Super-prior Distribution Model For Multiple Local Sequence Alignment And Layered Bayes Method Under Gibbs Sampling Strategies

A large variety of proteins exist in the body of living beings and each variety of protein has its own particular function. When the protein carries out its function, what involves in the process is only a certein section of amino acid sequence constituting the protein that is closely related with the function. We call the section "element" here. Jun S .Liu et al. gave bayesian models for multiple local sequence alignment and Gibbs sampling strategies in 1995. In the actual expe-rienment, the selection of parameter affects the experienmental result to a certain extent. In accordance with the question, superprior distribution Bayesian modles for multiple local sequence alignment are set forth in this article. At the same time, in order to overcome the integral difficulty in calculating the full conditional distribution under Gibbs sampling strategies, a layered Bayes method based on NTM is proposed that has reduced the difficulty.Section 1: Relating the Biological background of the above-mentioned problemsSection 2: Reviewing briefly the bayesian models for multiple local sequence alignment and Gibbs sampling strategiesMain Results1: One sequence containing one" element" i): Product multinomial distribution treating the alignment data A as missingii)Bayesian model under prior distributionLet the prior distribution f(00) for 00 be a Dirichlet distribution Dir(0),with 0= (10, 20, , p0)T . let the prior for . g( ).g( )be a product Dirichlet distribution. PD(B).withnamely j is mutually independent p dimension random variable and its distribution is Dir(( j),j = 0,1,2, , J. thus2 : One sequence containing "multi-element"i): Product multinomial distribution treating the alignment data A as missingii):Bayesian model under prior distribution.Selecting a prior distribution analogous to that in 1, we get3: Multiple sequence containing "multi-element" In this case, the method weemploy is similar to the former one.4: Introducing the ways of obtaining the simulated samples by Gibbs samplingstrategiesEmploying the conditional distribution in section 1, we can obtain a full conditional distributionSection 3: Setting up a Superprior Distribution Model for Multiple Local Sequence Alignment and by using NTM overcoming the integral difficulties in the process of Gibbs samplingMain Results:1: Bayes model under superprior distribution Givinga prior distribution. Let 10, , p0, 11, , p1, , 1J, , pJ be iid which are in line with the same contiguous distribution F with the density function II(0, B), and the value of integral is finite, thus2: By using NTM overcoming the integral difficulties in calculating the full conditional distributionIf the contiguous distribution F meets with the the above-mentioned condition, the integral of (4) will be complex. In order to solve the problem, wepropose a layered Baycsian model based on NTM, and the difficulty of integralwill be greatly reduced.Definition 1 : LetF(x)be a contiguous distribution function in (s)-space and w -{xk, k = 1, 2, , n}be a set of points in (s)-space, then,D/r(n, w) = sup |Fn(x) -F(x)|is called F - deviation about w. HereFn(x)is the empirical distribution ofrespective variant.is a set of n points in cs with the deviation d, and cs is a s-dimension cube unit, then the F-deviation of the set of pointsabout F(x) is rf, namely, the independent inverse transformation of the distribution function is a invariant transformation of deviation(DPT).According to the above conclusion, we can find a set of points about the above-mentioned F-deviation, so that we can discretize a contiguous distribution.3:The new explorative methods in the case of multi-elememts in a sequenceExplorative data-analyzing methods and the so-called"knife-cutting method."...