SMART MONTE CARLO METHODS FOR ANALYZING CATEGORICAL DATA

二元Logistic回归及其在无序多值问题上的推广 响应、有序多点响应和泊松响应属于 用于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。和往常一样 对这类模型的推断方法是无条件最大似然。 对于较大的平衡良好的数据集，或只有几个参数的数据 这种方法是令人满意的。然而，无条件最大似然 估计可能会产生不一致的点估计、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度区间， 并且对于具有大量参数相对于 观察。有时这种方法完全失败，因为没有任何估计可以做到。 找到了使无条件似然函数最大化的方法。一个 在方法论上合理的替代方法，因为以上都不是 缺点是确切的有条件的方法。在这里，人们估计 通过计算精确的排列分布来计算感兴趣的参数 他们的充分统计数据，条件是观察到的 其余的“麻烦”参数有足够的统计数据。少校 准确的置换推理的绊脚石一直是 它带来了沉重的计算负担。尽管可以使用FAST 精确计算的数值算法，有无数实例 如果数据集的工具量很大，需要通过精确的方法进行分析，但 对于最大似然法来说，太稀疏或不平衡了 可靠。我们需要的是一个可靠的蒙特卡罗替代方案 精确条件方法，可以弥合精确和条件之间的差距 推理的渐近方法。这个问题在技术上是困难的，因为 传统的蒙特卡罗方法会导致样本的大量拒收 不满足条件分布的约束。我们 提出了一种蒙特卡罗问题的网络抽样方法 Believe是对这一困难但重要的 有问题。

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.