Revisiting the compositional data. Some fundamental questions and new prospects in Archaeometry and Archaeology

In this paper we examine the problem of compositional data from a different startingpoint. Chemical compositional data, as used in provenance studies on archaeologicalmaterials, will be approached from the measurement theory. The results will show, in avery intuitive way that chemical data can only be treated by using the approachdeveloped for compositional data. It will be shown that compositional data analysis is aparticular case in projective geometry, when the projective coordinates are in thepositive orthant, and they have the properties of logarithmic interval metrics. Moreover,it will be shown that this approach can be extended to a very large number ofapplications, including shape analysis. This will be exemplified with a case study inarchitecture of Early Christian churches dated back to the 5th-7th centuries AD

Modelling structural zeros in compositional data

This analysis was stimulated by the real data analysis problem of householdexpenditure data. The full dataset contains expenditure data for a sample of 1224 households. The expenditure is broken down at 2 hierarchical levels: 9 major levels (e.g. housing, food, utilities etc.) and 92 minor levels. There are also 5 factors and 5 covariates at the household level. Not surprisingly, there are a small number of zeros at the major level, but many zeros at the minor level. The question is how best to model the zeros. Clearly, models that tryto add a small amount to the zero terms are not appropriate in general as at least some of the zeros are clearly structural, e.g. alcohol/tobacco for households that are teetotal. The key question then is how to build suitable conditional models. For example, is the sub-composition of spendingexcluding alcohol/tobacco similar for teetotal and non-teetotal households?In other words, we are looking for sub-compositional independence. Also, what determines whether a household is teetotal? Can we assume that it is independent of the composition? In general, whether teetotal will clearly depend on the household level variables, so we need to be able to model this dependence. The other tricky question is that with zeros on more than onecomponent, we need to be able to model dependence and independence of zeros on the different components. Lastly, while some zeros are structural, others may not be, for example, for expenditure on durables, it may be chance as to whether a particular household spends money on durableswithin the sample period. This would clearly be distinguishable if we had longitudinal data, but may still be distinguishable by looking at the distribution, on the assumption that random zeros will usually be for situations where any non-zero expenditure is not small.While this analysis is based on around economic data, the ideas carry over tomany other situations, including geological data, where minerals may be missing for structural reasons (similar to alcohol), or missing because they occur only in random regions which may be missed in a sample (similar to the durables)

Structural components in functional data

Analyzing functional data often leads to finding common factors, for which functional principal component analysis proves to be a useful tool to summarize and characterize the random variation in a function space. The representation in terms of eigenfunctions is optimal in the sense of L-2 approximation. However, the eigenfunctions are not always directed towards an interesting and interpretable direction in the context of functional data and thus could obscure the underlying structure. To overcome such difficulty, an alternative to functional principal component analysis is proposed that produces directed components which may be more informative and easier to interpret. These structural components are similar to principal components, but are adapted to situations in which the domain of the function may be decomposed into disjoint intervals such that there is effectively independence between intervals and positive correlation within intervals. The approach is demonstrated with synthetic examples as well as real data. Properties for special cases are also studied.

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completelyabsent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and byMartín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involvedparts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method isintroduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that thetheoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approachhas reasonable properties from a compositional point of view. In particular, it is “natural” in the sense thatit recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in thesame paper a substitution method for missing values on compositional data sets is introduced

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel densityestimation techniques in the context of compositional data analysis. Indeed, they gavetwo options for the choice of the kernel to be used in the kernel estimator. One ofthese kernels is based on the use the alr transformation on the simplex SD jointly withthe normal distribution on RD-1. However, these authors themselves recognized thatthis method has some deficiencies. A method for overcoming these dificulties based onrecent developments for compositional data analysis and multivariate kernel estimationtheory, combining the ilr transformation with the use of the normal density with a fullbandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu-Figueras (2006). Here we present an extensive simulation study that compares bothmethods in practice, thus exploring the finite-sample behaviour of both estimators

CODAMAT: a modern analogue techinque for compositional data

The quantitative estimation of Sea Surface Temperatures from fossils assemblages is afundamental issue in palaeoclimatic and paleooceanographic investigations. TheModern Analogue Technique, a widely adopted method based on direct comparison offossil assemblages with modern coretop samples, was revised with the aim ofconforming it to compositional data analysis. The new CODAMAT method wasdeveloped by adopting the Aitchison metric as distance measure. Modern coretopdatasets are characterised by a large amount of zeros. The zero replacement was carriedout by adopting a Bayesian approach to the zero replacement, based on a posteriorestimation of the parameter of the multinomial distribution. The number of modernanalogues from which reconstructing the SST was determined by means of a multipleapproach by considering the Proxies correlation matrix, Standardized Residual Sum ofSquares and Mean Squared Distance. This new CODAMAT method was applied to theplanktonic foraminiferal assemblages of a core recovered in the Tyrrhenian Sea.Kew words: Modern analogues, Aitchison distance, Proxies correlation matrix,Standardized Residual Sum of Squares

