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Binary multinomial processing tree (MPT) models parameterize the multinomial distribution over a set of J categories, such that each of its parameters, θ1,θ2,…,θS, is functionally independent and free to vary in the interval [0,1]. This paper analyzes binary MPT models subject to parametric order-constraints of the form 0⩽θs⩽θt⩽1. Such constraints arise naturally in multi-trial learning and memory paradigms, where some parameters representing cognitive processes would naturally be expected to be non-decreasing over learning trials or non-increasing over forgetting trials. The paper considers the case of one or more, non-overlapping linear orders of parametric constraints. Several ways to reparameterize the model to reflect the constraints are presented, and for each it is shown how to construct a new binary MPT that has the same number of parameters and is statistically equivalent to the original model with the order constraints. The results both extend the mathematical analysis of the MPT class as well as offering an approach to order restricted inference at the level of the entire class. An empirical example of this approach is provided. [Copyright &y& Elsevier]

This paper investigates the classical type I and type II error probabilities of default Bayes factors for a Bayesian t test. Default Bayes factors quantify the relative evidence between the null hypothesis and the unrestricted alternative hypothesis without needing to specify prior distributions for the unknown parameters based on one’s prior beliefs. It is shown that in most typical situations in psychological research (when either observing no, small, medium or large effects) default Bayes factors are asymmetric in information, i.e., they result in unequal error probabilities. The tendency to either prefer the null hypothesis or the alternative hypothesis varies for different default Bayes factors. Although this asymmetry in information is a natural property of a Bayes factor, severe cases of asymmetry may be undesirable in a default setting because the underlying default priors are not a translation of one’s prior beliefs. A calibration scheme is presented to make a default Bayes factor symmetric in information under certain conditions. [ABSTRACT FROM AUTHOR]

This note is a discussion commenting on the paper by Ly et al. on “Harold Jeffreys’s Default Bayes Factor Hypothesis Tests: Explanation, Extension, and Application in Psychology” and on the perceived shortcomings of the classical Bayesian approach to testing, while reporting on an alternative approach advanced by Kamary et al. (2014) as a solution to this quintessential inference problem. [ABSTRACT FROM AUTHOR]

Abstract: This paper provides a tutorial on key issues in hidden Markov modeling. Hidden Markov models have become very popular models for time series and longitudinal data in recent years due to a combination of (relative) simplicity and flexibility in adapting the model to novel situations. The tutorial covers the conceptual description of the model, estimation of parameters through maximum likelihood, and ends with an application to real data illustrating the possibilities. [Copyright &y& Elsevier]

Abstract: This paper continues the development of the Dissimilarity Cumulation theory and its main psychological application, Universal Fechnerian Scaling [Dzhafarov, E.N and Colonius, H. (2007). Dissimilarity Cumulation theory and subjective metrics. Journal of Mathematical Psychology, 51, 290–304]. In arc-connected spaces the notion of a chain length (the sum of the dissimilarities between the chain’s successive elements) can be used to define the notion of a path length, as the limit inferior of the lengths of chains converging to the path in some well-defined sense. The class of converging chains is broader than that of converging inscribed chains. Most of the fundamental results of the metric-based path length theory (additivity, lower semicontinuity, etc.) turn out to hold in the general dissimilarity-based path length theory. This shows that the triangle inequality and symmetry are not essential for these results, provided one goes beyond the traditional scheme of approximating paths by inscribed chains. We introduce the notion of a space with intermediate points which generalizes (and specializes to when the dissimilarity is a metric) the notion of a convex space in the sense of Menger. A space is with intermediate points if for any distinct there is a different point such that (where is dissimilarity). In such spaces the metric induced by is intrinsic: coincides with the infimum of lengths of all arcs connecting to In Universal Fechnerian Scaling stands for either of the two canonical psychometric increments and ( denoting discrimination probability). The choice between the two makes no difference for the notions of arc-connectedness, convergence of chains and paths, intermediate points, and other notions of the Dissimilarity Cumulation theory. [Copyright &y& Elsevier]

