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Current Trends in Bayesian Methodology with Applications
book

Current Trends in Bayesian Methodology with Applications

by Satyanshu K. Upadhyay, Umesh Singh, Dipak K. Dey, Appaia Loganathan
May 2015
Intermediate to advanced content levelIntermediate to advanced
680 pages
22h 33m
English
Chapman and Hall/CRC
Content preview from Current Trends in Bayesian Methodology with Applications
230 Current Trends in Bayesian Methodology with Applications
−3 −2 −1
0 1
2 3
β
π(β)
GDP
Cauchy
Laplace
HS
Optimal
4.0 4.5 5.0 5.5 6.0 6.5 7.0
0.0 0.2 0.4 0.6 0.8
0.00 0.01 0.02 0.03 0.04
β
π(β)
GDP
Cauchy
Laplace
HS
Optimal
(a) Shrinkage near zero (b) Tail behaviour
FIGURE 11.1
Probability density functions for generalized double Pareto, Cauchy, Laplace,
Horseshoe and Robust prior.
n i.i.d. N(0, σ
2
) r.v.s. For convenience in presentation, σ
2
is assumed known.
The parameter dimension p may be larger than n, i.e. p > n in which ca se we
have a high-dimensional problem, but we may also have p < n. Various details
in the Lasso based analysis dep e nd o n whether p > n or
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Publisher Resources

ISBN: 9781482235128