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Nikolaus Kriegeskorte - One of the best experts on this subject based on the ideXlab platform.

  • representational models a common framework for understanding encoding pattern component and representational similarity analysis
    2017
    Co-Authors: Jorn Diedrichsen, Nikolaus Kriegeskorte
    Abstract:

    Representational models specify how activity patterns in populations of neurons (or, more generally, in multivariate brain-activity measurements) relate to sensory stimuli, motor responses, or cognitive processes. In an experimental context, representational models can be defined as hypotheses about the distribution of activity profiles across experimental conditions. Currently, three different methods are being used to Test such hypotheses: encoding analysis, pattern component modeling (PCM), and representational similarity analysis (RSA). Here we develop a common mathematical framework for understanding the relationship of these three methods, which share one core commonality: all three evaluate the second moment of the distribution of activity profiles, which determines the representational geometry, and thus how well any feature can be decoded from population activity. Using simulated data for three different experimental designs, we compare the power of the methods to adjudicate between competing representational models. PCM implements a likelihood-ratio Test and therefore provides the Most Powerful Test if its assumptions hold. However, the other two approaches—when conducted appropriately—can perform similarly. In encoding analysis, the linear model needs to be appropriately regularized, which effectively imposes a prior on the activity profiles. With such a prior, an encoding model specifies a well-defined distribution of activity profiles. In RSA, the unequal variances and statistical dependencies of the dissimilarity estimates need to be taken into account to reach near-optimal power in inference. The three methods render different aspects of the information explicit (e.g. single-response tuning in encoding analysis and population-response representational dissimilarity in RSA) and have specific advantages in terms of computational demands, ease of use, and extensibility. The three methods are properly construed as complementary components of a single data-analytical toolkit for understanding neural representations on the basis of multivariate brain-activity data.

  • representational models a common framework for understanding encoding pattern component and representational similarity analysis
    2017
    Co-Authors: Jorn Diedrichsen, Nikolaus Kriegeskorte
    Abstract:

    Representational models specify how activity patterns in populations of neurons (or, more generally, in multivariate brain-activity measurements) relate to sensory stimuli, motor responses, or cognitive processes. In an experimental context, representational models can be defined as hypotheses about the distribution of activity profiles across experimental conditions. Previous studies have used three different methods to Test such hypotheses: encoding analysis, pattern component modeling (PCM), and representational similarity analysis (RSA). Here we develop a common mathematical framework for understanding the relationship of these three methods, which all share one core commonality: all three evaluate the second moment of the distribution of activity profiles, which determines how well any feature can be linearly decoded from population activity. Using simulated data for three different experimental designs, we compare the power of the methods to adjudicate between competing representational models. PCM implements a likelihood-ratio Test and therefore provides the Most Powerful Test if its assumptions hold. However, the other two approaches, when conducted appropriately, can perform similarly. In encoding analysis, the linear model needs to be appropriately regularized, which effectively imposes a prior on the activity profiles. With such a prior, an encoding model specifies a well-defined distribution of activity profiles. In RSA, the unequal variances and statistical dependencies of the dissimilarity estimates need to be taken into account to enable near-optimal inference. The three methods render different aspects of the information explicit (e.g. single-response tuning in encoding analysis and population-response representational dissimilarity in RSA) and have specific advantages in terms of computational demands, ease of use, and extensibility. The three methods are properly construed as complementary components of a comprehensive data-analytical toolkit for understanding neural representations on the basis of multivariate brain-activity data.

Jorn Diedrichsen - One of the best experts on this subject based on the ideXlab platform.

  • representational models a common framework for understanding encoding pattern component and representational similarity analysis
    2017
    Co-Authors: Jorn Diedrichsen, Nikolaus Kriegeskorte
    Abstract:

