Mixture Models (Mathematics)

Towards measles elimination in Italy: monitoring herd immunity by Bayesian mixture modelling of serological data

by Emanuele Del Fava

Del Fava E, Shkedy Z, Bechini A, Bonanni P, and Manfredi P (2012) Towards measles elimination in Italy: monitoring herd immunity by Bayesian mixture modelling of serological data. Epidemics, accepted manuscript, in press. DOI: 10.1016/j.epidem.2012.05.001

The analysis of post-vaccination serological data poses nontrivial issues to the epidemiologists and policy makers who... more The analysis of post-vaccination serological data poses nontrivial issues to the epidemiologists and policy makers who want to assess the effects of immunisation programs. This is especially true for infections on the path to elimination as is the case for measles. We address these problems by using Bayesian normal mixture models fitted to antibody counts data. This methodology allows us to estimate the seroprevalence of measles by age and, in contrast to conventional methods based on fixed cut-off points, to also distinguish between groups of individuals with different degrees of immunisation. We applied our methodology to two serological samples collected in Tuscany (Italy) in 2003 and in 2005–2006 respectively, i.e., before and after a large vaccination campaign targeted to school-age children. Besides showing the impact of the campaign, we were able to accurately identify a large pocket of susceptible individuals aged about 13-14 in 2005–2006, and a larger group of weakly immune individuals aged about 20 in 2005–2006. These cohorts therefore represent possible targets for further interventions towards measles elimination.

Blind signal separation and identification of mixtures of images

by Vania V. Estrela

Nonparametric estimation of multivariate scale mixtures of uniform densities

by Marios Pavlides

Journal of Multivariate Analysis, Volume 107, May 2012, Pages 71–89

Suppose that $\boldsymbol{U} = (U_1, \ldots , U_d) $ has a Uniform$([0,1]^d)$ distribution, that $\boldsymbol{Y} =... more Suppose that $\boldsymbol{U} = (U_1, \ldots , U_d) $ has a Uniform$([0,1]^d)$ distribution, that $\boldsymbol{Y} = (Y_1 , \ldots , Y_d) $ has the distribution $G$ on $\mathds{R}_+^d$, and let $\m{X} = (X_1 , \ldots , X_d) = (U_1 Y_1 , \ldots , U_d Y_d )$. The resulting class of distributions of $\boldsymbol{X}$ (as $G$ varies over all distributions on $\mathds{R}_+^d$) is called the {\sl Scale Mixture of Uniforms} class of distributions, and the corresponding class of densities on $\mathds{R}_+^d$ is denoted by $\mathcal {F}_{\text{SMU}}(d)$. We study maximum likelihood estimation in the family $\mathcal {F}_{\text{SMU}}(d)$. We prove existence of the MLE, establish Fenchel characterizations, and prove strong consistency of the almost surely unique maximum likelihood estimator (MLE) in $\mathcal {F}_{\text{SMU}}(d)$. We also provide an asymptotic minimax lower bound for estimating the functional $f \mapsto f(\boldsybol{x})$ under reasonable differentiability assumptions on $f\in\mathcal {F}_{\text{SMU}}(d)$ in a neighborhood of $\boldsymbol{x}$. We conclude the paper with discussion, conjectures and open problems pertaining to global and local rates of convergence of the MLE.

On the Grenander estimator at zero

by Marios Pavlides

Statistica Sinica 21 (2011), 873-899

We establish limit theory for the Grenander estimator of a monotone density near zero. In particular we consider the... more We establish limit theory for the Grenander estimator of a monotone density near zero. In particular we consider the situation when the true density $f_0$ is unbounded at zero, with different rates of growth to infinity. In the course of our study we develop new switching relations by use of tools from convex analysis. The theory is applied to a problem involving mixtures.

The Possible Use of Mixture Model Analysis Technique in the Educational Sciences: A Case Study

by Halil Eksi

Murat KAYRİ, İbrahim GÖKDAŞ
Educational Sciences: Theory & Practice
6 (3) • September 2006 • 769-778

In this article, it is explored that the issue about applicability of the Mixture Model
analyses technique which... more In this article, it is explored that the issue about applicability of the Mixture Model
analyses technique which can be used in the searches of education sciences. Therefore
in this search, for the semester of 2005-2006, the 643 individuals participated in
the Private Skill Examination of Physical and Sport Education Department, Education
Faculty of Yüzüncü Y›l University (YYU). During interview, information was taken
with regard to AOOBP, gender, occupation of father and mother, settlement and
high school branch from which they graduated. The search data has been gathered
by the structured - interview technique. During the interview, the questions about
the personal features of the participants were asked and the answers were recorded.
The effect level of the variables have indicated the personal features of the registered
participants who had the grade of OSS (Student Selection Examination) examination.
These effect levels have been solved by Mixture Model which belongs to
Latent Class family. This model is a new statistical method for education sciences
in Turkey. At the end of this search, 5 sub-classes have been identified and the variables
have influenced each identified class from different aspects and levels. Besides,
it was observed that the interaction of the variables has been an affective matter
in regard of different sides and level.