Elemental analysis of New Zealand Nephrite Jade (pounamu) for forensic purposes

Pounamu (NZ jade), or nephrite, is a protected mineral in its natural form following thetransfer of ownership back to Ngai Tahu under the Ngai Tahu (Pounamu Vesting) Act 1997.Any theft of nephrite is prosecutable under the Crimes Act 1961. Scientific evidence isessential in cases where origin is disputed. A robust method for discrimination of thismaterial through the use of elemental analysis and compositional data analysis is required.Initial studies have characterised the variability within a given nephrite source. This hasincluded investigation of both in situ outcrops and alluvial material. Methods for thediscrimination of two geographically close nephrite sources are being developed.Key Words: forensic, jade, nephrite, laser ablation, inductively coupled plasma massspectrometry, multivariate analysis, elemental analysis, compositional data analysis

A Factor analysis of hidrochemical composition of Llobregat river basin

Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing modelsbetween end-members. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the end-member problem in a compositional framework.We present here a possible solution based on factor analysis of compositions illustrated with a case study.We find two factors on the compositional bi-plot fitting two non-centered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables thatlay nearest to it. With each subcomposition a log-contrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric log-ratio coordinates (ilr) of three hiddencomponents, that can be plotted in a ternary diagram. These hidden components might be interpreted as end-members.We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a bi-plot with a 57% of explained totalvariance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphicalrepresentation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysisof diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, exceptfertilisers due to the heterogeneity of their composition.This approach is a useful tool to distinguish end-members, and characterise them, an issue generally difficult to solve. It is worth note that the end-member composition cannot be fully estimated but only characterised through log-ratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations areintrinsic to the relative nature of compositional data

Exome sequencing of index patients with retinal dystrophies as a tool for molecular diagnosis.

BACKGROUND: Retinal dystrophies (RD) are a group of hereditary diseases that lead to debilitating visual impairment and are usually transmitted as a Mendelian trait. Pathogenic mutations can occur in any of the 100 or more disease genes identified so far, making molecular diagnosis a rather laborious process. In this work we explored the use of whole exome sequencing (WES) as a tool for identification of RD mutations, with the aim of assessing its applicability in a diagnostic context. METHODOLOGY/PRINCIPAL FINDINGS: We ascertained 12 Spanish families with seemingly recessive RD. All of the index patients underwent mutational pre-screening by chip-based sequence hybridization and resulted to be negative for known RD mutations. With the exception of one pedigree, to simulate a standard diagnostic scenario we processed by WES only the DNA from the index patient of each family, followed by in silico data analysis. We successfully identified causative mutations in patients from 10 different families, which were later verified by Sanger sequencing and co-segregation analyses. Specifically, we detected pathogenic DNA variants (∼50% novel mutations) in the genes RP1, USH2A, CNGB3, NMNAT1, CHM, and ABCA4, responsible for retinitis pigmentosa, Usher syndrome, achromatopsia, Leber congenital amaurosis, choroideremia, or recessive Stargardt/cone-rod dystrophy cases. CONCLUSIONS/SIGNIFICANCE: Despite the absence of genetic information from other family members that could help excluding nonpathogenic DNA variants, we could detect causative mutations in a variety of genes known to represent a wide spectrum of clinical phenotypes in 83% of the patients analyzed. Considering the constant drop in costs for human exome sequencing and the relative simplicity of the analyses made, this technique could represent a valuable tool for molecular diagnostics or genetic research, even in cases for which no genotypes from family members are available.

