Define a set of Li and Stephens parameters

Specify a parameter set to be used for a particular Li and Stephens hidden Markov model run.

Usage

Parameters(
  rho = rep(0, get("L", envir = pkgVars) - 1),
  mu = 1e-08,
  Pi = NULL,
  use.speidel = FALSE,
  check.rho = TRUE
)

Arguments

rho: recombination probability vector (must be \(L-1\) long). See CalcRho() for assistance constructing this from a recombination map/distances.
mu: a scalar (for uniform) or vector (for varying) mutation probabilities.
Pi: leaving the default of uniform copying probabilities is recommended for computational efficiency. If desired, a full matrix of background copying probabilities can be provided, such that the [j,i]-th element is the background probability that i copies from j. Hence, (a) the diagonal must be zero; and (b) the columns of Pi must sum to 1. Note: each column corresponds to an independent Li and Stephens hidden Markov model.
use.speidel: a logical, if TRUE, use the asymmetric mutation model used by RELATE (Speidel et al., 2019). WARNING: this model assumes that the cached haplotypes have an ancestral/derived encoding -- zeros denote ancestral variant carriers and ones denote derived variant carriers. Defaults to FALSE.
check.rho: if TRUE, a check that rho is within machine precision will be performed. If you have created rho using CalcRho() with floor = TRUE then this will be satisfied automatically. This can be important to ensure that the convex combination rho and (1-rho) normalises to 1 within machine precision, but an advanced user may wish to override this requirement.

Value

A kalisParameters object, suitable for use to create the standard forward and backward recursion tables with MakeForwardTable() and MakeBackwardTable(). Note you will also need to provide this parameters object when propagating those tables using either Forward() or Backward().

Details

There are 3 parameters which must be specified before the forward or backward equations in the Li and Stephens hidden Markov model can be run. These are the vector of recombination probabilities, the mutation probabilities, and the prior copying probabilities.

NOTE: the corresponding haplotype data must have already been inserted into the kalis cache by a call to CacheHaplotypes(), since this function performs checks to confirm the dimensionality matches.

Recombination probabilities, rho

This is a vector parameter which must have length \(L-1\), where \(L\) is the number of variants that have been loaded into the kalis memory cache (using CacheHaplotypes()). Note that element i of this vector should be the recombination probability between variants i and i+1.

There is a utility function, CalcRho(), to assist with creating these recombination probabilities from a recombination map.

By default, the recombination probabilities are set to zero everywhere.

Mutation probabilities, mu

The mutation probabilities may be specified either as uniform across all variants (by providing a single scalar value), or may be varying at each variant (by providing a vector of length equal to the number of variants, \(L\), which have been loaded into the kalis memory cache).

By default, mutation probabilities are set to \(10^{-8}\).

Copying probabilities, Pi

The original Li and Stephens model assumed that each haplotype has an equal prior probability of copying from any other. However, in the spirit of ChromoPainter (Lawson et al., 2012) we allow a matrix of prior copying probabilities.

The copying probabilities may be specified as a standard R matrix of size \(N \times N\) (where \(N\) is the number of haplotypes which have been loaded into the kalis memory cache). The element at row j, column i corresponds to the prior (background) probability that haplotype i copies from haplotype j. Note that the diagonal must by definition be zero and columns must sum to one. Alternatively, for uniform copying probabilities, this argument need not be specified (resulting in copying probability \(\frac{1}{N-1}\) everywhere).

Note that there is a computational cost associated with non-uniform copying probabilities, so it is recommended to leave the default of uniform probabilities when appropriate (Note: do not specify a uniform matrix when uniform probabilities are intended, since this would end up incurring the computational cost of non-uniform probabilities).

References

Lawson, D. J., Hellenthal, G., Myers, S., & Falush, D. (2012). Inference of population structure using dense haplotype data. PLoS genetics, 8(1).

Speidel, L., Forest, M., Shi, S., & Myers, S. (2019). A method for genome-wide genealogy estimation for thousands of samples. Nature Genetics, 51(1321–1329).

Examples

# Load the mini example data and recombination map from the package built-in #' # dataset
data("SmallHaps")
data("SmallMap")

# Load haplotypes into cache
CacheHaplotypes(SmallHaps)
#> Warning: haplotypes already cached ... overwriting existing cache.

# To use all the defaults
pars <- Parameters()
pars
#> Parameters object with:
#>   rho   = (0, 0, 0, ..., 0, 0, 1)
#>   mu    = 1e-08
#>   Pi    = 0.00334448160535117 

# Or perhaps use SmallMap to compute the recombination probabilities, leaving
# s and gamma as default
rho <- CalcRho(diff(SmallMap))
pars <- Parameters(rho)
pars
#> Parameters object with:
#>   rho   = (0.030722976221863, 0.00188322071638501, 6.79809190046651e-06, ..., 1.56898508137998e-05, 1.7924679243824e-05, 1)
#>   mu    = 1e-08
#>   Pi    = 0.00334448160535117 

# Then use these parameters to create a table (eg for forward) ...
fwd <- MakeForwardTable(pars)
# ... and to propagate it
Forward(fwd, pars, 10)
fwd
#> Full Forward Table object for 300 haplotypes. 
#>   Current variant = 10 
#>   Memory consumed: 723.98 kB