Developmental trajectories of conduct problems and hyperactivity from ages 2 to 10

by Eric Lacourse

A longitudinal-experimental approach to testing theories of antisocial behavior development

by Eric Lacourse

Developmental trajectories of boys' delinquent group membership and facilitation of violent behaviors during adolescence

by Eric Lacourse

Non-Parametric Discrete Mixture Model Recovery via Nonnegative Matrix Factorization

by Stefan Karpinski

Feng (2009) Mixed Responses: Why Readers Spend Less Time at Unfavorable Landing Positions

by Gary Feng

This paper investigates why the average fixation duration tends to decrease from the center to the two ends of a word.... more This paper investigates why the average fixation duration tends to decrease from the center to the two ends of a word. Specifically, it examines (a) whether unfavorable landing positions trigger a corrective mechanism, (b) whether the triggering is based on the internal efference copy mechanism, and (c) whether the corrective mechanism is specific to fixations that missed their targeted words. To estimate the mean and proportion of the corrective fixations, a 3-parameter mixture model was fitted to distributions of first fixation duration from two large eye movement databases in studies 1 and 2. Study 3 experimentally created mislocated fixations using a gaze-contingent screen shift paradigm. There is little evidence for the efference copy mechanism and limited support for the mislocated fixations hypothesis. Overall, data suggest a process that terminates fixations sooner than would during normal reading; it is triggered by the visual input during a fixation, and is flexibly engaged at eccentric landing positions and in reading short words. Implications to theories of reading eye movements are discussed.

Feng (2012) - Is there a Common Control Mechanism for Anti-saccades and Reading Eye Movements? Evidence from Distributional Analyses

by Gary Feng

Vision Research, 2012, 57, 35-50; with supplemental figures and R scripts

In the saccadic literature, the voluntary control of eye movement involves inhibiting automatic saccadic plans. In... more In the saccadic literature, the voluntary control of eye movement involves inhibiting automatic saccadic plans. In contrast, the dominant view in reading is that linguistic processes trigger saccade planning. The present study explores the possibility of a common control mechanism, in which cognitively driven responses compete to inhibit automatic, perceptually driven saccade plans. A probabilistic model is developed to account for empirical distributions of saccadic response time in anti-saccade tasks (Studies 1 and 2) and fixation duration in reading and reading-like tasks (Studies 3 and 4). In all cases the distributions can be decomposed into a perceptually based component and a component sensitive to cognitive demands. Parametric similarities among the models strongly suggest a shared cognitive control mechanism between reading and other voluntary saccadic tasks.

The Matter of Objects

by henry laycock

Forthcoming conference proceedings

Michael Pelis (ed.): The Logica Yearbook 2011,
College Publications, London, 2012..

The final sections of the work include discussion of the problem of MIXTURE, following from Aristotle's distinction between MIXIS and SYNTHESIS

THIS PAPER IS A BITE-SIZED MANIFESTO WHICH ATTACKS THE IDENTIFICATION OF EXISTENCE-STATEMENTS WITH QUANTIFIED SENTENCES. THE KEY INNOVATION OF THIS HIGHLY PROGRAMMATIC WORK CONSISTS IN ITS BRIEF ARGUMENT FOR THE VIEW THAT THERE ARE SENTENCES WITHOUT SUBJECTS AT ANY LEVEL BEYOND THE SYNTACTIC -: SENTENCES WHICH ARE NEITHER QUANTIFIED, NOR REFERENTIAL IN THE FULL-BLOODED (OR ANY OTHER) SENSE.

In formal, logico-semantic terms, the concept of an object, individual or thing is widely thought to be exhaustive.... more In formal, logico-semantic terms, the concept of an object, individual or thing is widely thought to be exhaustive. Whatever we may say or think – it is supposed – our thought or talk is always thought or talk of objects. Here, I briefly sketch out and defend a rival view: like that of a property, the concept of an object is best understood in terms of that which it excludes. Object-concepts correspond to count nouns; but count nouns are just one of two great categories of nouns, the other being that of non-count nouns. Both count nouns, and the concept of an object, are inseparable from reference and identity – but non-count nouns are not; and they are not a vehicle for thought or talk of objects in the first place.

