DEEST - Departamento de Estatística

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Browsing DEEST - Departamento de Estatística by Author "Assunção, Renato Martins"

Now showing 1 - 7 of 7
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    Bayesian spatial models with a mixture neighborhood structure.
    (2012) Rodrigues, Erica Castilho; Assunção, Renato Martins
    In Bayesian disease mapping, one needs to specify a neighborhood structure to make inference about the underlying geographical relative risks. We propose a model in which the neighborhood structure is part of the parameter space. We retain the Markov property of the typical Bayesian spatial models: given the neighborhood graph, disease rates follow a conditional autoregressive model. However, the neighborhood graph itself is a parameter that also needs to be estimated. We investigate the theoretical properties of our model. In particular, we investigate carefully the prior and posterior covariance matrix induced by this random neighborhood structure, providing interpretation for each element of these matrices.
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    A closer look at the spatial exponential matrix specification.
    (2014) Rodrigues, Erica Castilho; Assunção, Renato Martins; Dey, Dipak K.
    In this paper we analyze the partial and marginal covariance structures of the spatial model with the covariance structure based on a exponential matrix specification. We show that this model presents a puzzling behavior for many types of geographical neighborhood graphs, from the simplest to the most complex. In particular, we show that for this model it is usual to have opposite signs for the marginal and conditional correlations between two areas. We show these results through experimental examples and analytical demonstrations.
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    A critical look at prospective surveillance using a scan statistic.
    (2015) Correa, Thais Rotsen; Assunção, Renato Martins; Costa, Marcelo Azevedo
    The scan statistic is a very popular surveillance technique for purely spatial, purely temporal, and spatialtemporal disease data. It was extended to the prospective surveillance case, and it has been applied quite extensively in this situation.When the usual signal rules, as those implemented in SaTScanTM( Boston, MA, USA) software, are used, we show that the scan statistic method is not appropriate for the prospective case. The reason is that it does not adjust properly for the sequential and repeated tests carried out during the surveillance. We demonstrate that the nominal significance level 𝛼 is notmeaningful and there is no relationship between 𝛼 and the recurrence interval or the average run length (ARL). In some cases, the ARL may be equal to ∞, which makes the method ineffective. This lack of control of the type-I error probability and of the ARL leads us to strongly oppose the use of the scan statistic with the usual signal rules in the prospective context.
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    Exploring multiple evidence to inferusers’ location in twitter.
    (2015) Rodrigues, Erica Castilho; Assunção, Renato Martins; Pappa, Gisele Lobo; Renno, Diogo
    Online social networks are valuable sources of information to monitor real-time events, such as earthquakes and epidemics. For this type of surveillance, users’ location is an essential piece of information, but a substantial number of users choose not to disclose their geographical location. However, characteristics of the users' behavior, such as the friends they associate with and the types of messages published may hint on their spatial location. In this paper, we propose a method to infer the spatial location of Twitter users. Unlike the approaches proposed so far, it incorporates two sources of information to learn geographical position: the text posted by users and their friendship network. We propose a probabilistic approach that jointly models the geographical labels and Twitter texts of users organized in the form of a graph representing the friendship network. We use the Markov random field probability model to represent the network, and learning is carried out through a Markov Chain Monte Carlo simulation technique to approximate the posterior probability distribution of the missing geographical labels. We show the accuracy of the algorithm in a large dataset of Twitter users, where the ground truth is the location given by GPS. The method presents promising results, with little sensitivity to parameters and high values of precision.
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    Optimal generalized truncated sequential Monte Carlo test.
    (2013) Silva, Ivair Ramos; Assunção, Renato Martins
    When it is not possible to obtain the analytical null distribution of a test statistic U, Monte Carlo hypothesis tests can be used to perform the test. Monte Carlo tests are commonly used in a wide variety of applications, including spatial statistics, and biostatistics. Conventional Monte Carlo tests require the simulation of m independent copies from U under the null hypothesis, what is computationally intensive for large data sets. Truncated sequential Monte Carlo designs can be performed to reduce computational effort in such situations. Different truncated sequential procedures have been proposed. They work under restrictive assumptions on the distribution of U aiming to bound the power loss and to reduce execution time. Since the use of Monte Carlo tests are based on the situations where the null distribution of U is unknown, their results are not valid for the general case of any test statistic. In this paper, we derive an optimal scheme for truncated sequential Monte Carlo hypothesis tests. This scheme minimizes the expected number of simulations under any alternative hypothesis, and bounds the power loss in arbitrarily small values. The first advantage from this scheme is that the results concerning the power and the expected time are valid for any test statistic. Also, we present practical examples of optimal procedures for which the expected number of simulations are reduced by 60% in comparison with some of the best procedures in the literature.
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    Surveillance to detect emerging space time clusters.
    (2009) Assunção, Renato Martins; Correa, Thais Rotsen
    The interest is on monitoring incoming space time events to detect an emergent space time cluster as early as possible. Assume that point process events are continuously recorded in space and time. In a certain unknown moment, a small localized cluster of increased intensity starts to emerge. Its location is also unknown. The aim is to let an alarm to go off as soon as possible after its emergence, but avoiding that it goes off unnecessarily. The alarm system should also provide an estimate of the cluster location. In addition to that, the alarm system should take into account the purely spatial and the purely temporal heterogeneity, which are not specified by the user. A space time surveillance system with these characteristics using a martingale approach to derive the surveillance system properties is proposed. The average run length for the situation when there are clusters present in the data is appropriately defined and the method is illustrated in practice. The algorithm is implemented in a freely available stand-alone software and it is also a feature in a freely available GIS system.
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    Truncated sequential Monte Carlo test with exact power.
    (2018) Silva, Ivair Ramos; Assunção, Renato Martins
    Monte Carlo hypothesis testing is extensively used for statistical inference. Surprisingly, despite the many theoretical advances in the field, statistical power performance of Monte Carlo tests remains an open question. Because the last assertion may sound questionable for some, the first goal in this paper is to show that the power performance of truncated Monte Carlo tests is still an unsolved question. The second goal here is to present a solution for this issue, that is, we introduce a truncated sequential Monte Carlo procedure with statistical power arbitrarily close to the power of the theoretical exact test. The most significant contribution of this work is the validity of our method for the general case of any test statistic.