# Ronny VallejosUniversidad Técnica Federico Santa María · Department of Mathematics

Ronny Vallejos

Ph.D. in Statistics

Associate Professor, Department of Mathematics, UTFSM, Chile

## About

65

Publications

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Introduction

I am interested in the theory and methodology of spatial statistics, image modeling and time series, and applications mainly in environmental and forest sciences, and fisheries. My research focuses on the development of theoretical and methodological tools to address the association between two spatial processes, and the development of effective sample size for different scenarios. I am also interested in 3D spatial data visualization

Additional affiliations

January 2010 - November 2019

January 2010 - present

## Publications

Publications (65)

Computing the agreement between 2 continuous sequences is of great interest in statistics when comparing 2 instruments or one instrument with a gold standard. The probability of agreement quantifies the similarity between 2 variables of interest, and it is useful for determining what constitutes a practically important difference. In this article,...

Warmer and drier conditions increase forest mortality worldwide. At the same time, nitrogen deposition, longer growing seasons and higher atmospheric CO 2 concentrations may increase site productivity accelerating forest growth. However, tree physiological studies suggest that increased site productivity can also have adverse effects , reducing ada...

The correlation integral of a time series is a normalized coefficient that represents the number of close pairs of points of the series lying in phase space. It has been widely studied in a number of disciplines such as phisycs, mechanical engineering, bioengineering, among others, allowing the estimation of the dimension of an attractor in a chaot...

The structural similarity (SSIM) index has been studied from different perspectives in the last decade. Most of the developments consider its parameters fixed. Because each of these parameters corresponds to the weight of a factor in the final SSIM coefficient, the usual assumption that all parameters are equal to one is questionable. In this artic...

The problem of characterizing the passengers’ movement in a public transport system has been considered in the literature for analysis, simulation and optimization purposes. In particular, origin-destination matrices are commonly used to describe the total number of passengers that travel between two points during a given time interval. In this pap...

In the past few decades, many image quality indices have been developed. However, they stem from different theoretical frameworks, application scenarios and purposes. Thus, users and researchers are often faced with the time-consuming task of deciding which quality index to choose when they require a reliable image quality index that is capable of...

Effective sample size accounts for the equivalent number of independent observations contained in a sample of correlated data. This notion has been widely studied in the context of univariate spatial variables. In that case, the effective sample size determines the reduction in the sample size due to the existing spatial correlation. In this paper,...

The development of new techniques for sample size reduction has attracted growing interest in recent decades. Recent findings allow us to quantify the amount of duplicated information within a sample of spatial data through the so-called effective sample size (ESS), whose definition arises from the Fisher information that is associated with maximum...

This book offers essential, systematic information on the assessment of the spatial association between two processes from a statistical standpoint. Divided into eight chapters, the book begins with preliminary concepts, mainly concerning spatial statistics. The following seven chapters focus on the methodologies needed to assess the correlation be...

In this chapter, we study another measure to quantify the assessment of two spatial or temporal series. This coefficient, called the codispersion coefficient, was first introduced by Matheron (1965) and has been used in several applications (Goovaerts 1994, 1997, 1998; Chiles and Delfiner 1999; Blanco-Moreno et al. 2005; Vallejos 2008, 2012; Buckle...

Digital images are subject to a variety of contaminations (distortions) during the acquisition, processing, compression, storage transmission, and reproduction. This can significantly affect the posterior visualization of images. In image processing there are at least two ways to approach this issue, objective and subjective image quality assessmen...

Determining measures of association between two processes on the space is not a simple task. Clifford and Richardson (1985) and Clifford et al. (1989), (see also Dutilleul 1993) introduced a modified t statistic based on a correction of both, the sample covariance and the degrees of freedom of the distribution under the null hypothesis. This proced...

The goal of the current chapter is to introduce a nonparametric version of the codispersion coefficient. Extensions of this nature have previously been considered in the spatial statistics literature. For example, Hall et al. (1994) studied nonparametric estimations of the covariance function. Nonparametric estimations of the semivariogram were exa...

Addressing the spatial association between three or more processes is a challenging problem. Here, similarly as in the previous chapters we focus our attention in a continuous multivariate process with more than two components. Although motivation could be theoretical, there are several applications in the context of image processing. For instance,...

In the previous chapters, we studied the association between two georeferenced sequences from a hypothesis testing perspective. In the following three chapters, we focus on some coefficients of spatial association. These coefficients are not simple modifications of the correlation coefficient, but the underlying idea of its construction relies on t...

Assessing the significance of the correlation between the components of a bivariate random field is of great interest in the analysis of spatial-spatial data. In this chapter, testing the association between two georeferenced correlated variables is addressed for the components of a bivariate Gaussian random field using the asymptotic distribution...

In this work we define a spatial concordance coefficient for second-order stationary processes. This problem has been widely addressed in a non-spatial context, but here we consider a coefficient that for a fixed spatial lag allows one to compare two spatial sequences along a 45°line. The proposed coefficient was explored for the bivariate Matérn a...

