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.

A little learning is a dangerous thing: an experimental demonstration of ignorance-driven inference

Studies of ignorance-driven decision making have been employed to analyse when ignorance should prove advantageous on theoretical grounds or else they have been employed to examine whether human behaviour is consistent with an ignorance-driven inference strategy (e. g., the recognition heuristic). In the current study we examine whether-under conditions where such inferences might be expected-the advantages that theoretical analyses predict are evident in human performance data. A single experiment shows that, when asked to make relative wealth judgements, participants reliably use recognition as a basis for their judgements. Their wealth judgements under these conditions are reliably more accurate when some of the target names are unknown than when participants recognize all of the names (a "less-is-more effect"). These results are consistent across a number of variations: the number of options given to participants and the nature of the wealth judgement. A basic model of recognition-based inference predicts these effects.

When does ignorance make us smart? Additional factors guiding heuristic inference

“Fast & frugal” heuristics represent an appealing way of implementing bounded rationality and decision-making under pressure. The recognition heuristic is the simplest and most fundamental of these heuristics. Simulation and experimental studies have shown that this ignorance-driven heuristic inference can prove superior to knowledge based inference (Borges, Goldstein, Ortman & Gigerenzer, 1999; Goldstein & Gigerenzer, 2002) and have shown how the heuristic could develop from ACT-R’s forgetting function (Schooler & Hertwig, 2005). Mathematical analyses also demonstrate that, under certain conditions, a “less-is-more effect” will always occur (Goldstein & Gigerenzer, 2002). The further analyses presented in this paper show, however, that these conditions may constitute a special case and that the less-is-more effect in decision-making is subject to the moderating influence of the number of options to be considered and the framing of the question.

Less-is-more effects in knowledge-based heuristic inference

Inference on the basis of recognition alone is assumed to occur prior to accessing further information (Pachur & Hertwig, 2006). A counterintuitive result of this is the “less-is-more” effect: a drop in the accuracy with which choices are made as to which of two or more items scores highest on a given criterion as more items are learned (Frosch, Beaman & McCloy, 2007; Goldstein & Gigerenzer, 2002). In this paper, we show that less-is-more effects are not unique to recognition-based inference but can also be observed with a knowledge-based strategy provided two assumptions, limited information and differential access, are met. The LINDA model which embodies these assumptions is presented. Analysis of the less-is-more effects predicted by LINDA and by recognition-driven inference shows that these occur for similar reasons and casts doubt upon the “special” nature of recognition-based inference. Suggestions are made for empirical tests to compare knowledge-based and recognition-based less-is-more effects

Geostatistical radar-raingauge combination with nonparametric correlograms: methodological considerations and application in Switzerland

Modelling spatial covariance is an essential part of all geostatistical methods. Traditionally, parametric semivariogram models are fit from available data. More recently, it has been suggested to use nonparametric correlograms obtained from spatially complete data fields. Here, both estimation techniques are compared. Nonparametric correlograms are shown to have a substantial negative bias. Nonetheless, when combined with the sample variance of the spatial field under consideration, they yield an estimate of the semivariogram that is unbiased for small lag distances. This justifies the use of this estimation technique in geostatistical applications. Various formulations of geostatistical combination (Kriging) methods are used here for the construction of hourly precipitation grids for Switzerland based on data from a sparse realtime network of raingauges and from a spatially complete radar composite. Two variants of Ordinary Kriging (OK) are used to interpolate the sparse gauge observations. In both OK variants, the radar data are only used to determine the semivariogram model. One variant relies on a traditional parametric semivariogram estimate, whereas the other variant uses the nonparametric correlogram. The variants are tested for three cases and the impact of the semivariogram model on the Kriging prediction is illustrated. For the three test cases, the method using nonparametric correlograms performs equally well or better than the traditional method, and at the same time offers great practical advantages. Furthermore, two variants of Kriging with external drift (KED) are tested, both of which use the radar data to estimate nonparametric correlograms, and as the external drift variable. The first KED variant has been used previously for geostatistical radar-raingauge merging in Catalonia (Spain). The second variant is newly proposed here and is an extension of the first. Both variants are evaluated for the three test cases as well as an extended evaluation period. It is found that both methods yield merged fields of better quality than the original radar field or fields obtained by OK of gauge data. The newly suggested KED formulation is shown to be beneficial, in particular in mountainous regions where the quality of the Swiss radar composite is comparatively low. An analysis of the Kriging variances shows that none of the methods tested here provides a satisfactory uncertainty estimate. A suitable variable transformation is expected to improve this.

Synthesis, crystal structures, magnetic properties and catecholase activity of double phenoxido-bridged penta-coordinated dinuclear nickel(II) complexes derived from reduced Schiff-base ligands: mechanistic inference of catecholase activity

Three double phenoxido-bridged dinuclear nickel(II) complexes, namely [Ni-2(L-1)(2)(NCS)(2)] (1), [Ni-2(L-2)(2)(NCS)(2)] (2), and [Ni-2(L-3)(2)(NCS)(2)] (3) have been synthesized using the reduced tridentate Schiff-base ligands 2-[1-(3-methylamino-propylamino)-ethyl]-phenol (HL1), 2-[1-(2-dimethylamino-ethylamino)-ethyl]-phenol (HL2), and 2-[1-(3-dimethylarnino-propylamino)-ethyl]-phenol (HL3), respectively. The coordination compounds have been characterized by X-ray structural analyses, magnetic-susceptibility measurements, and various spectroscopic methods. In all complexes, the nickel(II) ions are penta-coordinated in a square-pyramidal environment, which is severely distorted in the case of 1 (Addison parameter tau = 0.47) and 3 (tau = 0.29), while it is almost perfect for 2 (tau = 0.03). This arrangement leads to relatively strong antiferromagnetic interactions between the Ni(II) (S = 1) metal centers as mediated by double phenoxido bridges (with J values of -23.32 (1), -35.45 (2), and -34.02 (3) cm(3) K mol(-1), in the convention H = -2JS(1)S(2)). The catalytic activity of these Ni compounds has been investigated for the aerial oxidation of 3,5-di-tert-butylcatechol. Kinetic data analysis following Michaelis-Menten treatment reveals that the catecholase activity of the complexes is influenced by the flexibility of the ligand and also by the geometry around the metal ion. Electrospray ionization mass spectroscopy (ESI-MS) studies (in the positive mode) have been performed for all the coordination compounds in the presence of 3,5-DTBC to characterize potential complex-substrate intermediates. The mass-spectrometry data, corroborated by electron paramagnetic resonance (EPR) measurements, suggest that the metal centers are involved in the catecholase activity exhibited by the complexes.

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.