http://hdl.handle.net/10256/638 2013-05-26T08:08:46Z 2013-05-26T08:08:46Z Daunis i Estadella, Josep Martín Fernández, Josep Antoni Palarea Albaladejo, Javier http://hdl.handle.net/10256/713 2012-11-19T08:54:39Z 2008-05-27T00:00:00Z

Bayesian tools for zero counts in compositional data Daunis i Estadella, Josep; Martín Fernández, Josep Antoni; Palarea Albaladejo, Javier Daunis i Estadella, Josep; Martín Fernández, Josep Antoni The log-ratio methodology makes available powerful tools for analyzing compositional data. Nevertheless, the use of this methodology is only possible for those data sets without null values. Consequently, in those data sets where the zeros are present, a previous treatment becomes necessary. Last advances in the treatment of compositional zeros have been centered especially in the zeros of structural nature and in the rounded zeros. These tools do not contemplate the particular case of count compositional data sets with null values. In this work we deal with \count zeros" and we introduce a treatment based on a mixed Bayesian-multiplicative estimation. We use the Dirichlet probability distribution as a prior and we estimate the posterior probabilities. Then we apply a multiplicative modi¯cation for the non-zero values. We present a case study where this new methodology is applied. Key words: count data, multiplicative replacement, composition, log-ratio analysis

2008-05-27T00:00:00Z Bacon Shone, John http://hdl.handle.net/10256/712 2012-06-28T12:30:36Z 2008-05-27T00:00:00Z

Discrete and continuous compositions Bacon Shone, John Daunis i Estadella, Josep; Martín Fernández, Josep Antoni This paper examines a dataset which is modeled well by the Poisson-Log Normal process and by this process mixed with Log Normal data, which are both turned into compositions. This generates compositional data that has zeros without any need for conditional models or assuming that there is missing or censored data that needs adjustment. It also enables us to model dependence on covariates and within the composition

2008-05-27T00:00:00Z Valls Alvarez, Ricardo.A. http://hdl.handle.net/10256/711 2013-01-08T10:53:15Z 2008-05-27T00:00:00Z

When zero doesn't mean it and other geomathematical mischief Valls Alvarez, Ricardo.A. Daunis i Estadella, Josep; Martín Fernández, Josep Antoni There is almost not a case in exploration geology, where the studied data doesn’t includes below detection limits and/or zero values, and since most of the geological data responds to lognormal distributions, these “zero data” represent a mathematical challenge for the interpretation. We need to start by recognizing that there are zero values in geology. For example the amount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-exists with nepheline. Another common essential zero is a North azimuth, however we can always change that zero for the value of 360°. These are known as “Essential zeros”, but what can we do with “Rounded zeros” that are the result of below the detection limit of the equipment? Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimes we need to differentiate between a sodic and a potassic alteration. Pre-classification into groups requires a good knowledge of the distribution of the data and the geochemical characteristics of the groups which is not always available. Considering the zero values equal to the limit of detection of the used equipment will generate spurious distributions, especially in ternary diagrams. Same situation will occur if we replace the zero values by a small amount using non-parametric or parametric techniques (imputation). The method that we are proposing takes into consideration the well known relationships between some elements. For example, in copper porphyry deposits, there is always a good direct correlation between the copper values and the molybdenum ones, but while copper will always be above the limit of detection, many of the molybdenum values will be “rounded zeros”. So, we will take the lower quartile of the real molybdenum values and establish a regression equation with copper, and then we will estimate the “rounded” zero values of molybdenum by their corresponding copper values. The method could be applied to any type of data, provided we establish first their correlation dependency. One of the main advantages of this method is that we do not obtain a fixed value for the “rounded zeros”, but one that depends on the value of the other variable. Key words: compositional data analysis, treatment of zeros, essential zeros, rounded zeros, correlation dependency

2008-05-27T00:00:00Z Olea, Ricardo A. http://hdl.handle.net/10256/708 2012-06-28T12:30:36Z 2008-05-27T00:00:00Z

Inference of distributional parameters from compositional samples containing nondetects Olea, Ricardo A. Daunis i Estadella, Josep; Martín Fernández, Josep Antoni Low concentrations of elements in geochemical analyses have the peculiarity of being compositional data and, for a given level of significance, are likely to be beyond the capabilities of laboratories to distinguish between minute concentrations and complete absence, thus preventing laboratories from reporting extremely low concentrations of the analyte. Instead, what is reported is the detection limit, which is the minimum concentration that conclusively differentiates between presence and absence of the element. A spatially distributed exhaustive sample is employed in this study to generate unbiased sub-samples, which are further censored to observe the effect that different detection limits and sample sizes have on the inference of population distributions starting from geochemical analyses having specimens below detection limit (nondetects). The isometric logratio transformation is used to convert the compositional data in the simplex to samples in real space, thus allowing the practitioner to properly borrow from the large source of statistical techniques valid only in real space. The bootstrap method is used to numerically investigate the reliability of inferring several distributional parameters employing different forms of imputation for the censored data. The case study illustrates that, in general, best results are obtained when imputations are made using the distribution best fitting the readings above detection limit and exposes the problems of other more widely used practices. When the sample is spatially correlated, it is necessary to combine the bootstrap with stochastic simulation

2008-05-27T00:00:00Z