A low cost robotic-assisted prototype for finger and hand rehabilitation of people affected by a stroke is presented. The system was developed by a team of undergraduate students led by a Design lecturer in collaboration with the Rehabilitation Unit of the Peñablanca Public Hospital in Chile.
The system consists of a flexion sensor equipped glove,...

In this work we define a spatial concordance coefficient for second-order stationary processes. This problem has been widely addressed in a non-spatial context, but here we consider a coefficient that for a fixed spatial lag allows one to compare two spatial sequences along a 45-degree line. The proposed coefficient was explored for the bivariate M...

In the last decade, image quality indices have received considerable attention to quantify the dissimilarity between two images. The codispersion coefficient, commonly used in spatial statistics to address the association between two processes has also been used for this aim. Here we introduce an image quality index (CQmax) that is based on codispe...

Griffith [Effective geographic sample size in the presence of spatial autocorrelation. Ann Assoc Amer Geogr. 2005;95:740–760] suggested a formula to compute the effective sample size, say n∗, for georeferenced data. In this article, we provide mathematical support that enhances the use of this definition in practice. We prove that n∗∈[1,n] and that...

Codispersion analysis is a new statistical method developed to assess spatial covariation between two spatial processes that may not be isotropic or stationary. Its application to anisotropic ecological datasets have provided new insights into mechanisms underlying observed patterns of species distributions and the relationship between individual s...

We propose a new definition of effective sample size. Although the recent works of Griffith (2005, 2008) and Vallejos and Osorio (2014) provide a theoretical framework to address the reduction of information in a spatial sample due to spatial autocorrelation, the asymptotic properties of the estimations have not been studied in those studies or in...

The measurement of comovement among economic variables is key in several areas of economics and finance. This article examines the comovement among Pension Fund Administrators (AFPs) in the Chilean private pension system from 2005 to 2016. We use several statistical methods to assess the comovement among the returns during this period. We found evi...

An R package SpatialPack that implements routines to compute point estimators and perform hypothesis testing of the spatial association between two stochastic sequences is introduced. These methods address the spatial association between two processes that have been observed over the same spatial locations. We briefly review the methodologies for w...

This paper focuses on the construction of image similarity indices that consider the hidden spatial association between two images. The proposal is a variant of a structural similarity (SSIM) coefficient and introduces a codispersion coefficient to capture the hidden spatial association between two images in a particular direction on a plane. The n...

Codispersion analysis allows us to detect and describe relatively subtle changes in bivariate relationships across environmental gradients, which is something that has traditionally been hard to tackle with spatial pattern analysis. When combined with null models, we can test how unexpected these observed patterns are. Our ongoing research is explo...

This paper focuses on the construction of image similarity indices that consider the hidden spatial association between two images. The proposal is a variant of a structural similarity (SSIM) coefficient and introduces a codispersion coefficient to capture the hidden spatial association between two images in a particular direction on a plane. The n...

n this paper, we present a novel objetive measure for image fusion based on the codispersion quality index, following the structure of Piella’s metric. The measure quantifies the maximum local similarity between two images for many directions using the maximum codispersion quality index. This feature is not commonly assessed by other measures of si...

This paper provides a framework for estimating the effective sample size in a spatial regression model context when the data have been sampled using a line transect scheme and there is an evident serial correlation due to the chronological order in which the observations were collected. We propose a linear regression model with a partially linear c...

An R package SpatialPack that implements routines to compute point estimators and
perform hypothesis testing of the spatial association between two stochastic sequences is introduced.
These methods address the spatial association between two processes that have been observed over
the same spatial locations. We briefly review the methodologies for w...

This package provides tools to assess the association between two spatial processes. Currently, three methodologies are implemented: An adapted t-test to perform hypothesis testing about the independence between the processes, a suitable nonparametric correlation coefficient, and the codispersion coefficient. SpatialPack gives methods to complement...

This paper proposes a methodology to address the classification of images that have been acquired from remote sensors. One common problem in classification is the high dimensionality of multivariate characteristics. The methodology we propose consists of reducing the dimensionality of the spectral bands associated with a multispectral satellite ima...

The codispersion coefficient quantifies the association between two spatial processes for a particular direction (spatial lag) on a two-dimensional space. When this coefficient is computed for many directions, it is useful to display those values on a single graph. In this article, we suggest a graphical tool called a codispersion map to visualize...

Assessing the significance of the correlation between the components of a bivariate random field is of great interest in the analysis of spatial data. This problem has been addressed in the literature using suitable hypothesis testing procedures or using coefficients of spatial association between two sequences. In this paper, testing the associati...

This paper focuses on the reduction of sample sizes due to the effect of autocorrelation for the most common models used in spatial statistics. This work is an extension of a simple illustration highlighted in several books for an autoregressive-type correlation structure. The paper briefly reviews existing proposals to quantify the effective sampl...

