Log-concavity and strong log-concavity: A review
نویسندگان
چکیده
منابع مشابه
Strong log-concavity is preserved by convolution
We review and formulate results concerning strong-log-concavity in both discrete and continuous settings. Although four different proofs of preservation of strong log-concavity are known in the discrete setting (where strong log-concavity is known as “ultra-log-concavity”), preservation of strong log-concavity under convolution has apparently not been investigated previously in the continuous c...
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This is a small observation concerning scale mixtures and their log-concavity. A function f(x) ≥ 0, x ∈ Rn is called log-concave if f (λx + (1− λ)y) ≥ f(x)f(y) (1) for all x,y ∈ Rn, λ ∈ [0, 1]. Log-concavity is important in applied Bayesian Statistics, since a distribution with a log-concave density is easy to treat with many different approximate inference techniques. For example, log-concavit...
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ژورنال
عنوان ژورنال: Statistics Surveys
سال: 2014
ISSN: 1935-7516
DOI: 10.1214/14-ss107