Skill Rating by Bayesian Inference

Systems Engineering often involves computer modelling the behaviour of proposed systems and their components. Where a component is human, fallibility must be modelled by a stochastic agent. The identification of a model of decision-making over quantifiable options is investigated using the game-domain of Chess. Bayesian methods are used to infer the distribution of players’ skill levels from the moves they play rather than from their competitive results. The approach is used on large sets of games by players across a broad FIDE Elo range, and is in principle applicable to any scenario where high-value decisions are being made under pressure.

A nonparametric ensemble transform method for Bayesian inference

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables. © 2013, Society for Industrial and Applied Mathematics

Online bayesian inference in some time-frequency representations of non-stationary processes

The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data.

How large is congressional dependence in agriculture. Bayesian inference about ‘scale’ and ‘scope’ in measuring a spatial externality

The political economy literature on agriculture emphasizes influence over political outcomes via lobbying conduits in general, political action committee contributions in particular and the pervasive view that political preferences with respect to agricultural issues are inherently geographic. In this context, ‘interdependence’ in Congressional vote behaviour manifests itself in two dimensions. One dimension is the intensity by which neighboring vote propensities influence one another and the second is the geographic extent of voter influence. We estimate these facets of dependence using data on a Congressional vote on the 2001 Farm Bill using routine Markov chain Monte Carlo procedures and Bayesian model averaging, in particular. In so doing, we develop a novel procedure to examine both the reliability and the consequences of different model representations for measuring both the ‘scale’ and the ‘scope’ of spatial (geographic) co-relations in voting behaviour.

Inference on microsatellite mutation processes in the invasive mite, Varroa destructor, using reversible jump Markov chain Monte Carlo

Varroa destructor is a parasitic mite of the Eastern honeybee Apis cerana. Fifty years ago, two distinct evolutionary lineages (Korean and Japanese) invaded the Western honeybee Apis mellifera. This haplo-diploid parasite species reproduces mainly through brother sister matings, a system which largely favors the fixation of new mutations. In a worldwide sample of 225 individuals from 21 locations collected on Western honeybees and analyzed at 19 microsatellite loci, a series of de novo mutations was observed. Using historical data concerning the invasion, this original biological system has been exploited to compare three mutation models with allele size constraints for microsatellite markers: stepwise (SMM) and generalized (GSM) mutation models, and a model with mutation rate increasing exponentially with microsatellite length (ESM). Posterior probabilities of the three models have been estimated for each locus individually using reversible jump Markov Chain Monte Carlo. The relative support of each model varies widely among loci, but the GSM is the only model that always receives at least 9% support, whatever the locus. The analysis also provides robust estimates of mutation parameters for each locus and of the divergence time of the two invasive lineages (67,000 generations with a 90% credibility interval of 35,000-174,000). With an average of 10 generations per year, this divergence time fits with the last post-glacial Korea Japan land separation. (c) 2005 Elsevier Inc. All rights reserved.

Energetic constraints on precipitation under climate change

Energetic constraints on precipitation are useful for understanding the response of the hydrological cycle to ongoing climate change, its response to possible geoengineering schemes, and the limits on precipitation in very warm climates of the past. Much recent progress has been made in quantifying the different forcings and feedbacks on precipitation and in understanding how the transient responses of precipitation and temperature might differ qualitatively. Here, we introduce the basic ideas and review recent progress. We also examine the extent to which energetic constraints on precipitation may be viewed as radiative constraints and the extent to which they are confirmed by available observations. Challenges remain, including the need to better demonstrate the link between energetics and precipitation in observations and to better understand energetic constraints on precipitation at sub-global length scales.

Triple isotope (δD, δ17O, δ18O) study on precipitation, drip water and speleothem fluid inclusions for a central European cave (NW Switzerland)

