If x † n = sc, we could obtain the MAP estimation of channel gain by (35).
These results have implications for the preparation of isopach maps, estimation of tephra volumes and elaboration of the potential consequences of tephra falls.
It is worth to note that there exist some subtle differences between the i-supervector extraction and the classical MAP estimation of GMM [36].
This threshold-based approach is actually equivalent to a maximum a posteriori (MAP) estimation of the optimal decision, as shown below.
The novel aspects include the formulation of a source model suitable for distributed processing, the design of a distributed particle for the estimation of the posterior distribution of field and source states, and the development of a modified version of the maximum consensus (MC) algorithm [14] for the maximum a-posteriori (MAP) estimation of the source location.
On the basis of the previous work, firstly, we can easily derive the MAP estimation of x: x ^ MAP = arg min x ln f x y = arg min x ln f y x + ln f x = arg min x ln f n y − Ωx + ln f x (5).
If we use the denotation for the wavelet coefficients of the noise-free image and for the wavelet coefficients of the noise then it can be written, The MAP estimation of,, realized using the observation is given by the following MAP filter equation: (1).
As we all know, p(θ|y) = p y|θ p/p y); thus, the MAP estimation of θ could be represented as θ ^ = arg max θ p y | θ p θ p y = arg max θ p y | θ p θ (23).
Drawing the LD map, estimation of haplotype frequencies and analysis of haplotype association were performed by Haploview software.
The algorithm can be used for both Bayesian maximum a-posteriori (MAP) estimation of the most likely spatial distribution of clusters and Bayesian model averaging over a large space of spatial cluster distributions to compute the posterior probability of an unusual spatial clustering.
For longer time series or larger number of regulators, MAP estimation of the hidden values might not work so well any more and alternative methods, such as Markov Chain Monte Carlo methods, need to be considered to sample from the hidden values (Neal (1998) [ 12]).
