Accurate prediction of software defects is of crucial importance in software engineering. Software defect prediction comprises two major procedures: (i) Design of appropriate software metrics to represent characteristic software system properties; and (ii) development of effective regression models for count data, allowing for accurate prediction of the number of software defects. Although significant research effort has been devoted to software metrics design, research in count data regression has been rather limited. More specifically, most used methods have not been explicitly designed to tackle the problem of metrics driven software defect counts prediction, thus postulating irrelevant assumptions, such as (log-)linearity of the modeled data. In addition, a lack of simple and efficient algorithms for posterior computation has made more elaborate hierarchical Bayesian approaches appear unattractive in the context of software defect prediction. To address these issues, in this paper we introduce a doubly stochastic Poisson process for count data regression, the failure log-rate of which is driven by a novel latent space stochastic feed forward neural network. Our approach yields simple and efficient updates for its complicated conditional distributions by means of sampling importance resampling and error backpropagation. We exhibit the efficacy of our approach using publicly available and benchmark datasets. (C) 2016 Elsevier Inc. All rights reserved.