The Matter of Objects

by henry laycock

Forthcoming conference proceedings

Michael Pelis (ed.): The Logica Yearbook 2011,
College Publications, London, 2012..

The final sections of the work include discussion of the problem of MIXTURE, following from Aristotle's distinction between MIXIS and SYNTHESIS

THIS PAPER IS A BITE-SIZED MANIFESTO WHICH ATTACKS THE IDENTIFICATION OF EXISTENCE-STATEMENTS WITH QUANTIFIED SENTENCES. THE KEY INNOVATION OF THIS HIGHLY PROGRAMMATIC WORK CONSISTS IN ITS BRIEF ARGUMENT FOR THE VIEW THAT THERE ARE SENTENCES WITHOUT SUBJECTS AT ANY LEVEL BEYOND THE SYNTACTIC -: SENTENCES WHICH ARE NEITHER QUANTIFIED, NOR REFERENTIAL IN THE FULL-BLOODED (OR ANY OTHER) SENSE.

In formal, logico-semantic terms, the concept of an object, individual or thing is widely thought to be exhaustive.... more In formal, logico-semantic terms, the concept of an object, individual or thing is widely thought to be exhaustive. Whatever we may say or think – it is supposed – our thought or talk is always thought or talk of objects. Here, I briefly sketch out and defend a rival view: like that of a property, the concept of an object is best understood in terms of that which it excludes. Object-concepts correspond to count nouns; but count nouns are just one of two great categories of nouns, the other being that of non-count nouns. Both count nouns, and the concept of an object, are inseparable from reference and identity – but non-count nouns are not; and they are not a vehicle for thought or talk of objects in the first place.

Polar Bear Population Forecasts: A Public-Policy Forecasting Audit

by J Armstrong

Co-authored with Kesten C. Green and Willie Soon.

Calls to list polar bears as a threatened species under the United States Endangered Species Act are based on... more Calls to list polar bears as a threatened species under the United States Endangered Species Act are based on forecasts of substantial long-term declines in their population. Nine government reports were written to help US Fish and Wildlife Service managers decide whether or not to list polar bears as a threatened species. We assessed these reports based on evidence-based (scientific) forecasting principles. None of the reports referred to sources of scientific forecasting methodology. Of the nine, Amstrup et al. [Amstrup, S. C., B. G. Marcot, D. C. Douglas. 2007. Forecasting the rangewide status of polar bears at selected times in the 21st century. Administrative Report, USGS Alaska Science Center, Anchorage, AK.] and Hunter et al. [Hunter, C. M., H. Caswell, M. C. Runge, S. C. Amstrup, E. V. Regehr, I. Stirling. 2007. Polar bears in the Southern Beaufort Sea II: Demography and population growth in relation to sea ice conditions. Administrative Report, USGS Alaska Science Center,
Anchorage, AK.] were the most relevant to the listing decision, and we devoted our attention to them. Their forecasting procedures depended on a complex set of assumptions, including the erroneous assumption that general circulation models provide valid forecasts of summer sea ice in the regions that polar bears inhabit. Nevertheless, we audited their conditional forecasts of what would happen to the polar bear population assuming, as the authors did, that the extent of summer sea ice would decrease substantially during the coming decades. We found that Amstrup et al. properly applied 15 percent of relevant forecasting principles and Hunter et al. 10 percent. Averaging across the two papers, 46 percent of the principles were clearly contravened and 23 percent were apparently contravened. Consequently, their forecasts are unscientific and inconsequential to decision makers. We recommend that researchers apply all relevant principles properly when important public-policy decisions depend on their forecasts.

Localised Mixtures of Experts for Mixture of Regressions

by Guillaume Bouchard

Regression density estimation using smooth adaptive Gaussian mixtures

by Mattias Villani

Robust Fuzzy Clustering Using Mixtures of Student's-t Distributions

by Sotirios Chatzis

Signal Modeling and Classification Using a Robust Latent Space Model Based on t Distributions

by Sotirios Chatzis

A possibilistic clustering approach toward generative mixture models

by Sotirios Chatzis

A Method for Training Finite Mixture Models Under a Fuzzy Clustering Principle

by Sotirios Chatzis