Rules of origin : from analysis to reform

General Introduction This thesis can be divided into two main parts :the first one, corresponding to the first three chapters, studies Rules of Origin (RoOs) in Preferential Trade Agreements (PTAs); the second part -the fourth chapter- is concerned with Anti-Dumping (AD) measures. Despite wide-ranging preferential access granted to developing countries by industrial ones under North-South Trade Agreements -whether reciprocal, like the Europe Agreements (EAs) or NAFTA, or not, such as the GSP, AGOA, or EBA-, it has been claimed that the benefits from improved market access keep falling short of the full potential benefits. RoOs are largely regarded as a primary cause of the under-utilization of improved market access of PTAs. RoOs are the rules that determine the eligibility of goods to preferential treatment. Their economic justification is to prevent trade deflection, i.e. to prevent non-preferred exporters from using the tariff preferences. However, they are complex, cost raising and cumbersome, and can be manipulated by organised special interest groups. As a result, RoOs can restrain trade beyond what it is needed to prevent trade deflection and hence restrict market access in a statistically significant and quantitatively large proportion. Part l In order to further our understanding of the effects of RoOs in PTAs, the first chapter, written with Pr. Olivier Cadot, Celine Carrère and Pr. Jaime de Melo, describes and evaluates the RoOs governing EU and US PTAs. It draws on utilization-rate data for Mexican exports to the US in 2001 and on similar data for ACP exports to the EU in 2002. The paper makes two contributions. First, we construct an R-index of restrictiveness of RoOs along the lines first proposed by Estevadeordal (2000) for NAFTA, modifying it and extending it for the EU's single-list (SL). This synthetic R-index is then used to compare Roos under NAFTA and PANEURO. The two main findings of the chapter are as follows. First, it shows, in the case of PANEURO, that the R-index is useful to summarize how countries are differently affected by the same set of RoOs because of their different export baskets to the EU. Second, it is shown that the Rindex is a relatively reliable statistic in the sense that, subject to caveats, after controlling for the extent of tariff preference at the tariff-line level, it accounts for differences in utilization rates at the tariff line level. Finally, together with utilization rates, the index can be used to estimate total compliance costs of RoOs. The second chapter proposes a reform of preferential Roos with the aim of making them more transparent and less discriminatory. Such a reform would make preferential blocs more "cross-compatible" and would therefore facilitate cumulation. It would also contribute to move regionalism toward more openness and hence to make it more compatible with the multilateral trading system. It focuses on NAFTA, one of the most restrictive FTAs (see Estevadeordal and Suominen 2006), and proposes a way forward that is close in spirit to what the EU Commission is considering for the PANEURO system. In a nutshell, the idea is to replace the current array of RoOs by a single instrument- Maximum Foreign Content (MFC). An MFC is a conceptually clear and transparent instrument, like a tariff. Therefore changing all instruments into an MFC would bring improved transparency pretty much like the "tariffication" of NTBs. The methodology for this exercise is as follows: In step 1, I estimate the relationship between utilization rates, tariff preferences and RoOs. In step 2, I retrieve the estimates and invert the relationship to get a simulated MFC that gives, line by line, the same utilization rate as the old array of Roos. In step 3, I calculate the trade-weighted average of the simulated MFC across all lines to get an overall equivalent of the current system and explore the possibility of setting this unique instrument at a uniform rate across lines. This would have two advantages. First, like a uniform tariff, a uniform MFC would make it difficult for lobbies to manipulate the instrument at the margin. This argument is standard in the political-economy literature and has been used time and again in support of reductions in the variance of tariffs (together with standard welfare considerations). Second, uniformity across lines is the only way to eliminate the indirect source of discrimination alluded to earlier. Only if two countries face uniform RoOs and tariff preference will they face uniform incentives irrespective of their initial export structure. The result of this exercise is striking: the average simulated MFC is 25% of good value, a very low (i.e. restrictive) level, confirming Estevadeordal and Suominen's critical assessment of NAFTA's RoOs. Adopting a uniform MFC would imply a relaxation from the benchmark level for sectors like chemicals or textiles & apparel, and a stiffening for wood products, papers and base metals. Overall, however, the changes are not drastic, suggesting perhaps only moderate resistance to change from special interests. The third chapter of the thesis considers whether Europe Agreements of the EU, with the current sets of RoOs, could be the potential model for future EU-centered PTAs. First, I have studied and coded at the six-digit level of the Harmonised System (HS) .both the old RoOs -used before 1997- and the "Single list" Roos -used since 1997. Second, using a Constant Elasticity Transformation function where CEEC exporters smoothly mix sales between the EU and the rest of the world by comparing producer prices on each market, I have estimated the trade effects of the EU RoOs. The estimates suggest that much of the market access conferred by the EAs -outside sensitive sectors- was undone by the cost-raising effects of RoOs. The chapter also contains an analysis of the evolution of the CEECs' trade with the EU from post-communism to accession. Part II The last chapter of the thesis is concerned with anti-dumping, another trade-policy instrument having the effect of reducing market access. In 1995, the Uruguay Round introduced in the Anti-Dumping Agreement (ADA) a mandatory "sunset-review" clause (Article 11.3 ADA) under which anti-dumping measures should be reviewed no later than five years from their imposition and terminated unless there was a serious risk of resumption of injurious dumping. The last chapter, written with Pr. Olivier Cadot and Pr. Jaime de Melo, uses a new database on Anti-Dumping (AD) measures worldwide to assess whether the sunset-review agreement had any effect. The question we address is whether the WTO Agreement succeeded in imposing the discipline of a five-year cycle on AD measures and, ultimately, in curbing their length. Two methods are used; count data analysis and survival analysis. First, using Poisson and Negative Binomial regressions, the count of AD measures' revocations is regressed on (inter alia) the count of "initiations" lagged five years. The analysis yields a coefficient on measures' initiations lagged five years that is larger and more precisely estimated after the agreement than before, suggesting some effect. However the coefficient estimate is nowhere near the value that would give a one-for-one relationship between initiations and revocations after five years. We also find that (i) if the agreement affected EU AD practices, the effect went the wrong way, the five-year cycle being quantitatively weaker after the agreement than before; (ii) the agreement had no visible effect on the United States except for aone-time peak in 2000, suggesting a mopping-up of old cases. Second, the survival analysis of AD measures around the world suggests a shortening of their expected lifetime after the agreement, and this shortening effect (a downward shift in the survival function postagreement) was larger and more significant for measures targeted at WTO members than for those targeted at non-members (for which WTO disciplines do not bind), suggesting that compliance was de jure. A difference-in-differences Cox regression confirms this diagnosis: controlling for the countries imposing the measures, for the investigated countries and for the products' sector, we find a larger increase in the hazard rate of AD measures covered by the Agreement than for other measures.