Deuterium (dD) and oxygen (d18O) isotopes are powerful tracers of the hydrological cycle and have been extensively used for paleoclimate reconstructions as they can provide information on past precipitation, temperature and atmospheric circulation. More recently, the use of 17Oexcess derived from precise measurement of d17O and d18O gives new and additional insights in tracing the hydrological cycle whereas uncertainties surround this proxy. However, 17Oexcess could provide additional information on the atmospheric conditions at the moisture source as well as about fractionations associated with transport and site processes. In this paper we trace water stable isotopes (dD, d17O and d18O) along their path from precipitation to cave drip water and finally to speleothem fluid inclusions for Milandre cave in northwestern Switzerland. A two year-long daily resolved precipitation isotope record close to the cave site is compared to collected cave drip water (3 months average resolution) and fluid inclusions of modern and Holocene stalagmites. Amount weighted mean dD, d18O and d17O are �71.0‰, �9.9‰, �5.2‰ for precipitation, �60.3‰, �8.7‰, �4.6‰ for cave drip water and �61.3‰, �8.3‰, �4.7‰ for recent fluid inclusions respectively. Second order parameters have also been derived in precipitation and drip water and present similar values with 18 per meg for 17Oexcess whereas d-excess is 1.5‰ more negative in drip water. Furthermore, the atmospheric signal is shifted towards enriched values in the drip water and fluid inclusions (D of ~ þ 10‰ for dD). The isotopic composition of cave drip water exhibits a weak seasonal signal which is shifted by around 8e10 months (groundwater residence time) when compared to the precipitation. Moreover, we carried out the first d17O measurement in speleothem fluid inclusions, as well as the first comparison of the d17O behaviour from the meteoric water to the fluid inclusions entrapment in speleothems. This study on precipitation, drip water and fluid inclusions will be used as a speleothem proxy calibration for Milandre cave in order to reconstruct paleotemperatures and moisture source variations for Western Central Europe.

Skilloscopy: Bayesian modeling of decision makers' skill

This paper proposes and demonstrates an approach, Skilloscopy, to the assessment of decision makers. In an increasingly sophisticated, connected and information-rich world, decision making is becoming both more important and more difficult. At the same time, modelling decision-making on computers is becoming more feasible and of interest, partly because the information-input to those decisions is increasingly on record. The aims of Skilloscopy are to rate and rank decision makers in a domain relative to each other: the aims do not include an analysis of why a decision is wrong or suboptimal, nor the modelling of the underlying cognitive process of making the decisions. In the proposed method a decision-maker is characterised by a probability distribution of their competence in choosing among quantifiable alternatives. This probability distribution is derived by classic Bayesian inference from a combination of prior belief and the evidence of the decisions. Thus, decision-makers’ skills may be better compared, rated and ranked. The proposed method is applied and evaluated in the gamedomain of Chess. A large set of games by players across a broad range of the World Chess Federation (FIDE) Elo ratings has been used to infer the distribution of players’ rating directly from the moves they play rather than from game outcomes. Demonstration applications address questions frequently asked by the Chess community regarding the stability of the Elo rating scale, the comparison of players of different eras and/or leagues, and controversial incidents possibly involving fraud. The method of Skilloscopy may be applied in any decision domain where the value of the decision-options can be quantified.

On the environmental valuation of catastrophe: revisiting mining disasters in the United Kingdom, 1851-1962

In the context of environmental valuation of natural disasters, an important component of the evaluation procedure lies in determining the periodicity of events. This paper explores alternative methodologies for determining such periodicity, illustrating the advantages and the disadvantages of the separate methods and their comparative predictions. The procedures employ Bayesian inference and explore recent advances in computational aspects of mixtures methodology. The procedures are applied to the classic data set of Maguire et al (Biometrika, 1952) which was subsequently updated by Jarrett (Biometrika, 1979) and which comprise the seminal investigations examining the periodicity of mining disasters within the United Kingdom, 1851-1962.

Detection and attribution of human influence on regional precipitation

Understanding how human influence on climate is affecting precipitation around the world is immensely important for defining mitigation policies, and for adaptation planning. Yet despite increasing evidence for the influence of climate change on global patterns of precipitation, and expectations that significant changes in regional precipitation should have already occurred as a result of human influence on climate, compelling evidence of anthropogenic fingerprints on regional precipitation is obscured by observational and modelling uncertainties and is likely to remain so using current methods for years to come. This is in spite of substantial ongoing improvements in models, new reanalyses and a satellite record that spans over thirty years. If we are to quantify how human-induced climate change is affecting the regional water cycle, we need to consider novel ways of identifying the effects of natural and anthropogenic influences on precipitation that take full advantage of our physical expectations.

