Condition Of Exact Infer Completely Arranged Algorithm Research And Medical Applications

Based on comprehensive study for literature and algorithms of exact inference, this thesis point out the main problems at present. Firstly, there is a shortage in exact inference system, for most statistical software only support exact test for contingency table. Secondly, there is a shortage in application of algorithms, for the network algorithm is the only algorithm available in most statistical softwares. Thereat, it's of much importance to study efficient exact inference method applying to other types of data and models. Under this background, focusing on data in medical field, this thesis analyses relative exact inference methods on contingency table, Hardy-Weinberg equilibrium and log-linear model, and develops total enumeration algorithms which are based on recursion and database. In the aspect of contingency table exact test, data structure, test methods, reference set and enumerated table probability are discussed for 2×2, 2 ×c, r×c table and s ( 2×2), s ( 2×c), s ( r×c) stratified table. For 2×2 table, different data collecting methods –paired or independent samples –correspond to different exact tests, owing to different reference set and different total enumeration algorithms. For 2 ×c table, even for single-ordered table, although there are many kinds of tests, they have the same reference set, so just one algorithm is needed, and different tests can be realized by different statistics. r×c tables are more like 2 ×c tables, different data collecting methods and different classified variable attributes correspond to different types of exact tests, but reference sets are the same. So, by constructing different statistics, and by employing common algorithm, different types of exact tests can be achieved. For stratified table, generally speaking, homogeneity tests should be considered first, and if so, tests for associations can be conducted. These two tests correspond to two kinds of algorithms. Homogeneity test is of equivalence with exact test of homogeneous association model, and association test equals to exact test of conditionally independent model in log-linear models. As for algorithms, starting with one-way contingency table, by analyzing recursive relationship between cells and totals of the table, recursive total enumeration algorithms are constructed. For two-way tables, recursive relationship is put forward by analyzing the relationship between the first row and the remaining table. And the problem of over-enumeration is solved through strict definition of recursive relationship. In the aspect of Hardy-Weinberg equilibrium exact test, data structure, proper test method, reference set and enumerated table probability are discussed for 2-allele and multi-allele system in population genetics. For 2-allele system is the special case of multi-allele system, common algorithms are needed. Recursive total enumeration algorithm is put forward and more important, a newer algorithm which can solve over-enumeration completely is developed. By separating the name and position of alleles in the table, the algorithm can reposition the alleles in the enumeration process and the problem of over-enumeration is solved completely for multi-allele system. In the aspect of goodness-of-fit exact test of contingency table log-linear models, data structure, proper test method, reference set and enumerated table probability are discussed for mutually independent model, jointly independent model, conditionally independent model and homogeneous association model for three-way table, and respective recursive total enumeration algorithm is put forward. For mutually independent model (C,A,B), for its loose reference set, three-way table is converted to one-way table with equal cells. A proper recursive algorithm is constructed referencing the relational algorithm for one-way table. For jointly independent model (C,AB), the exact test is of equivalence with exact test of two-way table stratified by C and cross of A and B. For conditionally independent model (CA,CB), the numbers of enumerated tables is the Ca...