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

A concept of approximated densities for efficient nonlinear estimation

This paper presents the theoretical development of a nonlinear adaptive filter based on a concept of filtering by approximated densities (FAD). The most common procedures for nonlinear estimation apply the extended Kalman filter. As opposed to conventional techniques, the proposed recursive algorithm does not require any linearisation. The prediction uses a maximum entropy principle subject to constraints. Thus, the densities created are of an exponential type and depend on a finite number of parameters. The filtering yields recursive equations involving these parameters. The update applies the Bayes theorem. Through simulation on a generic exponential model, the proposed nonlinear filter is implemented and the results prove to be superior to that of the extended Kalman filter and a class of nonlinear filters based on partitioning algorithms.

Motion estimation through approximated densities

Many techniques are currently used for motion estimation. In the block-based approaches the most common procedure applied is the block-matching based on various algorithms. To refine the motion estimates resulting from the full search or any coarse search algorithm, one can find few applications of Kalman filtering, mainly in the intraframe scheme. The Kalman filtering technique applicability for block-based motion estimation is rather limited due to discontinuities in the dynamic behaviour of the motion vectors. Therefore, we propose an application of the concept of the filtering by approximated densities (FAD). The FAD, originally introduced to alleviate limitations due to conventional Kalman modelling, is applied to interframe block-motion estimation. This application uses a simple form of FAD involving statistical characteristics of multi-modal distributions up to second order.

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.

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