infer_profiles_gibbs: Infer methylation profiles using Gibbs sampling
In BPRMeth: Model higher-order methylation profiles

Description Usage Arguments Value Details Author(s) See Also Examples

General purpose functions for inferring latent profiles for different observation models using Gibbs sampling. Currently implemented observation models are: 'bernoulli' and 'binomial' and the auxiliary variable approach is used.

infer_profiles_gibbs(
  X,
  model = NULL,
  basis = NULL,
  H = NULL,
  w = NULL,
  mu_0 = NULL,
  cov_0 = NULL,
  gibbs_nsim = 500,
  gibbs_burn_in = 100,
  store_gibbs_draws = FALSE,
  is_parallel = FALSE,
  no_cores = NULL,
  ...
)

`X`	The input data, either a `matrix` or a `list` of elements of length N, where each element is an `L X C` matrix, where L are the total number of observations. The first column contains the input observations x (i.e. CpG locations). If "binomial" model then C=3, and 2nd and 3rd columns contain total number of trials and number of successes respectively. If "bernoulli" then C=2 containing the output y (e.g. methylation level).
`model`	Observation model name as character string. It can be either 'bernoulli' or 'binomial'.
`basis`	A 'basis' object. E.g. see `create_basis`. If NULL, will an RBF object will be created.
`H`	Optional, design matrix of the input data X. If NULL, H will be computed inside the function.
`w`	A vector of initial parameters (i.e. coefficients of the basis functions). If NULL, it will be initialized inside the function.
`mu_0`	The prior mean hyperparameter vector for w.
`cov_0`	The prior covariance hyperparameter matrix for w.
`gibbs_nsim`	Total number of simulations for the Gibbs sampler.
`gibbs_burn_in`	Burn in period of the Gibbs sampler.
`store_gibbs_draws`	Logical indicating if we should keep the whole MCMC chain for further analysis.
`is_parallel`	Logical, indicating if code should be run in parallel.
`no_cores`	Number of cores to be used, default is max_no_cores - 1.
`...`	Additional parameters.

An object of class infer_profiles_gibbs_"obs_model" with the following elements:

W: An Nx(M+1) matrix with the posterior mean of the parameters w. Each row of the matrix corresponds to each element of the list X; if X is a matrix, then N = 1. The columns are of the same length as the parameter vector w (i.e. number of basis functions).
W_sd: An Nx(M+1) matrix with the posterior standard deviation (sd) of the parameters W.
basis: The basis object.
nll_feat: NLL fit feature.
rmse_feat: RMSE fit feature.
coverage_feat: CpG coverage feature.
W_draws: Optional, draws of the Gibbs sampler.

The modelling and mathematical details for inferring profiles using Gibbs sampling are explained here: http://rpubs.com/cakapourani/ . More specifically:

For Binomial observation model check: http://rpubs.com/cakapourani/bayesian-bpr-model
For Bernoulli observation model check: http://rpubs.com/cakapourani/bayesian-bpr-model

C.A.Kapourani C.A.Kapourani@ed.ac.uk

create_basis, infer_profiles_mle, infer_profiles_vb, create_region_object

# Example of inferring parameters for synthetic data using 3 RBFs
basis <- create_rbf_object(M=3)
out <- infer_profiles_gibbs(X = binomial_data, model = "binomial",
   basis = basis, is_parallel = FALSE, gibbs_nsim = 10, gibbs_burn_in = 5)

#-------------------------------------