Abstract: This is the third paper in the series introducing the Dissimilarity Cumulation theory and its main psychological application, Universal Fechnerian Scaling. The previously developed dissimilarity-based theory of path length is used to construct the notion of a smooth path, defined by the property that the ratio of the dissimilarity between its points to the length of the subtended fragment of the path tends to unity as the points get closer to each other. We consider a class of stimulus spaces in which for every path there is a series of piecewise smooth paths converging to it pointwise and in length; and a subclass of such spaces where any two sufficiently close points can be connected by a smooth “geodesic in the small”. These notions are used to construct a broadly understood Finslerian geometry of stimulus spaces representable by regions of Euclidean -spaces. With an additional assumption of comeasurability in the small between the canonical psychometric increments of the first and second kind, this establishes a link between Universal Fechnerian Scaling and Multidimensional Fechnerian Scaling in Euclidean -spaces. The latter was a starting point for our theoretical program generalizing Fechner’s idea that sensation magnitudes can be computed by integration of a local discriminability measure. [Copyright &y& Elsevier]

Abstract: In this paper, we describe a new algorithmic approach for parameter estimation in Ratcliff''s [(1978). A theory of memory retrieval. Psychological Review, 85 (2), 59–108] diffusion model. This problem, especially if inter-trial variabilities of parameters are included in the model, is computationally very expensive; the parameter estimation procedure often takes a long time even with today''s high-speed computers. The algorithm described here makes the calculation of the cumulative distribution functions for predicted process durations computationally much less expensive. This improvement is achieved by solving the Kolmogorov backward equation numerically instead of employing the previously used closed form solution. Additionally, the algorithm can determine the optimum fit for one of the model parameters (the starting point z) directly, thereby reducing the dimension of the parameter search space by one. The resulting method is shown to be notably faster than the standard (closed-form solution) method for parameter estimation. [Copyright &y& Elsevier]

Abstract: Many empirical data support the hypothesis that the sensitivity function grows as a power function of the stimulus intensity. This is usually referred to as the near-miss-to-Weber''s law. The aim of the paper is to examine the near-miss-to-Weber''s law in the context of psychometric models of discrimination. We study two types of psychometric functions, characterized by the representations (type A), and (type B). A central result shows that both types of psychometric functions are compatible with the near-miss-to-Weber''s law. If a representation of type B exists, then the exponent in the near-miss is necessarily a constant function, that is, does not depend on the criterion value used to define “just noticeably different”. If, on the other hand, a representation of type A exists, then the exponent in the near-miss-to-Weber''s law can vary with the criterion value. In that case, the parameters in the near-miss co-vary systematically. [Copyright &y& Elsevier]

Abstract: Most probabilistic paired comparison models treat inconsistent choices as caused by independent and random errors in the pairwise judgments. In this paper, we argue that this assumption is too restrictive for the analysis of paired comparison data obtained from multiple judges when transitivity violations are systematic. We present a new framework that contains the random error assumption as a special case but also allows for systematic changes in an option''s utility assessments over the pairwise comparisons. Accounting for both between- and within-judge sources of variability, we demonstrate in an application on intertemporal choice that the proposed framework can capture systematic transitivity violations as well as individual taste differences. [Copyright &y& Elsevier]

Abstract: Learning spaces, partial cubes, and preference orderings are just a few of the many structures that can be captured by a ‘medium,’ a set of transformations on a possibly infinite set of states, constrained by four strong axioms. In this paper, we introduce a method for summarizing an arbitrary medium by gathering its states into equivalence classes and treating each equivalence class as a state in a new structure. When the new structure is also a medium, it can be characterized as a projection of the original medium. We show that any subset of tokens from an arbitrary medium generates a projection, and that each state in the projection determines a submedium. [Copyright &y& Elsevier]

Abstract: We study the recently discovered phenomenon [Conder, M. D. E., & Slinko, A. M. (2004). A counterexample to Fishburn''s conjecture. Journal of Mathematical Psychology, 48(6), 425–431] of existence of comparative probability orderings on finite sets that violate the Fishburn hypothesis [Fishburn, P. C. (1996). Finite linear qualitative probability. Journal of Mathematical Psychology, 40, 64–77; Fishburn, P. C. (1997). Failure of cancellation conditions for additive linear orders. Journal of Combinatorial Designs, 5, 353–365]—we call such orderings and the discrete cones associated with them extremal. Conder and Slinko constructed an extremal discrete cone on a set of elements and showed that no extremal cones exist on a set of elements. In this paper we construct an extremal cone on a finite set of prime cardinality p if p satisfies a certain number theoretical condition. This condition has been computationally checked to hold for 1725 of the 1842 primes between 132 and 16,000, hence for all these primes extremal cones exist. [Copyright &y& Elsevier]

