Outputs an index I of isolated points from their integer coordinates, XYZ (3, n), and under k-connectivity, k = 6, 18 or 24.
Sample from test statistic null distribution Syntax: S = null_distribution(n,nsimu) n,nsimu: Number of observations, sample size S (nsimu,): sample Pretty costly. Simpler is to use the approximate tail probability: P(T > 0.65 | H0) = 0.05
Wrapper for random threshold functions (without connexity constraints) In: Y (n,) Observations
K <int> Some positive integer (lower bound on the number of null hypotheses) p <float> lp norm stop <bool> Stop when minimum is attained (save computation time) verbose <bool> ‘Chatty’ mode varwind <bool> Varying window variant (vs. fixed window, with width K) knownull <bool> Known null distribution (observations assumed Exp(1) under H0)
versus unknown (observations assumed Gaussian under H0)
Wrapper for random threshold functions under connexity constraints In: Y (n,) Observations
K <int> Some positive integer (lower bound on the number of null hypotheses) XYZ (3,n) voxel coordinates p <float> lp norm stop <bool> Stop when minimum is attained (save computation time) verbose <bool> ‘Chatty’ mode varwind <bool> Varying window variant (vs. fixed window, with width K) knownull <bool> Known null distribution (observations assumed Exp(1) under H0)
versus unknown (observations assumed Gaussian under H0)
Random threshold with fixed window and null gaussian distribution In: Y (n,) Observations (assumed Gaussian under H0, with unknown variance)
K <int> Some positive integer (lower bound on the number of null hypotheses) p <float> lp norm stop <bool> Stop when minimum is attained (save computation time) one_sided <bool> If nonzero means are positive only (vs. positive or negative)
Out: C (n-K) Lp norm of partial sums fluctuation about their conditional expectation
Random threshold with fixed-window and gaussian null distribution, using connexity constraint on non-null set. In: X (n,): Observations (assumed Gaussian under H0)
XYZ (3,n): voxel coordinates K <int>: Some positive integer (lower bound on the number of null hypotheses) p <float>: Lp norm stop <bool>: Stop when minimum is attained (save computation time)
Out: C (n-K): Lp norm of partial sums fluctuation about their conditional expectation
Random threshold with fixed-window and known null distribution In: X (n,): Observations (must be Exp(1) under H0)
K <int>: Some positive integer (lower bound on the number of null hypotheses) p <float>: Lp norm stop <bool>: Stop when minimum is attained (save computation time)
Out: C (n-K): Lp norm of partial sums fluctuation about their conditional expectation
Random threshold with fixed-window and known null distribution, using connexity constraint on non-null set. In: X (n,): Observations (must be Exp(1) under H0)
XYZ (3,n): voxel coordinates K <int>: Some positive integer (lower bound on the number of null hypotheses) p <float>: Lp norm stop <bool>: Stop when minimum is attained (save computation time)
Out: C (n-K): Lp norm of partial sums fluctuation about their conditional expectation
Wrapper for random threshold functions In: Y (n,) Observations
K <int> Some positive integer (lower bound on the number of null hypotheses) XYZ (3, n) voxel coordinates. If not empty, connexity constraints are used
on the non-null setp <float> lp norm varwind <bool> Varying window variant (vs. fixed window, with width K) knownull <bool> Known null distribution (observations assumed Exp(1) under H0)
versus unknown (observations assumed Gaussian under H0)stop <bool> Stop when minimum is attained (save computation time) verbose <bool> ‘Chatty’ mode
Random threshold with fixed window and gaussian null distribution In: Y (n,) Observations (assumed Gaussian under H0, with unknown variance)
K <int> Some positive integer (lower bound on the number of null hypotheses) p <float> lp norm stop <bool> Stop when minimum is attained (save computation time) one_sided <bool> If nonzero means are positive only (vs. positive or negative)
Out: C (n-K) Lp norm of partial sums fluctuation about their conditional expectation
Random threshold with fixed-window and gaussian null distribution, using connexity constraint on non-null set. In: X (n,): Observations (assumed Gaussian under H0)
XYZ (3,n): voxel coordinates K <int>: Some positive integer (lower bound on the number of null hypotheses) p <float>: Lp norm stop <bool>: Stop when minimum is attained (save computation time)
Out: C (n-K): Lp norm of partial sums fluctuation about their conditional expectation
Random threshold with varying window and known null distribution In: X (n,): Observations (Exp(1) under H0)
K <int>: Some positive integer (lower bound on the number of null hypotheses) p <float>: lp norm stop <bool>: Stop when minimum is attained (save computation time)
Out: C (n-K): Lp norm of partial sums fluctuation about their conditional expectation
Random threshold with varying window and known null distribution In: X (n,): Observations (Exp(1) under H0)
K <int>: Some positive integer (lower bound on the number of null hypotheses) XYZ (3,n): voxel coordinates p <float>: lp norm stop <bool>: Stop when minimum is attained (save computation time)
Out: C (n-K): Lp norm of partial sums fluctuation about their conditional expectation
Test statistic of global null hypothesis that all observations have zero-mean In: X (n,) : X[j] = -log(1-F(|Y[j]|)) where F: cdf of |Y[j]| under null hypothesis
(must be computed beforehand)p : Lp norm (<= inf) to use for computing test statistic
Out: D <float> : test statistic