Bayesian nonparametrics

Overview document describing various BNP models and samplers.

Overview document tex .tex file for document describing various BNP models and samplers.

Todo items for DP-related work:

• finish nonconjugate dCRP sampler
  • need MCMC configuration to recognize this case and assign sampler (Chris)
  • finalize sampler (Claudia)
  • allow zero intermediate nodes (Claudia / Chris)
  • what BUGS code could a user write that would make the sampler illegitimate (Claudia)
  • allow upper bound on number of components
  • only compute curLogProb for unique thetas
  • identify conjugacy for variance in a model with non-deterministic nodes (Claudia, could you check if this is working now?)
  • move code from dCRP sampler setup code to MCMC configuration (Chris)
  • discuss inefficiency of sampling all tilde variables even though most have no observations
• initial conjugate dCRP sampler (i.e., marginalized with respect to new component)
  • determine conjugacy in setup code, including for zero intermediate nodes (Chris)
  • determine conjugacy for normal-inverse gamma prior in normal model (wait for now)
  • use conjugacy determination to develop conjugate sampler run code for a few examples (Claudia). List of examples:
    • normal sampling with unknown normal mean and known variance: dCRP_conjugate_dnorm_dnorm
    • Poisson sampling with unknown gamma rate: dCRP_conjugate_dgamma_dpois
    • Bernoulli sampling with unknown Beta probability: dCRP_conjugate_dbeta_dbern
    • Multinomial sampling with unknown Dirichlet probability: dCRP_conjugate_ddirch_dmulti
    • exponential sampling with unknown gamma rate, known shape: dCRP_conjugate_dgamma_dexp
    • gamma sampling with unknown gamma rate, both shapes known: dCRP_conjugate_dgamma_dgamma
  • immediately sample new component parameters when create new component (Claudia)
  • try to reuse setup code and run code so we don't duplicate code (Chris)
  • ask Perry if using model[ something ][i] or model$values(something) makes a difference in efficiency
• stickbreaking approach
  • determine syntax for stickbreaking and write stickbreaking function (Claudia)
    • determine possible NaN situations
  • detect conjugacy in this setting (Chris)
  • clean up conjugacy for this setting (Chris)
• Generalized Dirichlet
  • write GenDirichlet distributions (Claudia)
  • add GenDirichlet conjugacy (Chris)
• CRP distribution
  • determine possible NaN situations (Claudia)
  • write help (Claudia)
• standardized output for G when using dCRP (input posterior modelValues and augment with columns for weights and atoms). Not in total generality yet. (Claudia / Nick / Chris)
  • figure out how a user will call this (current rough plan is to have an R function that user calls with that R function using a stand-alone nimbleFunction that sets number of columns in a matrix (not a modelValues)) (Chris / Claudia / Abel / other nimble-devs)
• write help for BNP sampler with some examples.
• write a quasi conjugate sampler for the "conc" parameter when a gamma distribution is assumed
  • write the sampler (Claudia)
  • write help with some examples (Claudia)
  • automatically assign this sampler (Claudia / Chris)
• fully marginalized dCRP sampler for conjugate models
  • write sampler
  • write help
  • add sampling for tilde variables only every 'thin' iterations if monitoring for them requested
  • determine conjugacy for normal-inverse gamma prior in normal model