Extension of spherical nonparametric estimators to nonisotropic kernels: An oceanographic application

In a recently published paper. spherical nonparametric estimators were applied to feature-track ensembles to determine a range of statistics for the atmospheric features considered. This approach obviates the types of bias normally introduced with traditional estimators. New spherical isotropic kernels with local support were introduced. Ln this paper the extension to spherical nonisotropic kernels with local support is introduced, together with a means of obtaining the shape and smoothing parameters in an objective way. The usefulness of spherical nonparametric estimators based on nonisotropic kernels is demonstrated with an application to an oceanographic feature-track ensemble.

Spherical nonparametric estimators applied to the UGAMP model integration for AMIP

The aim of this paper is essentially twofold: first, to describe the use of spherical nonparametric estimators for determining statistical diagnostic fields from ensembles of feature tracks on a global domain, and second, to report the application of these techniques to data derived from a modern general circulation model. New spherical kernel functions are introduced that are more efficiently computed than the traditional exponential kernels. The data-driven techniques of cross-validation to determine the amount elf smoothing objectively, and adaptive smoothing to vary the smoothing locally, are also considered. Also introduced are techniques for combining seasonal statistical distributions to produce longer-term statistical distributions. Although all calculations are performed globally, only the results for the Northern Hemisphere winter (December, January, February) and Southern Hemisphere winter (June, July, August) cyclonic activity are presented, discussed, and compared with previous studies. Overall, results for the two hemispheric winters are in good agreement with previous studies, both for model-based studies and observational studies.

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.

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.

Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon-known as heterotachy-can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our 'pattern-heterogeneity' mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of 'significance' such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.

A note on the accuracy of PAC-likelihood inference with microsatellite data

Stephens and Donnelly have introduced a simple yet powerful importance sampling scheme for computing the likelihood in population genetic models. Fundamental to the method is an approximation to the conditional probability of the allelic type of an additional gene, given those currently in the sample. As noted by Li and Stephens, the product of these conditional probabilities for a sequence of draws that gives the frequency of allelic types in a sample is an approximation to the likelihood, and can be used directly in inference. The aim of this note is to demonstrate the high level of accuracy of "product of approximate conditionals" (PAC) likelihood when used with microsatellite data. Results obtained on simulated microsatellite data show that this strategy leads to a negligible bias over a wide range of the scaled mutation parameter theta. Furthermore, the sampling variance of likelihood estimates as well as the computation time are lower than that obtained with importance sampling on the whole range of theta. It follows that this approach represents an efficient substitute to IS algorithms in computer intensive (e.g. MCMC) inference methods in population genetics. (c) 2006 Elsevier Inc. All rights reserved.

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.

Ranald Macdonald and statistical inference

Ranald Roderick Macdonald (1945-2007) was an important contributor to mathematical psychology in the UK, as a referee and action editor for British Journal of Mathematical and Statistical Psychology and as a participant and organizer at the British Psychological Society's Mathematics, statistics and computing section meetings. This appreciation argues that his most important contribution was to the foundations of significance testing, where his concern about what information was relevant in interpreting the results of significance tests led him to be a persuasive advocate for the 'Weak Fisherian' form of hypothesis testing.

The relative success of recognition-based inference in multichoice decisions

The utility of an "ecologically rational" recognition-based decision rule in multichoice decision problems is analyzed, varying the type of judgment required (greater or lesser). The maximum size and range of a counterintuitive advantage associated with recognition-based judgment (the "less-is-more effect") is identified for a range of cue validity values. Greater ranges of the less-is-more effect occur when participants are asked which is the greatest of to choices (m > 2) than which is the least. Less-is-more effects also have greater range for larger values of in. This implies that the classic two-altemative forced choice task, as studied by Goldstein and Gigerenzer (2002), may not be the most appropriate test case for less-is-more effects.