Reference / binference.priors.LogisticRandomWalk

binference.priors.LogisticRandomWalk

class binference.priors.LogisticRandomWalk(order=2, scale=None, mean=None, trend_scale=3.0)

Random-walk (intrinsic GMRF) smoothness prior on log-fractions over a grid.

The order-th differences of \(\eta = \log\rho\) (between adjacent bins along each axis) are Gaussian with standard deviation scale: order=1 penalises jumps, order=2 penalises curvature. N-D grids use the Kronecker-sum (ICAR-type) precision. Polynomial modes not penalised by the random walk (e.g. a linear trend for order=2) get a broad Gaussian prior set by trend_scale. On N-D grids these are the products of each axis’s unpenalised polynomials, so for order=2 in 2-D the surface \(xy\) is unpenalised too (and \(x^2y^2\) for order=3).

Smoothness is measured per bin step, so the natural scale of scale depends on the binning.

Parameters:

order{1, 2, 3}

Order of the differences.

scaleHyperprior or float

Standard deviation of the differences; inferred with a HalfNormal(1.0) prior by default.

meanarray_like (K,), optional

Mean of the log-fractions, e.g. log(reference) to shrink toward reference fractions. Defaults to a density flat in the measure coordinate, so differences penalise the log-density.

trend_scalefloat

Prior size of the unpenalised polynomial trends. It is the standard deviation of the root-mean-square size, across the grid, of each such mode (a linear trend of root-mean-square size t changes the log-density by about 3.5 t end to end), whatever the number of bins.

__init__(order=2, scale=None, mean=None, trend_scale=3.0)

Methods

__init__([order, scale, mean, trend_scale])
bind(bins)

Attributes

kind	"fractions" (a distribution on the simplex) or "rates"