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Information theoretic interpretation of frequency domain connectivity measures

Takahashi, Daniel Yasumasa; Baccala, Luiz Antonio; Sameshima, Koichi
Fonte: SPRINGER Publicador: SPRINGER
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
36.02%
In order to provide adequate multivariate measures of information flow between neural structures, modified expressions of partial directed coherence (PDC) and directed transfer function (DTF), two popular multivariate connectivity measures employed in neuroscience, are introduced and their formal relationship to mutual information rates are proved.; FAPESP[2005/56464-9]; FAPESP[2008/08171-0]; Programa Interunidades de Pos-Graduacao em Bioinformatica da Universidade de Sao Paulo (USP); CNPq[06964/2006-6]; CNPq[3044 04/2009-8]

Causalidade Granger em medidas de risco; Granger Causality with Risk Measures

Murakami, Patricia Nagami
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 02/05/2011 Português
Relevância na Pesquisa
36.25%
Esse trabalho apresenta um estudo da causalidade de Granger em Risco bivariado aplicado a séries temporais financeiras. Os eventos de risco, no caso de séries financeiras, estão relacionados com a avaliação do Valor em Risco das posições em ativos. Para isso, os modelos CaViaR, que fazem parte do grupo de modelos de Regressão Quantílica, foram utilizado para identificação desses eventos. Foram expostos os conceitos principais envolvidos da modelagem, assim como as definições necessárias para entendê-las. Através da análise da causalide de Granger em risco entre duas séries, podemos investigar se uma delas é capaz de prever a ocorrência de um valor extremo da outra. Foi realizada a análise de causalidade de Granger usual somente para como comparativo.; Quantile Regression, Value at Risk, CAViaR Model, Granger Causality, Granger Causality in Risk

More discussions for granger causality and new causality measures

Hu, Sanqing; Cao, Yu; Zhang, Jianhai; Kong, Wanzeng; Yang, Kun; Zhang, Yanbin; Li, Xun
Fonte: Springer Netherlands Publicador: Springer Netherlands
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
36.4%
Granger causality (GC) has been widely applied in economics and neuroscience to reveal causality influence of time series. In our previous paper (Hu et al., in IEEE Trans on Neural Netw, 22(6), pp. 829–844, 2011), we proposed new causalities in time and frequency domains and particularly focused on new causality in frequency domain by pointing out the shortcomings/limitations of GC or Granger-alike causality metrics and the advantages of new causality. In this paper we continue our previous discussions and focus on new causality and GC or Granger-alike causality metrics in time domain. Although one strong motivation was introduced in our previous paper (Hu et al., in IEEE Trans on Neural Netw, 22(6), pp. 829–844, 2011) we here present additional motivation for the proposed new causality metric and restate the previous motivation for completeness. We point out one property of conditional GC in time domain and the shortcomings/limitations of conditional GC which cannot reveal the real strength of the directional causality among three time series. We also show the shortcomings/limitations of directed causality (DC) or normalize DC for multivariate time series and demonstrate it cannot reveal real causality at all. By calculating GC and new causality values for an example we demonstrate the influence of one of the time series on the other is linearly increased as the coupling strength is linearly increased. This fact further supports reasonability of new causality metric. We point out that larger instantaneous correlation does not necessarily mean larger true causality (e.g....

Causality Analysis of Neural Connectivity: Critical Examination of Existing Methods and Advances of New Methods

