SMART MONTE CARLO METHODS FOR ANALYZING CATEGORICAL DATA

二元Logistic回归及其对无序多变量的推广 响应、有序多胎响应和泊松响应是其中之一。 分类数据分析的最流行的数学模型 在生物医学科学中具有广泛的适用性。 通常的 这种模型的推理方法是无条件最大似然法。 对于大型平衡数据集，或只有几个参数的数据 这种做法令人满意。 无条件最大似然法 估计可能会产生不一致的点估计值、不准确的p值 以及对于小的或不平衡的数据集的不准确的置信区间， 对于相对于参数数目而言具有大量参数的集合， 意见。 有时这种方法完全失败，因为没有任何估计可以 最大化无条件似然函数。 一 方法上合理的替代方法， 缺点是精确的条件方法。 在这里，人们估计， 通过计算精确的排列分布 他们的充分统计，条件是观察值的 对于剩余的“滋扰”参数有足够的统计数据。 主要 精确置换推理的绊脚石一直是 它带来了沉重的计算负担。 尽管快速的可用性 精确计算的数值算法，有许多实例 其中数据集对于通过精确方法进行分析而言是工具大的，然而 对于最大似然方法来说太稀疏或不平衡， 可靠 我们需要的是一个可靠的蒙特卡罗替代方法， 精确的条件方法，它可以弥合精确和 渐近推理方法 这个问题在技术上很难，因为 传统的蒙特卡罗方法会导致大量的样本拒绝 不满足条件分布的约束。 我们 提出了一个网络抽样方法的蒙特卡罗问题，我们 我相信这是一个重大突破， 问题.

Binary logistic regression and its extensions to unordered polytocous response, ordered polytocous response, and Poisson response are among the most popular mathematical models for the analysis of categorical data with widespread applicability in the biomedical sciences. The usual method of inference for such models is unconditional maximum likelihood. For large well balanced data sets, or for data with only a few parameters this approach is satisfactory. However, unconditional maximum likelihood estimation can produce inconsistent point estimates, inaccurate p-values and inaccurate confidence intervals for small or imbalanced data sets, and for sets with a large number of parameters relative to the number of observations. Sometimes the method fails entirely as no estimates can be found which maximize the unconditional likelihood function. A methodologically sound alternative approach which as none of the above drawbacks is the exact conditional approach. Here one estimates the parameters of interest by computing the exact permutation distributions of their sufficient statistics, conditional on the observed values of the sufficient statistics for the remaining "nuisance" parameters. The major stumbling block to exact permutational inference has always been the heavy computational burden it imposes. Despite the availability of fast numerical algorithms for the exact computations, there numerous instances where a data set is tool large to be analyses by the exact methods, yet too sparse or imbalanced for the maximum likelihood approach to be reliable. What is needed is a reliable Monte Carlo alternative to the exact conditional approach which can bridge the gap between the exact and asymptotic methods of inference. The problem is technically hard because conventional Monte Carlo methods lead to massive rejection of samples that do not satisfy the constraints of the conditional distribution. We propose a network sampling approach to the Monte Carlo problem that we believe is a major break-through for this difficult but important problem.