Hence,, contradicting the assumption, so.
The uncertainties here make the etiological assumption, (hence antibiotic prescription) culturally arbitrary [ 25].
Hitczenko [8] proved the above inequality for conditionally symmetric martingale difference sequences, and De la Peña [7] obtained the above inequality without the martingale difference assumption, hence without any integrability assumptions.
This Naïve assumption (hence: the name "Naïve Bayes") significantly mitigates the difficulty of estimating the fully joint class-conditional probability density function (p(mathbf{x}|omega _{j})) to that of estimating (L) statistically independent class-conditional univariate probability density functions (p(x_{l}|omega _{j})).
(b) By our assumption Λ k (f t ) is continuous for t ∈ I and k = 1,..., 4; then by using Proposition 1.15, we get exponential convexity of the function t ↦ Λ k (f t ) on I for k = 1,..., 4. (c) As Λ k (f t ) is positive and the function t ↦ Λ k (f t ) is derivable for k = 1,..., 4 by our assumption, hence the result follows directly by using (c) part of Theorem 2.1.
By our assumption Λ k (f t ) is continuous for t ∈ I and k = 1,..., 4; then by using Proposition 1.15, we get exponential convexity of the function t ↦ Λ k (f t ) on I for k = 1,..., 4. As Λ k (f t ) is positive and the function t ↦ Λ k (f t ) is derivable for k = 1,..., 4 by our assumption, hence the result follows directly by using (c) part of Theorem 2.1.
This contradicts our assumption; hence, we conclude that x 1 ∗ = x 2 ∗ = x ∗. □.
The choice of leak scenario is guided by only a small number of available observations and requires several assumptions; hence the simulations reported on are engineered to be worse case scenarios.
which contradicts the assumption that and hence the claim is true provided is suitably small.
The two models are theoretically equivalent under certain assumptions, hence are expected to yield similar results.
