The neural network models implemented in my software for flexible Bayesian modeling are described in my book:
Neal, R. M. (1996) Bayesian Learning for Neural Networks, Lecture Notes in Statistics No. 118, New York: Springer-Verlag: blurb, associated references.
The slides from my talk on ``Survival analysis using a Bayesian neural network'', given at the Joint Statistical Meetings, August 2001, are also available: postscript, pdf.
Neural network learning using gradient descent, early stopping, and ensembles is discussed in the following paper:
Neal, R. M. (1998) ``Assessing relevance determination methods using DELVE'', in C. M. Bishop (editor), Neural Networks and Machine Learning, pp. 97-129, Springer-Verlag: abstract, associated references, postscript, pdf.
Neal, R. M. (1998) ``Regression and classification using Gaussian process priors'' (with discussion), in J. M. Bernardo, et al (editors) Bayesian Statistics 6, Oxford University Press, pp. 475-501: abstract, postscript (without discussion), pdf (without discussion).Neal, R. M. (1997) ``Monte Carlo implementation of Gaussian process models for Bayesian regression and classification'', Technical Report No. 9702, Dept. of Statistics, University of Toronto, 24 pages: abstract, postscript, pdf.
You might also want to read Carl Rasmussen's thesis on Evaluation of Gaussian Processes and Other Methods for Non-Linear Regression, and visit his Gaussian process page.
Neal, R. M. (1998) ``Markov chain sampling methods for Dirichlet process mixture models'', Technical Report No. 9815, Dept. of Statistics, University of toronto, 17 pages: abstract, postscript, pdf, associated references, associated software.Neal, R. M. (1991) ``Bayesian mixture modeling by Monte Carlo simulation'', Technical Report CRG-TR-91-2, Dept. of Computer Science, University of Toronto, 23 pages: abstract, postscript, pdf, associated reference.
Neal, R. M. (2003) ``Density modeling and clustering using Dirichlet diffusion trees'', in J. M. Bernardo, et al. (editors) Bayesian Statistics 7, pp. 619-629: abstract, associated references, associated software.You can also get to the slides for my talk on ``Markov chain Monte Carlo computations for Dirichlet diffusion trees'', NTOC 2001, Kyoto, December 2001: postscript, pdf.Neal, R. M. (2001) ``Defining priors for distributions using Dirichlet diffusion trees'', Technical Report No. 0104, Dept. of Statistics, University of Toronto, 25 pages: abstract, postscript, pdf, associated software.
Many Markov chain methods are implemented in the software, some of which are described in the following papers:
Neal, R. M. (2020) ``Non-reversibly updating a uniform [0,1] value for Metropolis accept/reject decisions'', Technical Report, 14 pages: abstract, pdf.Neal, R. M. (2010) ``MCMC using Hamiltonian dynamics'', in the Handbook of Markov Chain Monte Carlo, S. Brooks, A. Gelman, G. L. Jones, and X.-L. Meng (editors), Chapman & Hall / CRC Press, pp. 113-162: abstract, postscript, pdf, associated software.
Neal, R. M. (2000) ``Slice sampling'', Technical Report No. 2005, Dept. of Statistics, University of Toronto, 40 pages: abstract, postscript, pdf, associated references, associated software.
Neal, R. M. (2002) ``Circularly-coupled Markov chain sampling'', Technical Report No. 9910 (revised), Dept. of Statistics, University of Toronto, 49 pages: abstract, postscript, pdf.
Neal, R. M. (1998) ``Annealed importance sampling'', Technical Report No. 9805 (revised), Dept. of Statistics, University of Toronto, 25 pages: abstract, associated references, postscript, pdf.
Neal, R. M. (1994) ``Sampling from multimodal distributions using tempered transitions'', Technical Report No. 9421, Dept. of Statistics, University of Toronto, 22 pages: abstract, associated references, postscript, pdf.
Neal, R. M. (1994) ``An improved acceptance procedure for the hybrid Monte Carlo algorithm'', Journal of Computational Physics, vol. 111, pp. 194-203: abstract.
Neal, R. M. (1993) Probabilistic Inference Using Markov Chain Monte Carlo Methods, Technical Report CRG-TR-93-1, Dept. of Computer Science, University of Toronto, 144 pages: abstract, contents, postscript, pdf.