The ultimate product of distributed sensing is normally a model that describes the data or a set of processes for which the data is an observation. The sensor network itself affects the collected data, often due to the need to conserve deployment costs, including energy provisioning. These effects include data compression and transmission censoring in addition to the typical noise and distortion of signal transduction. This paper describes a framework for performing data and model inference that incorporates network effects into the sophisticated data/model inference techniques used in environmental and ecological field studies. Both the monitored processes and the effects of network data gathering tend to be strongly non-linear and, with uncertainty arising at different levels, hierarchical. Hence closed-form solutions for estimation are beyond reach. Hierarchical Bayesian modeling can jointly capture models and the effects of compression/censoring, and Markov chain Monte Carol (MCMC) simulation at the data center can form posterior estimates. Integral to the inference are estimates of the uncertainty of data and parameters. As the model evolves at the data center, continuously updated estimates of uncertainty can drive adaptation of source/channel coding and data transmission policies at the sensor nodes. As an example application, this paper considers strongly asymmetric data processing to minimize computational complexity and energy cost at the sensor nodes and exploit abundant data center resources. Using an example of compression via simple requantization of the data, we show that MCMC-based inference can yield good performance even at substantial compression rates.