We design, analyze, and optimize distributed detection and estimation algorithms in a large, shared-channel, single-hop wireless sensor network (WSN). The fusion center (FC) is allocated a shared transmission channel to collect local decisions/estimates but cannot collect all of them because of limited energy, bandwidth, or time. We propose a strategy called reliability-based splitting algorithm that enables the FC to collect local decisions/estimates in descending order of their reliabilities through a shared collision channel. The algorithm divides the transmission channel into time frames and the sensor nodes into groups based on their observation reliabilities. Only nodes with a specified range of reliabilities compete for the channel using slotted ALOHA within each frame. Nodes with the most reliable decisions/estimates attempt transmission in the first frame; nodes with the next most reliable set of decisions/estimates attempt in the next frame; etc. The reliability-based splitting algorithm is applied in three scenarios: time-constrained distributed detection; sequential distributed detection; and time-constrained estimation. Performance measures of interest - including detection error probability, efficacy, asymptotic relative efficiency, and estimator variance - are derived. In addition, we propose and analyze algorithms that exploit information from the occurrence of collisions to improve the performance of both time-constrained distributed detection and sequential distributed detection.