AI 中文总结
该研究借鉴博弈论统计学，将神经尖峰序列保留对数似然转化为以记录秒为单位的可解释单元，通过显著性时间τΔ实现模型排序，在小鼠头方向细胞数据上验证了其有效性。
AI 中文摘要
保留对数似然是比较神经尖峰序列统计模型的标准指标，通常以相对于齐次泊松基线的比特/尖峰形式报告。该指标的单位难以理解：比如，比特/尖峰提升0.34是大效应还是可忽略的效应，往往并不明确。本注记借鉴博弈论统计学对保留对数似然进行解释：拟合模型Q被视为按基线模型B设定的价格对每个即将到来的观测值下注的玩家。在最优（凯利）下注策略下，玩家的合约函数恰好是似然比q/b，期望对数似然比L是玩家财富的指数增长率。由于在数据由B生成的原假设下，财富过程是非负鞅，维勒不等式将其转化为随时有效的检验：一旦财富超过1/α，即可在显著性水平α下拒绝基线。这产生了一个简单的汇总统计量——显著性时间τΔ = -Δlog(α)/L，即平均拒绝基线所需的保留记录时长。因τ是L的严格递减函数，其对模型的排序与比特/尖峰完全一致；它并非新统计量，而是现有统计量的更可解释单元，以记录秒而非比特表示。我们在小鼠前丘脑记录的头方向细胞上说明该构造：广义线性模型针对齐次泊松基线，在强调谐细胞的约120ms保留数据中达到显著性，在中度调谐细胞的约11s保留数据中达到显著性。
英文摘要
Held-out log-likelihood is the standard currency for comparing statistical models of neural spike trains, and is often reported as bits per spike relative to a homogeneous Poisson baseline. The units of this metric are difficult to reason about: it is rarely obvious whether an improvement of, say, $0.34$ bits per spike is a large effect or a negligible one. This note develops an interpretation of held-out log-likelihood borrowed from game-theoretic statistics. If $L$ denotes a model's expected log-likelihood ratio to the homogeneous Poisson baseline, then we show that $-\log(α) / L$ represents the number of heldout time bins of recording needed to reject the baseline at level $α$ under a particular null hypothesis testing procedure based on a betting game. Thus, a simple re-scaling of the log-likelihood yields an intuitive metric of model performance in units of recording time which answers "how much held out data would I need, on average, to disprove the null." We illustrate the construction on head-direction cells recorded in mouse anterior thalamus, where a generalized linear model reaches significance in roughly $120$ ms of held-out data for a strongly tuned cell and roughly $11$ s for a moderately tuned cell.
Comments13 pages, 4 figures. Companion blog post: https://neurostatsblog.github.io/2026/05/27/model-comparison-by-betting/