Hu, Sanqing; Dai, Guojun; Worrell, Gregory A.; Dai, Qionghai; Liang, Hualou
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
36.71%
Granger causality (GC) is one of the most popular measures to reveal causality influence of time series and has been widely applied in economics and neuroscience. Especially, its counterpart in frequency domain, spectral GC, as well as other Granger-like causality measures have recently been applied to study causal interactions between brain areas in different frequency ranges during cognitive and perceptual tasks. In this paper, we show that: 1) GC in time domain cannot correctly determine how strongly one time series influences the other when there is directional causality between two time series, and 2) spectral GC and other Granger-like causality measures have inherent shortcomings and/or limitations because of the use of the transfer function (or its inverse matrix) and partial information of the linear regression model. On the other hand, we propose two novel causality measures (in time and frequency domains) for the linear regression model, called new causality and new spectral causality, respectively, which are more reasonable and understandable than GC or Granger-like measures. Especially, from one simple example, we point out that, in time domain, both new causality and GC adopt the concept of proportion, but they are defined on two different equations where one equation (for GC) is only part of the other (for new causality)...

Canonical Granger Causality between Regions of Interest

Ashrafulla, Syed; Haldar, Justin P.; Joshi, Anand A.; Leahy, Richard M.
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
36.35%
Estimating and modeling functional connectivity in the brain is a challenging problem with potential applications in the understanding of brain organization and various neurological and neuropsychological conditions. An important objective in connectivity analysis is to determine the connections between regions of interest in the brain. However, traditional functional connectivity analyses have frequently focused on modeling interactions between time series recordings at individual sensors, voxels, or vertices despite the fact that a single region of interest will often include multiple such recordings. In this paper, we present a novel measure of interaction between regions of interest rather than individual signals. The proposed measure, termed canonical Granger causality, combines ideas from canonical correlation and Granger causality analysis to yield a measure that reflects directed causality between two regions of interest. In particular, canonical Granger causality uses optimized linear combinations of signals from each region of interest to enable accurate causality measurements from substantially less data compared to alternative multivariate methods that have previously been proposed for this scenario. The optimized linear combinations are obtained using a variation of a technique developed for optimization on the Steifel manifold. We demonstrate the advantages of canonical Granger causality in comparison to alternative causality measures for a range of different simulated datasets. We also apply the proposed measure to local field potential data recorded in a macaque brain during a visuomotor task. Results demonstrate that canonical Granger causality can be used to identify causal relationships between striate and prestriate cortex in cases where standard Granger causality is unable to identify statistically significant interactions.

Granger causality revisited

Friston, Karl J.; Bastos, André M.; Oswal, Ashwini; van Wijk, Bernadette; Richter, Craig; Litvak, Vladimir
Fonte: Academic Press Publicador: Academic Press
Tipo: Artigo de Revista Científica
Publicado em 01/11/2014 Português
Relevância na Pesquisa
36.57%
This technical paper offers a critical re-evaluation of (spectral) Granger causality measures in the analysis of biological timeseries. Using realistic (neural mass) models of coupled neuronal dynamics, we evaluate the robustness of parametric and nonparametric Granger causality. Starting from a broad class of generative (state-space) models of neuronal dynamics, we show how their Volterra kernels prescribe the second-order statistics of their response to random fluctuations; characterised in terms of cross-spectral density, cross-covariance, autoregressive coefficients and directed transfer functions. These quantities in turn specify Granger causality — providing a direct (analytic) link between the parameters of a generative model and the expected Granger causality. We use this link to show that Granger causality measures based upon autoregressive models can become unreliable when the underlying dynamics is dominated by slow (unstable) modes — as quantified by the principal Lyapunov exponent. However, nonparametric measures based on causal spectral factors are robust to dynamical instability. We then demonstrate how both parametric and nonparametric spectral causality measures can become unreliable in the presence of measurement noise. Finally...

