Qvalue

Q-value is a term used in multiple disciplines, most commonly in statistics and reinforcement learning, to denote a quantity used to make decisions under uncertainty.

In statistics, the q-value is a measure used to control the false discovery rate (FDR) in multiple hypothesis testing. A q-value for a given test is the minimum FDR at which that test would be considered significant. Conceptually, it is p-values adjusted to account for the number of simultaneous tests, providing a way to balance discovery with the rate of false positives. Estimation typically requires the proportion of true null hypotheses (pi0) and the distribution of p-values; one common approach is Storey’s q-value method, which yields a q-value for each test. Software implementations are available in packages such as R’s qvalue. Interpretation is straightforward: smaller q-values indicate stronger evidence against the null hypothesis, and researchers often declare results significant at a chosen FDR threshold (for example, q ≤ 0.05). Limitations include dependence on accurate pi0 estimation and assumptions about p-value dependence across tests; q-values control the expected proportion of false discoveries among declared positives, not the probability that a single test is truly non-null.

In reinforcement learning, Q-value refers to the action-value function Q(s, a): the expected cumulative reward obtainable by taking action a in state s and thereafter following a given policy. Q-values are learned by methods such as Q-learning or deep Q-networks, using updates that incorporate observed rewards and estimates of future values. They guide action selection via policies that pick actions with the highest Q-values, balancing exploration and exploitation.

Thus, Q-value denotes distinct but central concepts in statistics and machine learning, both essential for decision making under uncertainty.