    Representational models specify how activity patterns in populations of neurons (or, more generally, in multivariate brain-activity measurements) relate to sensory stimuli, motor responses, or cognitive processes. In an experimental context, representational models can be defined as hypotheses about the distribution of activity profiles across experimental conditions. Currently, three different methods are being used to Test such hypotheses: encoding analysis, pattern component modeling (PCM), and representational similarity analysis (RSA). Here we develop a common mathematical framework for understanding the relationship of these three methods, which share one core commonality: all three evaluate the second moment of the distribution of activity profiles, which determines the representational geometry, and thus how well any feature can be decoded from population activity. Using simulated data for three different experimental designs, we compare the power of the methods to adjudicate between competing representational models. PCM implements a likelihood-ratio Test and therefore provides the Most Powerful Test if its assumptions hold. However, the other two approaches—when conducted appropriately—can perform similarly. In encoding analysis, the linear model needs to be appropriately regularized, which effectively imposes a prior on the activity profiles. With such a prior, an encoding model specifies a well-defined distribution of activity profiles. In RSA, the unequal variances and statistical dependencies of the dissimilarity estimates need to be taken into account to reach near-optimal power in inference. The three methods render different aspects of the information explicit (e.g. single-response tuning in encoding analysis and population-response representational dissimilarity in RSA) and have specific advantages in terms of computational demands, ease of use, and extensibility. The three methods are properly construed as complementary components of a single data-analytical toolkit for understanding neural representations on the basis of multivariate brain-activity data.

  • representational models a common framework for understanding encoding pattern component and representational similarity analysis
    2017
    Co-Authors: Jorn Diedrichsen, Nikolaus Kriegeskorte
    Abstract:

    Representational models specify how activity patterns in populations of neurons (or, more generally, in multivariate brain-activity measurements) relate to sensory stimuli, motor responses, or cognitive processes. In an experimental context, representational models can be defined as hypotheses about the distribution of activity profiles across experimental conditions. Previous studies have used three different methods to Test such hypotheses: encoding analysis, pattern component modeling (PCM), and representational similarity analysis (RSA). Here we develop a common mathematical framework for understanding the relationship of these three methods, which all share one core commonality: all three evaluate the second moment of the distribution of activity profiles, which determines how well any feature can be linearly decoded from population activity. Using simulated data for three different experimental designs, we compare the power of the methods to adjudicate between competing representational models. PCM implements a likelihood-ratio Test and therefore provides the Most Powerful Test if its assumptions hold. However, the other two approaches, when conducted appropriately, can perform similarly. In encoding analysis, the linear model needs to be appropriately regularized, which effectively imposes a prior on the activity profiles. With such a prior, an encoding model specifies a well-defined distribution of activity profiles. In RSA, the unequal variances and statistical dependencies of the dissimilarity estimates need to be taken into account to enable near-optimal inference. The three methods render different aspects of the information explicit (e.g. single-response tuning in encoding analysis and population-response representational dissimilarity in RSA) and have specific advantages in terms of computational demands, ease of use, and extensibility. The three methods are properly construed as complementary components of a comprehensive data-analytical toolkit for understanding neural representations on the basis of multivariate brain-activity data.

Benjamin M Neale - One of the best experts on this subject based on the ideXlab platform.

  • the weighting is the hardest part on the behavior of the likelihood ratio Test and the score Test under a data driven weighting scheme in sequenced samples
    2017
    Co-Authors: Camelia C Minică, Giulio Genovese, Christina M Hultman, Rene Pool, Jacqueline M Vink, Michael C Neale, Conor V Dolan, Benjamin M Neale
    Abstract:

    Sequence-based association studies are at a critical inflexion point with the increasing availability of exome-sequencing data. A popular Test of association is the sequence kernel association Test (SKAT). Weights are embedded within SKAT to reflect the hypothesized contribution of the variants to the trait variance. Because the true weights are generally unknown, and so are subject to misspecification, we examined the efficiency of a data-driven weighting scheme. We propose the use of a set of theoretically defensible weighting schemes, of which, we assume, the one that gives the largest Test statistic is likely to capture best the allele frequency-functional effect relationship. We show that the use of alternative weights obviates the need to impose arbitrary frequency thresholds. As both the score Test and the likelihood ratio Test (LRT) may be used in this context, and may differ in power, we characterize the behavior of both Tests. The two Tests have equal power, if the weights in the set included weights resembling the correct ones. However, if the weights are badly specified, the LRT shows superior power (due to its robustness to misspecification). With this data-driven weighting procedure the LRT detected significant signal in genes located in regions already confirmed as associated with schizophrenia - the PRRC2A (p = 1.020e-06) and the VARS2 (p = 2.383e-06) - in the Swedish schizophrenia case-control cohort of 11,040 individuals with exome-sequencing data. The score Test is currently preferred for its computational efficiency and power. Indeed, assuming correct specification, in some circumstances, the score Test is the Most Powerful Test. However, LRT has the advantageous properties of being generally more robust and more Powerful under weight misspecification. This is an important result given that, arguably, misspecified models are likely to be the rule rather than the exception in weighting-based approaches.