Compositional Data in Biomedical Research

Modern methods of compositional data analysis are not well known in biomedical research.Moreover, there appear to be few mathematical and statistical researchersworking on compositional biomedical problems. Like the earth and environmental sciences,biomedicine has many problems in which the relevant scienti c information isencoded in the relative abundance of key species or categories. I introduce three problemsin cancer research in which analysis of compositions plays an important role. Theproblems involve 1) the classi cation of serum proteomic pro les for early detection oflung cancer, 2) inference of the relative amounts of di erent tissue types in a diagnostictumor biopsy, and 3) the subcellular localization of the BRCA1 protein, and it'srole in breast cancer patient prognosis. For each of these problems I outline a partialsolution. However, none of these problems is \solved". I attempt to identify areas inwhich additional statistical development is needed with the hope of encouraging morecompositional data analysts to become involved in biomedical research

Compositions in life science data

The aim of this talk is to convince the reader that there are a lot of interesting statisticalproblems in presentday life science data analysis which seem ultimately connected withcompositional statistics.Key words: SAGE, cDNA microarrays, (1D-)NMR, virus quasispecies

Mapping of Environmental Data Using Kernel-Based Methods

Recently, kernel-based Machine Learning methods have gained great popularity in many data analysis and data mining fields: pattern recognition, biocomputing, speech and vision, engineering, remote sensing etc. The paper describes the use of kernel methods to approach the processing of large datasets from environmental monitoring networks. Several typical problems of the environmental sciences and their solutions provided by kernel-based methods are considered: classification of categorical data (soil type classification), mapping of environmental and pollution continuous information (pollution of soil by radionuclides), mapping with auxiliary information (climatic data from Aral Sea region). The promising developments, such as automatic emergency hot spot detection and monitoring network optimization are discussed as well.

Post-detection analysis for grating-based ultra-small angle X-ray scattering.

Until recently, the hard X-ray, phase-sensitive imaging technique called grating interferometry was thought to provide information only in real space. However, by utilizing an alternative approach to data analysis we demonstrated that the angular resolved ultra-small angle X-ray scattering distribution can be retrieved from experimental data. Thus, reciprocal space information is accessible by grating interferometry in addition to real space. Naturally, the quality of the retrieved data strongly depends on the performance of the employed analysis procedure, which involves deconvolution of periodic and noisy data in this context. The aim of this article is to compare several deconvolution algorithms to retrieve the ultra-small angle X-ray scattering distribution in grating interferometry. We quantitatively compare the performance of three deconvolution procedures (i.e., Wiener, iterative Wiener and Lucy-Richardson) in case of realistically modeled, noisy and periodic input data. The simulations showed that the algorithm of Lucy-Richardson is the more reliable and more efficient as a function of the characteristics of the signals in the given context. The availability of a reliable data analysis procedure is essential for future developments in grating interferometry.

Bayesian image reconstruction with space-variant noise suppression

In this paper we present a Bayesian image reconstruction algorithm with entropy prior (FMAPE) that uses a space-variant hyperparameter. The spatial variation of the hyperparameter allows different degrees of resolution in areas of different statistical characteristics, thus avoiding the large residuals resulting from algorithms that use a constant hyperparameter. In the first implementation of the algorithm, we begin by segmenting a Maximum Likelihood Estimator (MLE) reconstruction. The segmentation method is based on using a wavelet decomposition and a self-organizing neural network. The result is a predetermined number of extended regions plus a small region for each star or bright object. To assign a different value of the hyperparameter to each extended region and star, we use either feasibility tests or cross-validation methods. Once the set of hyperparameters is obtained, we carried out the final Bayesian reconstruction, leading to a reconstruction with decreased bias and excellent visual characteristics. The method has been applied to data from the non-refurbished Hubble Space Telescope. The method can be also applied to ground-based images.