Short and long run causality measures: theory and inference

Dufour, Jean-Marie; Taamouti, Abderrahim
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/workingPaper; info:eu-repo/semantics/workingPaper Formato: application/pdf
Publicado em /07/2008 Português
Relevância na Pesquisa
56.68%
The concept of causality introduced by Wiener (1956) and Granger (1969) is defined in terms of predictability one period ahead. This concept can be generalized by considering causality at a given horizon h, and causality up to any given horizon h [Dufour and Renault (1998)]. This generalization is motivated by the fact that, in the presence of an auxiliary variable vector Z, it is possible that a variable Y does not cause variable X at horizon 1, but causes it at horizon h > 1. In this case, there is an indirect causality transmitted by Z. Another related problem consists in measuring the importance of causality between two variables. Existing causality measures have been defined only for the horizon 1 and fail to capture indirect causal effects. This paper proposes a generalization of such measures for any horizon h. We propose nonparametric and parametric measures of unidirectional and instantaneous causality at any horizon h. Parametric measures are defined in the context of autoregressive processes of unknown order and expressed in terms of impulse response coefficients. On noting that causality measures typically involve complex functions of model parameters in VAR and VARMA models, we propose a simple method to evaluate these measures which is based on the simulation of a large sample from the process of interest. We also describe asymptotically valid nonparametric confidence intervals...

Measuring causality between volatility and returns with high-frequency data

Dufour, Jean-Marie; García, René; Taamouti, Abderrahim
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/workingPaper; info:eu-repo/semantics/workingPaper Formato: application/pdf
Publicado em /09/2008 Português
Relevância na Pesquisa
46.4%
We use high-frequency data to study the dynamic relationship between volatility and equity returns. We provide evidence on two alternative mechanisms of interaction between returns and volatilities: the leverage effect and the volatility feedback effect. The leverage hypothesis asserts that return shocks lead to changes in conditional volatility, while the volatility feedback effect theory assumes that return shocks can be caused by changes in conditional volatility through a time-varying risk premium. On observing that a central difference between these alternative explanations lies in the direction of causality, we consider vector autoregressive models of returns and realized volatility and we measure these effects along with the time lags involved through short-run and long-run causality measures proposed in Dufour and Taamouti (2008), as opposed to simple correlations. We analyze 5-minute observations on S&P 500 Index futures contracts, the associated realized volatilities (before and after filtering jumps through the bispectrum) and implied volatilities. Using only returns and realized volatility, we find a weak dynamic leverage effect for the first four hours at the hourly frequency and a strong dynamic leverage effect for the first three days at the daily frequency. The volatility feedback effect appears to be negligible at all horizons. By contrast...

Nonparametric estimation and inference for Granger causality measures

Taamouti, Abderrahim; Bouezmarni, Taoufik; El Ghouch, Anouar
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper Formato: application/pdf
Publicado em 29/03/2012 Português
Relevância na Pesquisa
66.64%
We propose a nonparametric estimator and a nonparametric test for Granger causality measures that quantify linear and nonlinear Granger causality in distribution between random variables. We first show how to write the Granger causality measures in terms of copula densities. We suggest a consistent estimator for these causality measures based on nonparametric estimators of copula densities. Further, we prove that the nonparametric estimators are asymptotically normally distributed and we discuss the validity of a local smoothed bootstrap that we use in finite sample settings to compute a bootstrap bias-corrected estimator and test for our causality measures. A simulation study reveals that the bias-corrected bootstrap estimator of causality measures behaves well and the corresponding test has quite good finite sample size and power properties for a variety of typical data generating processes and different sample sizes. Finally, we illustrate the practical relevance of nonparametric causality measures by quantifying the Granger causality between S&P500 Index returns and many exchange rates (US/Canada, US/UK and US/Japen exchange rates).

Causal Measures of Structure and Plasticity in Simulated and Living Neural Networks