Abstract: The security level models of Gilboa [1988. A combination of expected utility and maxmin decision criteria. Journal of Mathematical Psychology, 32, 405–420] and of Jaffray [1988. Choice under risk and the security factor: An axiomatic model. Theory and Decision, 24, 169–200] as well as the security and potential level model of Cohen [1992. Security level, potential level, expected utility: A three-criteria decision model under risk. Theory and Decision, 33, 101–104] and Essid [1997. Choice under risk with certainty and potential effects: A general axiomatic model. Mathematical Social Sciences, 34, 223–247] successfully accommodate classical Allais paradoxes while they offer an interesting explanation for their occurrence. However, experimental data suggest a systematic violation of these models when lotteries with low probabilities of bad or good outcomes are involved. In our opinion, one promising candidate for the explanation of these violations is the assumption of thresholds in the perception of security and potential levels. The present paper develops an axiomatic model that allows for such thresholds, so that the derived representation of preferences can accommodate the observed violations of the original security and potential level models. [Copyright &y& Elsevier]

Abstract: The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From this theory an entire branch of research has flourished: from the short-time or windowed Fourier transform to the wavelets, the frames, and lately the generic frequency analysis. The aim of this paper is to take the generic frequency analysis a step further. When a broader paradigm of functional analysis is defined, a much larger class of functions than those initially introduced in [Y. Wei, N. Chen, Square wave analysis, J. Math. Phys. 39 (8) (1998); Y. Wei, Frequency analysis based on general periodic functions, J. Math. Phys. 40 (7) (1999); Y. Wei, Frequency analysis based on easily generated functions, Appl. Comput. Harmon. Anal. (2000)] can be used to assemble bases in . New methods and algorithms can be employed in function decomposition on such generic bases. It will be shown that these algorithms are a generalization of the Fourier analysis, i.e., they are reduced to the familiar Fourier tools when using orthogonal bases. The differences between the generic frequency analysis and the wavelets and frames theories will be discussed. Examples of analysis and reconstruction of functions using the given algorithms and generic bases will be given. In this first part the focus will be on vectorial decomposition, while the second part will be on polar decomposition with its consequences and applications. [Copyright &y& Elsevier]

Abstract: Models for quantitative (or numerical) testing like e.g. educational testing have a relatively long tradition in psychology, while the qualitative (or nonnumerical) approach to psychometrics is more recent. The approach presented in this paper can be regarded as an attempt to integrate, to some extent, the numerical and nonnumerical fields. In numerical testing a subject is characterized by some real-valued parameter representing her level or ability. In the nonnumerical approach the knowledge state of an individual is represented by the subset of problems that the individual is capable of solving. We propose a model in which the relationship between the ability levels and the knowledge states is worked out on a probabilistic basis. The central idea is that the ability parameters and the knowledge states are not independent. A logistic model is derived which specifies the probabilities of the knowledge states conditional on the ability levels. We show that the Rasch model arises as a special case of the proposed model. [Copyright &y& Elsevier]

Abstract: A standard representation of a family of partial orders on a given finite set X is as a set of vertices of a cube. The metric and order structures on inherited from the cube are often used in applications. In this paper, following Stanley [(1996). Hyperplane arrangements, interval orders, and trees. Proceedings of the National Academy of Sciences of the United States of America, 93, 2620–2625], we represent relations in by regions and cells of a hyperplane arrangement arising from numerical representations of the partial orders in . To illustrate this approach, we establish wellgradedness of some families of generalized semiorders. Although the families of linear and weak orders are not well graded, our approach allows the recasting of such concepts as well graded families of sets. [Copyright &y& Elsevier]

