, p(r|s) ≈ p(r|K⊤s). When determining whether or not to use a diagnostic test, providers should consider the benefits and risks of the test, as well as the diagnostic accuracy. It is possible to continue this process, that is to derive the third-order bias-correction term, and so on. g. sfrac .
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Thus, where single-spike information quantifies the information conveyed by each spike alone (no matter how many spikes might co-occur in the same time bin) but neglects the information conveyed by silences, the Bernoulli information reflects the information conveyed by both spikes and silences. Thus the maximum likelihood estimator for p is 4980. The likelihood principle has been applied to the philosophy of science by R. e.
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A second-order basis represents f as a (transformed) sum of these bivariate functions, giving (k2)d2 parameters if we use d2 basis functions for each of the (k2) possible pairs of k filter outputs, or merely k2d2 if we instead partition the k filters into disjoint pairs. This makes it clear that the single-spike information Iss can be equally regarded as “LNP information”. By contrast, the empirical Iss evaluated on training data tends to over-estimate information due to over-fitting. However, real spike trains may exhibit more or less variability than a Poisson process [27].
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We can write the log-likelihood for the many-filter LNP model (from Equations 38–40) as:
(60)
where θ = {K,α} are the model parameters, Δ is the time bin size, and 1 denotes a vector of ones. 75 log 0. frac . The log-likelihood is therefore a sum over time bins:
(2)
where −(∑logrt!) is a constant that does not depend on θ.
X
1
,
X
2
,
X
m
{\displaystyle X_{1},\ X_{2},\ldots ,\ X_{m}}
are counts in cells / boxes 1 up to m; each box has a different probability (think of the boxes being bigger or smaller) and we fix the number of balls that fall to be
n
{\displaystyle n}
:
x
1
+
+
+
x
m
=
n
{\displaystyle x_{1}+x_{2}+\cdots +x_{m}=n}
.
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.