Cadotte, Alex J.; DeMarse, Thomas B.; He, Ping; Ding, Mingzhou
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Publicado em 07/10/2008 Português
Relevância na Pesquisa
26.33%
A major goal of neuroscience is to understand the relationship between neural structures and their function. Recording of neural activity with arrays of electrodes is a primary tool employed toward this goal. However, the relationships among the neural activity recorded by these arrays are often highly complex making it problematic to accurately quantify a network's structural information and then relate that structure to its function. Current statistical methods including cross correlation and coherence have achieved only modest success in characterizing the structural connectivity. Over the last decade an alternative technique known as Granger causality is emerging within neuroscience. This technique, borrowed from the field of economics, provides a strong mathematical foundation based on linear auto-regression to detect and quantify “causal” relationships among different time series. This paper presents a combination of three Granger based analytical methods that can quickly provide a relatively complete representation of the causal structure within a neural network. These are a simple pairwise Granger causality metric, a conditional metric, and a little known computationally inexpensive subtractive conditional method. Each causal metric is first described and evaluated in a series of biologically plausible neural simulations. We then demonstrate how Granger causality can detect and quantify changes in the strength of those relationships during plasticity using 60 channel spike train data from an in vitro cortical network measured on a microelectrode array. We show that these metrics can not only detect the presence of causal relationships...

Causality and the interpretation of epidemiologic evidence

Kundi,Michael
Fonte: ABRASCO - Associação Brasileira de Saúde Coletiva Publicador: ABRASCO - Associação Brasileira de Saúde Coletiva
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/04/2007 Português
Relevância na Pesquisa
36.04%
There is an ongoing debate regarding how and when an agent's or determinant's impact can be interpreted as causation with respect to some target disease. The criteria of causation, originating from the seminal work of Sir Austin Bradford Hill and Mervyn Susser, are often schematically applied and, furthermore, there is a tendency to misinterpret the lack of evidence for causation as evidence for lack of a causal relation. There are no criteria for the assessment of evidence concerning an agent's or determinant's propensity to cause a disease, nor are there criteria to dismiss the notion of causation. In this commentary, I propose a dialogue approach for the assessment of an agent or determinant. Starting from epidemiologic evidence, four issues need to be addressed: temporal relation, association, environmental equivalence, and population equivalence. If there are no valid counterarguments, a factor is attributed the potential of disease causation. More often, there will be insufficient evidence from epidemiologic studies. In these cases, other evidence can be used that increases or decreases confidence in a factor being causally related to a disease. Even though every verdict of causation is provisional, action must not be postponed if our present knowledge appears to demand immediate measures for health protection.

Reducing the Bias of Causality Measures

Papana, A.; Kugiumtzis, D.; Larsson, P. G.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/01/2011 Português
Relevância na Pesquisa
46.34%
Measures of the direction and strength of the interdependence between two time series are evaluated and modified in order to reduce the bias in the estimation of the measures, so that they give zero values when there is no causal effect. For this, point shuffling is employed as used in the frame of surrogate data. This correction is not specific to a particular measure and it is implemented here on measures based on state space reconstruction and information measures. The performance of the causality measures and their modifications is evaluated on simulated uncoupled and coupled dynamical systems and for different settings of embedding dimension, time series length and noise level. The corrected measures, and particularly the suggested corrected transfer entropy, turn out to stabilize at the zero level in the absence of causal effect and detect correctly the direction of information flow when it is present. The measures are also evaluated on electroencephalograms (EEG) for the detection of the information flow in the brain of an epileptic patient. The performance of the measures on EEG is interpreted, in view of the results from the simulation study.; Comment: 30 pages, 12 figures, accepted to Physical Review E

Measures of Causality in Complex Datasets with application to financial data

Zaremba, Anna; Aste, Tomaso
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.5%
This article investigates the causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and the Hilbert--Schmidt norm of the cross-covariance operator) and transfer entropy, examining each method and comparing their theoretical properties, with special attention given to the ability to capture nonlinear causality. We also present the theoretical benefits of applying non-symmetrical measures rather than symmetrical measures of dependence. We apply the measures to a range of simulated and real data. The simulated data sets were generated with linear and several types of nonlinear dependence, using bivariate, as well as multivariate settings. An application to real-world financial data highlights the practical difficulties, as well as the potential of the methods. We use two real data sets: (1) U.S. inflation and one-month Libor; (2) S$\&$P data and exchange rates for the following currencies: AUDJPY, CADJPY, NZDJPY, AUDCHF, CADCHF, NZDCHF. Overall, we reach the conclusion that no single method can be recognised as the best in all circumstances, and each of the methods has its domain of best applicability. We also highlight areas for improvement and future research.; Comment: 40 pages; 13 figures

Validity of time reversal for testing Granger causality

Winkler, Irene; Panknin, Danny; Bartz, Daniel; Müller, Klaus-Robert; Haufe, Stefan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 25/09/2015 Português
Relevância na Pesquisa
26.43%
Inferring causal interactions from observed data is a challenging problem, especially in the presence of measurement noise. To alleviate the problem of spurious causality, Haufe et al. (2013) proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time-reversed data. They show that this procedure, time-reversed Granger causality (TRGC), robustly rejects causal interpretations on mixtures of independent signals. While promising results have been achieved in simulations, it was so far unknown whether time reversal leads to valid measures of information flow in the presence of true interaction. Here we prove that, for linear finite-order autoregressive processes with unidirectional information flow, the application of time reversal for testing Granger causality indeed leads to correct estimates of information flow and its directionality. Using simulations, we further show that TRGC is able to infer correct directionality with similar statistical power as the net Granger causality between two variables, while being much more robust to the presence of measurement noise.

State Space Methods for Granger-Geweke Causality Measures

Solo, Victor
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/01/2015 Português
Relevância na Pesquisa
36.16%
At least two recent developments have put the spotlight on some significant gaps in the theory of multivariate time series. The recent interest in the dynamics of networks; and the advent, across a range of applications, of measuring modalities that operate on different temporal scales. Fundamental to the description of network dynamics is the direction of interaction between nodes, accompanied by a measure of the strength of such interactions. Granger causality (GC) and its associated frequency domain strength measures (GEMs) (due to Geweke) provide a framework for the formulation and analysis of these issues. In pursuing this setup, three significant unresolved issues emerge. Firstly computing GEMs involves computing submodels of vector time series mod- els, for which reliable methods do not exist; Secondly the impact of filtering on GEMs has never been definitively established. Thirdly the impact of downsampling on GEMs has never been established. In this work, using state space methods, we resolve all these issues and illustrate the results with some simulations. Our discussion is motivated by some problems in (fMRI) brain imaging but is of general applicability.; Comment: These results have been presented in a number of invited talks. HBM Conference...

Relating Granger causality to directed information theory for networks of stochastic processes

Amblard, Pierre-Olivier; Michel, Olivier J. J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.43%
This paper addresses the problem of inferring circulation of information between multiple stochastic processes. We discuss two possible frameworks in which the problem can be studied: directed information theory and Granger causality. The main goal of the paper is to study the connection between these two frameworks. In the case of directed information theory, we stress the importance of Kramer's causal conditioning. This type of conditioning is necessary not only in the definition of the directed information but also for handling causal side information. We also show how directed information decomposes into the sum of two measures, the first one related to Schreiber's transfer entropy quantifies the dynamical aspects of causality, whereas the second one, termed instantaneous information exchange, quantifies the instantaneous aspect of causality. After having recalled the definition of Granger causality, we establish its connection with directed information theory. The connection is particularly studied in the Gaussian case, showing that Geweke's measures of Granger causality correspond to the transfer entropy and the instantaneous information exchange. This allows to propose an information theoretic formulation of Granger causality.; Comment: submitted...

Comparing causality measures of fMRI data using PCA, CCA and vector autoregressive modelling

Shah, Adnan; Khalid, Muhammad; Seghouane, Abd-Krim
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Conference paper
Português
Relevância na Pesquisa
36.33%
Extracting the directional interaction between activated brain areas from functional magnetic resonance imaging (fMRI) time series measurements of their activity is a significant step in understanding the process of brain functions. In this paper, the directional interaction between fMRI time series characterizing the activity of two neuronal sites is quantified using two measures; one derived based on univariate autoregressive and autoregressive exogenous (AR/ARX) and other derived based on multivariate vector autoregressive and vector autoregressive exogenous (VAR/VARX) models. The significance and effectiveness of these measures is illustrated on both simulated and real fMRI data sets. It has been revealed that VAR modelling of the regions of interest is robust in inferring true causality compared to principal component analysis (PCA) and canonical correlation analysis (CCA) based causality methods.