Abstract: Over the past decade or so, a choice design in which a person is asked to select both the best and the worst option in an available set of options has been gaining favor over more traditional designs, such as where the person is asked, for instance, to: select the best option; select the worst option; rank the options; or rate the options. In this paper, we develop theoretical results for three overlapping classes of probabilistic models for best, worst, and best–worst choices, with the models in each class proposing specific ways in which such choices might be related. The models in these three classes are called random ranking and random utility, joint and sequential, and ratio scale. We include some models that belong to more than one class, with the best known being the maximum-difference (maxdiff) model, summarize estimation issues related to the models, and formulate a number of open theoretical problems. [Copyright &y& Elsevier]

Abstract: How can N individuals in a closed space meet and greet each other most efficiently? This paper presents a general solution to this problem—an algorithm or “dance” that will achieve universal pairing in the least possible number of moves or steps. A proof of the suggested algorithm is included, showing that it guarantees that every two participants will greet each other once and only once, and that no procedure with this property can be accomplished with fewer steps. Slightly different procedures are required for the odd and even cases. The algorithm has been applied in classroom settings, and could be applied in any social setting where the objective is to initiate efficiently a sense of group cohesion and common purpose. [Copyright &y& Elsevier]

Xausa, Beghi, and Zanforlin (J. Math. Psychol. 45(4) (2001) 635) provide an account of perceptual organization based on their ‘minimal relative motion’ principle. They claim that this principle can account for the percept generated by a contracting bar that is simultaneously translating laterally. We critique the mathematical analysis provided in the aforementioned paper. We conclude that the ‘minimal relative motion’ principle, in the form presented, cannot adequately explain the percept reported by observers. [Copyright &y& Elsevier]

This paper studies conjoint measurement models tolerating intransitivities that closely resemble Tversky''s additive difference model while replacing additivity and subtractivity by mere decomposability requirements. We offer a complete axiomatic characterisation of these models without having recourse to unnecessary structural assumptions on the set of objects. This shows the pure consequences of several cancellation conditions that have often been used in the analysis of more traditional conjoint measurement models. Our models contain as particular cases many aggregation rules that have been proposed in the literature. [Copyright &y& Elsevier]

In this paper, we present second-order-statistics (SOS) subspace-based blind channel estimation techniques, which exploit the receive antenna diversity in each of the following situations: cyclic prefix-OFDM (CP-OFDM), zero padded-OFDM (ZP-OFDM), and bandwidth efficient-OFDM (BWE-OFDM) systems. We also propose a number of combinations of pre-FFT equalizer, post-FFT equalizer, zero-forcing (ZF) equalizer, and minimum-mean-square-error (MMSE) equalizer. For any number of receive antennas, the pre-FFT equalizers require only one FFT at the receiver. As a result, a considerable reduction in hardware complexity and power saving may be obtained especially for systems with higher number of sub-carriers. In contrast, post-FFT equalizers result in considerable reduction in processing complexity at the cost of one FFT for each antenna. Adaptive linear-complexity implementations of the proposed receivers are considered, along with some modifications in the presence of null side carriers. The effectiveness of the new techniques is demonstrated through simulations. [Copyright &y& Elsevier]

The Dutch book argument is a coherence condition for the existence of subjective probabilities. This paper gives a general framework of analysis for this argument in a nonadditive probability setting. Particular cases are given by comonotonic and affinely related Dutch books that lead to Choquet expectations and Min expectations. [Copyright &y& Elsevier]

In this paper, an iteration algorithm based on interference iteration is proposed and referred to as I-PMF. Derived from the parametric matched filter (PMF), I-PMF has a low computational cost and reveals not only an iteration relationship between the autoregressive (AR) coefficient matrices and interferences in mathematics, but also a mechanism for PMF in suppressing interferences. Then the iteration of I-PMF is utilized in an adaptive method, namely I-PAMF. The average minimum output signal-to-interference-and-noise ratio (SINR) of I-PAMF is analyzed with separated interferences and verified by numerical results. It is shown that the computational cost of the proposed iterative algorithm, i.e. I-PMF, is low and the detection performance of the proposed adaptive iterative algorithm, i.e. I-PAMF, outperforms most of its counterparts with small training size. Although there might be a small loss of detection performance for I-PAMF compared with a few of its counterparts in some cases, I-PAMF still has a much lower computational cost than these counterparts. [ABSTRACT FROM AUTHOR]