  • the weighting is the hardest part on the behavior of the likelihood ratio Test and score Test under weight misspecification in rare variant association studies
    2015
    Co-Authors: Camelia C Minică, Giulio Genovese, Christina M Hultman, Rene Pool, Jacqueline M Vink, Conor V Dolan, Dorret I Boomsma, Benjamin M Neale
    Abstract:

    Rare variant association studies are gaining importance in human genetic research with the increasing availability of exome/genome sequence data. One important Test of association between a target set of rare variants (RVs) and a given phenotype is the sequence kernel association Test (SKAT). Assignment of weights reflecting the hypothesized contribution of the RVs to the trait variance is embedded within any set-based Test. As the true weights are generally unknown, it is of interest to establish the effect of weight misspecification in SKAT. We used simulated and real data to characterize the behavior of the likelihood ratio Test (LRT) and score Test under weight misspecification. Results revealed that LRT is generally more robust to weight misspecification, and more Powerful than score Test in such a circumstance. For instance, when the rare variants within the target were simulated to have larger betas than the more common ones, incorrect assignment of equal weights reduced the power of the LRT by ~5% while the power of score Test dropped by ~30%. Furthermore, LRT was more robust to the inclusion of weighed neutral variation in the Test. To optimize weighting we proposed the use of a data-driven weighting scheme. With this approach and the LRT we detected significant enrichment of case mutations with MAF below 5% (P-value=7E-04) of a set of highly constrained genes in the Swedish schizophrenia case-control cohort of 4940 individuals with observed exome-sequencing data. The score Test is currently widely used in sequence kernel association studies for both its computational efficiency and power. Indeed, assuming correct specification, in some circumstances the score Test is the Most Powerful Test. However, our results showed that LRT has the compelling qualities of being generally more robust and more Powerful under weight misspecification. This is a paramount result, given that, arguably, misspecified models are likely to be the rule rather than the exception in the weighting-based approaches.

Wayne A Fuller - One of the best experts on this subject based on the ideXlab platform.

  • alternative estimators and unit root Tests for the autoregressive process
    1995
    Co-Authors: Heon Jin Park, Wayne A Fuller
    Abstract:

    Abstract. We compare several estimators for the second-order autoregressive process and compare the associated Tests for a unit root. Monte Carlo results are reported for the ordinary least squares estimator, the simple symmetric least squares estimator and the weighted symmetric least squares estimator. The weighted symmetric least squares estimator of the autoregressive parameters generally has smaller mean square error than that of the ordinary least squares estimator, particularly when one root is close to one in absolute value. For the second-order model with known zero intercept, the one-sided ordinary least squares Test for a unit root is more Powerful than the symmetric Tests. For the model with an estimated intercept, the one-sided weighted symmetric least squares Test is the Most Powerful Test.

Douglas A Penfield - One of the best experts on this subject based on the ideXlab platform.

  • the effects of type i error rate and power of the ancova f Test and selected alternatives under nonnormality and variance heterogeneity
    2001
    Co-Authors: David C Rheinheimer, Douglas A Penfield
    Abstract:

    Abstract The authors sought to identify through Monte Carlo simulations those conditions for which analysis of covariance (ANCOVA) does not maintain adequate Type I error rates and power. The conditions that were manipulated included assumptions of normality and variance homogeneity, sample size, number of treatment groups, and strength of the covariate-dependent variable relationship. Alternative Tests studied were Quade's procedure, Puri and Sen's solution, Burnett and Barr's rank difference scores, Conover and Iman's rank transformation Test, Hettmansperger's procedure, and the Puri-Sen-Harwell-Serlin Test. For balanced designs, the ANCOVA F Test was robust and was often the Most Powerful Test through all sample-size designs and distributional configurations. With unbalanced designs, with variance heterogeneity, and when the largest treatment-group variance was matched with the largest group sample size, the nonparametric alternatives generally outperformed the ANCOVA Test. When sample size and varianc...