Time series analysis is a common tool in environmental and ecological studies to construct models to explain and forecast serially correlated data. There are several statistical techniques that are used to deal with univariate and multivariate (more than one series) chronological patterns of fisheries data. In this paper, an additive stochastic mod...

We propose a new method for estimating a codispersion coefficient to quantify the association between two spatial variables. Our proposal is based on a Nadaraya–Watson version of the codispersion coefficient through a suitable kernel. Under regularity conditions, we derive expressions for the bias and mean square error for a kernel version of the c...

The purpose of this paper is to elucidate the problem of testing for the absence of correlation between the trajectories of two stochastic processes. It is assumed that the process is homogeneous on a pre-specified partition of the index set. The hypothesis testing methodology developed in this article consists in estimating codispersion coefficien...

After the death of an animal, cell metabolism is controlled locally. The post-mortem oxygen depletion increases the glycolytic activity and lactate production. However, many mechanisms of post-mortem metabolic regulation have not been fully investigated in beef carcasses. In this work, we studied the post-mortem glycolytic behavior (including lacta...

We propose to use the codispersion coefficient to define a measure of
similarity between images. This coefficient has been widely used in
spatial statistics to quantify the association between two spatial
processes, and here we explore its capabilities in an image processing
context is mathematically simple to compute and possesses good
statistical...

This article describes a new approach to perform image segmentation. First an image is locally modeled using a spatial autoregressive model for the image intensity. Then the residual autoregressive image is computed. This resulting image possesses interesting texture features. The borders and edges are highlighted, suggesting that our algorithm can...

The objective of this review paper is to summarize the main prop-erties of the spatial ARMA models and describe some of the well-known methods used in image filtering based on estimation of spatial autoregressive models. A new proposal based on robust RA estimation is also presented. Previous studies have shown that under additive outliers the RA e...

In this work we study the asymptotic behavior of a robust class of estimators of the coefficient of a AR-2D process. We establish the precise conditions for the consistency and asymptotic normality of the RA estimator. The AR-2D model has many applications in image modeling and statistical image processing, therefore the relevance of knowing such p...

A method that allows testing the presence of spatial isotropy is
proposed. The procedure is based on a non-parametric bootstrap approach
where the means of the semi-variance are compared for two fixed azimuths
and an arbitrary lag distance. A simulation study and application in forest
science real data were developed to investigate the performance...

We examine the quantitative assessment of the association between two
spatial sequences to evaluate the performance between different spatial interpolators.
In the context of natural resources this problem is relevant in several different fields.
For example, in precision farming and forest productivity it is of interest to study the
performance of...

A method that allows testing the presence of spatial isotropy is proposed. The procedure is based on a non-parametric bootstrap approach where the means of the semi-variance are compared for two fixed azimuths and an arbitrary lag distance. A simulation study and application in forest science real data were developed to investigate the performance...

This paper deals with the codispersion coefficient for spatial and temporal series. We present some results and simulations concerning the codispersion coefficient in the context of spatial models. The results obtained are immediate consequences of the asymptotic normality of the sample codispersion coefficient and show certain limitations of the c...

The paper gives explicit formulas for the first moments of a sample codispersion coefficient defined as a suitably normalized sum of products of increments for time or space sequences. Derived formulas allow for the optimal choice of the lag in several spatial and temporal models and lead to tests of independence and confidence intervals for correl...

This article deals with Bayesian analysis of quarter plane moving average (MA) models observed on a rectangular part of a lattice. We present some properties concerning the autocorrelation function of MA models. These properties relate correlation parameters with the original model parameters providing much more understandable interpretation of res...

The objective of this article is to present a new image restoration algorithm. First, each pixel in the image is classified into k categories. Then we assume that the gray levels in each category follow a nonsymmetric half-plane (NSHP) autoregressive model. Robust estimation of the parameters of the model is considered to attenuate the effect of th...

The additive AR-2D model has been successfully related to the modeling of satelital images both optic and of radar of synthetic opening. Having in mind the errors that are produced in the process of captation and quantification of the image, an interesting subject, is the robust estimation of the parameters in this model. Besides the robust methods...

This paper is concerned with robust models for representing images. The robust methods in image models are also applied to some important image processing situations such as segmentation by texture and image restoration in the presence of outliers. We consider a non-symmetric half plane (NSHP) autoregressive image model, where the image intensity a...

In this work the performance of robust RA estimators in AR-2D models with two parameters and additive contamination, as applied to image processing, is analyzed. Five models were studied. In each case, the image of the model was simulated (original image); then the model was contaminated in an additive way and the RA estimators of the parameters we...

We consider an non-symmetric half plane autoregressive image, where the image intensity of a point is a linear combination of the intensitites of the eight nearest points located on one quadrant of the coordinate plane, plus a normal white noise innovations process. Two types of contaminations are considered. Innovation outliers, where a fraction o...