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estimation.reparam

estimation.reparam

Constrained/unconstrained parameter transforms.

The filter propagates a Gaussian belief. Metabolic parameters are not Gaussian quantities: time constants and gains are strictly positive, the adaptation gain lies in \([0, 1)\), and a Gaussian placed on any of them puts mass on impossible values. Worse, a sigma point drawn from such a belief can be an impossible value, and a negative time constant does not merely give a poor estimate – it makes the dynamics explode.

The fix is to filter in an unconstrained coordinate \(\eta\) and map to the natural parameter only inside the dynamics. Every transform here is centered so that \(\eta = 0\) recovers the prior and scaled so that \(\eta \sim N(0, 1)\) spans a physiologically plausible range. The prior is therefore exactly the standard normal, and the initial parameter covariance is the identity – which is not a coincidence but the point of choosing the scales this way.

Classes

Name Description
ParamTransform The full set of per-parameter transforms, in PARAM_NAMES order.
Transform One parameter’s map from unconstrained eta to natural units.

ParamTransform

estimation.reparam.ParamTransform(rmr_intercept_prior, rmr_slope_prior)

The full set of per-parameter transforms, in PARAM_NAMES order.

Built from the subject’s expenditure prior so that the two metabolic-rate coefficients are centered on Mifflin-St Jeor scaled by activity level, rather than on an arbitrary constant.

Methods

Name Description
constrain Unconstrained vector to natural-unit Params.
prior_cov The prior covariance, the identity by construction.
prior_eta The prior mean, which is the origin by construction.
unconstrain Natural-unit Params back to the unconstrained vector.
constrain
estimation.reparam.ParamTransform.constrain(eta)

Unconstrained vector to natural-unit Params.

prior_cov
estimation.reparam.ParamTransform.prior_cov(scale=1.0)

The prior covariance, the identity by construction.

scale above 1 widens the prior uniformly, which is the honest thing to do if you suspect your logging is unusual in some way the literature priors do not anticipate.

prior_eta
estimation.reparam.ParamTransform.prior_eta()

The prior mean, which is the origin by construction.

unconstrain
estimation.reparam.ParamTransform.unconstrain(p)

Natural-unit Params back to the unconstrained vector.

Transform

estimation.reparam.Transform(kind, center, scale)

One parameter’s map from unconstrained eta to natural units.

kind is one of:

"log" theta = center * exp(scale * eta). Strictly positive; scale is the standard deviation in log units, so 0.25 means roughly +-25 %. "logit" theta = sigmoid(logit(center) + scale * eta). Confined to (0, 1). "affine" theta = center + scale * eta. Unbounded, for parameters whose sign is genuinely unknown.