. Monotonous tasks provide little cognitive and motor stimulation and contribute to human errors. This paper aims to model and detect vigilance decline in real time through participant’s reaction times during a monotonous task. A lab-based experiment adapting the Sustained Attention to Response Task (SART) is conducted to quantify the effect of monotony on overall performance. Then relevant parameters are used to build a model detecting hypovigilance throughout the experiment. The accuracy of different mathematical models are compared to detect in real-time – minute by minute - the lapses in vigilance during the task. We show that monotonous tasks can lead to an average decline in performance of 45%. Furthermore, vigilance modelling enables to detect vigilance decline through reaction times with an accuracy of 72% and a 29% false alarm rate. Bayesian models are identified as a better model to detect lapses in vigilance as compared to Neural Networks and Generalised Linear Mixed Models. This modelling could be used as a framework to detect vigilance decline of any human performing monotonous tasks

Fully Bayesian experimental design for pharmacokinetic studies

Utility functions in Bayesian experimental design are usually based on the posterior distribution. When the posterior is found by simulation, it must be sampled from for each future data set drawn from the prior predictive distribution. Many thousands of posterior distributions are often required. A popular technique in the Bayesian experimental design literature to rapidly obtain samples from the posterior is importance sampling, using the prior as the importance distribution. However, importance sampling will tend to break down if there is a reasonable number of experimental observations and/or the model parameter is high dimensional. In this paper we explore the use of Laplace approximations in the design setting to overcome this drawback. Furthermore, we consider using the Laplace approximation to form the importance distribution to obtain a more efficient importance distribution than the prior. The methodology is motivated by a pharmacokinetic study which investigates the effect of extracorporeal membrane oxygenation on the pharmacokinetics of antibiotics in sheep. The design problem is to find 10 near optimal plasma sampling times which produce precise estimates of pharmacokinetic model parameters/measures of interest. We consider several different utility functions of interest in these studies, which involve the posterior distribution of parameter functions

Benchmarking and scalability of machine-learning methods for photometric redshift estimation

Obtaining accurate photometric redshift (photo-z) estimations is an important aspect of cosmology, remaining a prerequisite of many analyses. In creating novel methods to produce photo-z estimations, there has been a shift towards using machine-learning techniques. However, there has not been as much of a focus on how well different machine-learning methods scale or perform with the ever-increasing amounts of data being produced. Here, we introduce a benchmark designed to analyse the performance and scalability of different supervised machine-learning methods for photo-z estimation. Making use of the Sloan Digital Sky Survey (SDSS – DR12) data set, we analysed a variety of the most used machine-learning algorithms. By scaling the number of galaxies used to train and test the algorithms up to one million, we obtained several metrics demonstrating the algorithms’ performance and scalability for this task. Furthermore, by introducing a new optimization method, time-considered optimization, we were able to demonstrate how a small concession of error can allow for a great improvement in efficiency. From the algorithms tested, we found that the Random Forest performed best with a mean squared error, MSE = 0.0042; however, as other algorithms such as Boosted Decision Trees and k-Nearest Neighbours performed very similarly, we used our benchmarks to demonstrate how different algorithms could be superior in different scenarios. We believe that benchmarks like this will become essential with upcoming surveys, such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), which will capture billions of galaxies requiring photometric redshifts

An Upper Palaeolithic Proto-writing System and Phenological Calendar

In at least 400 European caves such as Lascaux, Chauvet and Altamira, Upper Palaeolithic Homo sapiens groups drew, painted and engraved non-figurative signs from at least ~42,000 BP and figurative images (notably animals) from at least 37,000 BP. Since their discovery ~150 years ago, the purpose or meaning of European Upper Palaeolithic non-figurative signs has eluded researchers. Despite this, specialists assume that they were notational in some way. Using a database of images spanning the European Upper Palaeolithic, we suggest how three of the most frequently occurring signs—the line , the dot , and the —functioned as units of communication. We demonstrate that when found in close association with images of animals the line and dot constitute numbers denoting months, and form constituent parts of a local phenological/meteorological calendar beginning in spring and recording time from this point in lunar months. We also demonstrate that the sign, one of the most frequently occurring signs in Palaeolithic non-figurative art, has the meaning . The position of the within a sequence of marks denotes month of parturition, an ordinal representation of number in contrast to the cardinal representation used in tallies. Our data indicate that the purpose of this system of associating animals with calendar information was to record and convey seasonal behavioural information about specific prey taxa in the geographical regions of concern. We suggest a specific way in which the pairing of numbers with animal subjects constituted a complete unit of meaning—a notational system combined with its subject—that provides us with a specific insight into what one set of notational marks means. It gives us our first specific reading of European Upper Palaeolithic communication, the first known writing in the history of Homo sapiens

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy