Modeling and inference of multisubject fMRI data

Functional magnetic resonance imaging (fMRI) is a rapidly growing technique for studying the brain in action. Since its creation [1], [2], cognitive scientists have been using fMRI to understand how we remember, manipulate, and act on information in our environment. Working with magnetic resonance physicists, statisticians, and engineers, these scientists are pushing the frontiers of knowledge of how the human brain works. The design and analysis of single-subject fMRI studies has been well described. For example, [3], chapters 10 and 11 of [4], and chapters 11 and 14 of [5] all give accessible overviews of fMRI methods for one subject. In contrast, while the appropriate manner to analyze a group of subjects has been the topic of several recent papers, we do not feel it has been covered well in introductory texts and review papers. Therefore, in this article, we bring together old and new work on so-called group modeling of fMRI data using a consistent notation to make the methods more accessible and comparable

Can parametric statistical methods be trusted for fMRI based group studies?

The most widely used task fMRI analyses use parametric methods that depend on a variety of assumptions. While individual aspects of these fMRI models have been evaluated, they have not been evaluated in a comprehensive manner with empirical data. In this work, a total of 2 million random task fMRI group analyses have been performed using resting state fMRI data, to compute empirical familywise error rates for the software packages SPM, FSL and AFNI, as well as a standard non-parametric permutation method. While there is some variation, for a nominal familywise error rate of 5% the parametric statistical methods are shown to be conservative for voxel-wise inference and invalid for cluster-wise inference; in particular, cluster size inference with a cluster defining threshold of p = 0.01 generates familywise error rates up to 60%. We conduct a number of follow up analyses and investigations that suggest the cause of the invalid cluster inferences is spatial auto correlation functions that do not follow the assumed Gaussian shape. By comparison, the non-parametric permutation test, which is based on a small number of assumptions, is found to produce valid results for voxel as well as cluster wise inference. Using real task data, we compare the results between one parametric method and the permutation test, and find stark differences in the conclusions drawn between the two using cluster inference. These findings speak to the need of validating the statistical methods being used in the neuroimaging field

Reply to Chen et al.: Parametric methods for cluster inference perform worse for two-sided t-tests

One-sided t-tests are commonly used in the neuroimaging field, but two-sided tests should be the default unless a researcher has a strong reason for using a one-sided test. Here we extend our previous work on cluster false positive rates, which used one-sided tests, to two-sided tests. Briefly, we found that parametric methods perform worse for two-sided t-tests, and that non-parametric methods perform equally well for one-sided and two-sided tests

Cluster Failure Revisited: Impact of First Level Design and Data Quality on Cluster False Positive Rates

Methodological research rarely generates a broad interest, yet our work on the validity of cluster inference methods for functional magnetic resonance imaging (fMRI) created intense discussion on both the minutia of our approach and its implications for the discipline. In the present work, we take on various critiques of our work and further explore the limitations of our original work. We address issues about the particular event-related designs we used, considering multiple event types and randomisation of events between subjects. We consider the lack of validity found with one-sample permutation (sign flipping) tests, investigating a number of approaches to improve the false positive control of this widely used procedure. We found that the combination of a two-sided test and cleaning the data using ICA FIX resulted in nominal false positive rates for all datasets, meaning that data cleaning is not only important for resting state fMRI, but also for task fMRI. Finally, we discuss the implications of our work on the fMRI literature as a whole, estimating that at least 10% of the fMRI studies have used the most problematic cluster inference method (P = 0.01 cluster defining threshold), and how individual studies can be interpreted in light of our findings. These additional results underscore our original conclusions, on the importance of data sharing and thorough evaluation of statistical methods on realistic null data

Do Casinos Export Bankruptcy?

This paper measures the extent to which destination resort casinos export bankruptcy back to visitors’ home states. Previous literature has alluded to this possibility, but to date studies have only examined the influence of local casinos on local bankruptcy. Using various survey data, we calculate the number of visits from each state to casino resort destinations in Nevada, New Jersey, and Mississippi. We find strong evidence that states having more residents who visit out-of-state casino resorts have higher bankruptcy filings. This effect is dominant in the south, suggesting that casinos located in wealthier regions are less likely to export bankruptcy.Casino gambling, bankruptcy, export

Do casinos export bankruptcy?

This paper measures the extent to which destination resort casinos export bankruptcy back to visitors' home states. Previous literature has alluded to this possibility, but to date studies have only examined the influence of local casinos on local bankruptcy. Using various survey data, we calculate the number of visits from each state to casino resort destinations in Nevada, New Jersey, and Mississippi. We find strong evidence that states having more residents who visit out-of-state casino resorts have higher bankruptcy filings. This effect is dominant in the south, suggesting that casinos located in wealthier regions are less likely to export bankruptcy.Gambling industry ; Bankruptcy

Striking First: Preemption and Prevention in International Conflict

Even before the United States and its al- lies embarked on war in Iraq in 2003, the question of whether it is acceptable to strike enemies without clear provo- cation was an increasingly vexing one to policy makers, academics, and legal ex- perts. “Preemptive war” (attacking an enemy who is clearly about to strike you first) has always been an acceptable response to a dire and clear threat. But “preventive war” (striking a potential enemy while circumstances are favor- able to the attacker, or striking in early anticipation of a possible, or even only theoretical, threat) has traditionally been regarded in the international community as not only unwise but immoral

Universal Two-Electron Correlation Operator on Excited States

Excited states of chemical systems are extremely important in understanding spectra, chemical phenomena, as well as how a particular compound behaves in reactions. Computationally, excited states are normally very expensive to calculate. The difficulty in calculating these states with wavefunction based methods can be mainly attributed to the calculation of large multi-determinant wavefunctions. One reason to use a complicated multi-determinant wavefunction is to include some of the effects of correlation energy. The quantity of correlation energy can most simply be defined as the reduction in energy caused by any two or more electrons trying to avoid each other. The most common way of avoiding these computational costs is through the use of time-dependent density functional theory (TD-DFT). TD-DFT has an exceptional ratio of accuracy to computational cost because it reduces the many-electron wavefunction to a single-electron density. A single-electron quantity, however, is an improper way to descibe an innately two-electron property like correlation energy. Within this research we seek to alleviate the large computational costs required to calculate excited states with a wavefunction-based method and reduce the costs to near Hartree-Fock theory levels. We do this by using two different inexpensive excited wavefunction methods. First we reduce our multi-determinant wavefunction to a single-determinant wavefunction. The single-determinant wavefunction used in this research comes from delta self-consistent field method that essentially creates excited Hartree-Fock states. Secondly we construct the simplest multi-configurational wavefunction using a linear combination of all singly excited states with the method known as configuration interaction singles (CIS). The reduction in wavefunction size, however, reduces nearly all correlation energy recovered by both methods. This is remedied by modeling correlation energy in a computationally inexpensive manner. A potentially accurate way to model electron correlation within the single determinant wavefunction formalism is through the expectation value of a linear two-electron operator over the Kohn-Sham single-determinant wavefunction. For practical reasons, it is desirable for such an operator to be universal, i.e. independent of the positions and types of nuclei in a molecule. We choose an operator expanded in a small number of Gaussians as a model for electron correlation. The accuracy of this method is tested by computing atomic and molecular adiabatic excited states in comparison with popular TD-DFT functionals. The correlation operator combined with SCF is found to be comparable in accuracy to TD-DFT methods for both atomic and molecular excited states. SCF is limited in its applications, however, due to its inability to guarantee orthogonal excited states which leads to unwanted spin contamination. The correlation operator combined with CIS is found to be comparable in accuracy to TD-DFT methods for atomic states but has a significant loss in accuracy for excited molecular states. This drop in accuracy is theorized to be the poor description Hartree Fock theory gives of some ground and excited state wavefunctions.. We offer some possible solutions to these problems in the form of orthogonality constraints and a potential hybrid method of SCF and CIS