Comparing causality measures of fMRI data using PCA, CCA and vector autoregressive modelling.

Shah, Adnan; Khalid, Muhammad; Seghouane, Abd-Krim
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
36.33%
Extracting the directional interaction between activated brain areas from functional magnetic resonance imaging (fMRI) time series measurements of their activity is a significant step in understanding the process of brain functions. In this paper, the directional interaction between fMRI time series characterizing the activity of two neuronal sites is quantified using two measures; one derived based on univariate autoregressive and autoregressive exogenous (AR/ARX) and other derived based on multivariate vector autoregressive and vector autoregressive exogenous (VAR/VARX) models. The significance and effectiveness of these measures is illustrated on both simulated and real fMRI data sets. It has been revealed that VAR modelling of the regions of interest is robust in inferring true causality compared to principal component analysis (PCA) and canonical correlation analysis (CCA) based causality methods.

Measures of causality in complex datasets with application to financial data

Zaremba, Anna; Aste, Tomaso
Fonte: Multidisciplinary Digital Publishing Institute (MDPI) Publicador: Multidisciplinary Digital Publishing Institute (MDPI)
Tipo: Article; PeerReviewed Formato: application/pdf
Publicado em //2014 Português
Relevância na Pesquisa
26.5%
This article investigates the causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and the Hilbert-Schmidt norm of the cross-covariance operator) and transfer entropy, examining each method and comparing their theoretical properties, with special attention given to the ability to capture nonlinear causality. We also present the theoretical benefits of applying non-symmetrical measures rather than symmetrical measures of dependence. We apply the measures to a range of simulated and real data. The simulated data sets were generated with linear and several types of nonlinear dependence, using bivariate, as well as multivariate settings. An application to real-world financial data highlights the practical difficulties, as well as the potential of the methods. We use two real data sets: (1) U.S. inflation and one-month Libor; (2) S&P data and exchange rates for the following currencies: AUDJPY, CADJPY, NZDJPY, AUDCHF, CADCHF, NZDCHF. Overall, we reach the conclusion that no single method can be recognised as the best in all circumstances, and each of the methods has its domain of best applicability. We also highlight areas for improvement and future research.

Causality and the interpretation of epidemiologic evidence

Kundi,Michael
Fonte: ABRASCO - Associação Brasileira de Saúde Coletiva Publicador: ABRASCO - Associação Brasileira de Saúde Coletiva
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/04/2007 Português
Relevância na Pesquisa
36.04%
There is an ongoing debate regarding how and when an agent's or determinant's impact can be interpreted as causation with respect to some target disease. The criteria of causation, originating from the seminal work of Sir Austin Bradford Hill and Mervyn Susser, are often schematically applied and, furthermore, there is a tendency to misinterpret the lack of evidence for causation as evidence for lack of a causal relation. There are no criteria for the assessment of evidence concerning an agent's or determinant's propensity to cause a disease, nor are there criteria to dismiss the notion of causation. In this commentary, I propose a dialogue approach for the assessment of an agent or determinant. Starting from epidemiologic evidence, four issues need to be addressed: temporal relation, association, environmental equivalence, and population equivalence. If there are no valid counterarguments, a factor is attributed the potential of disease causation. More often, there will be insufficient evidence from epidemiologic studies. In these cases, other evidence can be used that increases or decreases confidence in a factor being causally related to a disease. Even though every verdict of causation is provisional, action must not be postponed if our present knowledge appears to demand immediate measures for health protection.