Statistical inference of OH concentrations and air mass dilution rates from successive observations of non-methane hydrocarbons in single air masses

Bayesian inference has been used to determine rigorous estimates of hydroxyl radical concentrations () and air mass dilution rates (K) averaged following air masses between linked observations of nonmethane hydrocarbons (NMHCs) spanning the North Atlantic during the Intercontinental Transport and Chemical Transformation (ITCT)-Lagrangian-2K4 experiment. The Bayesian technique obtains a refined (posterior) distribution of a parameter given data related to the parameter through a model and prior beliefs about the parameter distribution. Here, the model describes hydrocarbon loss through OH reaction and mixing with a background concentration at rate K. The Lagrangian experiment provides direct observations of hydrocarbons at two time points, removing assumptions regarding composition or sources upstream of a single observation. The estimates are sharpened by using many hydrocarbons with different reactivities and accounting for their variability and measurement uncertainty. A novel technique is used to construct prior background distributions of many species, described by variation of a single parameter . This exploits the high correlation of species, related by the first principal component of many NMHC samples. The Bayesian method obtains posterior estimates of , K and following each air mass. Median values are typically between 0.5 and 2.0 × 106 molecules cm−3, but are elevated to between 2.5 and 3.5 × 106 molecules cm−3, in low-level pollution. A comparison of estimates from absolute NMHC concentrations and NMHC ratios assuming zero background (the “photochemical clock” method) shows similar distributions but reveals systematic high bias in the estimates from ratios. Estimates of K are ∼0.1 day−1 but show more sensitivity to the prior distribution assumed.

Water vapor variability in the tropics and its links to dynamics and precipitation

The distribution and variability of water vapor and its links with radiative cooling and latent heating via precipitation are crucial to understanding feedbacks and processes operating within the climate system. Column-integrated water vapor (CWV) and additional variables from the European Centre for Medium-Range Weather Forecasts (ECMWF) 40-year reanalysis (ERA40) are utilized to quantify the spatial and temporal variability in tropical water vapor over the period 1979–2001. The moisture variability is partitioned between dynamical and thermodynamic influences and compared with variations in precipitation provided by the Climate Prediction Center Merged Analysis of Precipitation (CMAP) and the Global Precipitation Climatology Project (GPCP). The spatial distribution of CWV is strongly determined by thermodynamic constraints. Spatial variability in CWV is dominated by changes in the large-scale dynamics, in particular associated with the El Niño–Southern Oscillation (ENSO). Trends in CWV are also dominated by dynamics rather than thermodynamics over the period considered. However, increases in CWV associated with changes in temperature are significant over the equatorial east Pacific when analyzing interannual variability and over the north and northwest Pacific when analyzing trends. Significant positive trends in CWV tend to predominate over the oceans while negative trends in CWV are found over equatorial Africa and Brazil. Links between changes in CWV and vertical motion fields are identified over these regions and also the equatorial Atlantic. However, trends in precipitation are generally incoherent and show little association with the CWV trends. This may in part reflect the inadequacies of the precipitation data sets and reanalysis products when analyzing decadal variability. Though the dynamic component of CWV is a major factor in determining precipitation variability in the tropics, in some regions/seasons the thermodynamic component cancels its effect on precipitation variability.

Performance and prediction: Bayesian modelling of fallible choice in chess

Evaluating agents in decision-making applications requires assessing their skill and predicting their behaviour. Both are well developed in Poker-like situations, but less so in more complex game and model domains. This paper addresses both tasks by using Bayesian inference in a benchmark space of reference agents. The concepts are explained and demonstrated using the game of chess but the model applies generically to any domain with quantifiable options and fallible choice. Demonstration applications address questions frequently asked by the chess community regarding the stability of the rating scale, the comparison of players of different eras and/or leagues, and controversial incidents possibly involving fraud. The last include alleged under-performance, fabrication of tournament results, and clandestine use of computer advice during competition. Beyond the model world of games, the aim is to improve fallible human performance in complex, high-value tasks.

Orographic Enhancement of Precipitation inside Hurricane Dean

On 17 August 2007, the center of Hurricane Dean passed within 92 km of the mountainous island of Dominica in the West Indies. Despite its distance from the island and its category 1–2 state, Dean brought significant total precipitation exceeding 500 mm and caused numerous landslides. Four rain gauges, a Moderate Resolution Imaging Spectroradiometer (MODIS) image, and 5-min radar scans from Guadeloupe and Martinique are used to determine the storm’s structure and the mountains’ effect on precipitation. The encounter is best described in three phases: (i) an east-northeast dry flow with three isolated drifting cells; (ii) a brief passage of the narrow outer rainband; and (iii) an extended period with south-southeast airflow in a nearly stationary spiral rainband. In this final phase, from 1100 to 2400 UTC, heavy rainfall from the stationary rainband was doubled by orographic enhancement. This enhancement pushed the sloping soils past the landslide threshold. The enhancement was caused by a modified seeder–feeder accretion mechanism that created a “dipole” pattern of precipitation, including a dry zone over the ocean in the lee. In contrast to normal trade-wind conditions, no terrain triggering of convection was identified in the hurricane environment.