# TransportMaps.Distributions.Inference.InferenceBase¶

## Module Contents¶

### Classes¶

 BayesPosteriorDistribution Given a log-likelihood and a prior, assemble the posterior density
class TransportMaps.Distributions.Inference.InferenceBase.BayesPosteriorDistribution(logL, prior)[source]

Bases: TransportMaps.Distributions.Distribution

Given a log-likelihood and a prior, assemble the posterior density

Given the log-likelihood $$\log\pi({\bf y}\vert{\bf x})$$ and the prior density $$\pi({\bf x})$$, assemble the Bayes’ posterior density

$\pi({\bf x}\vert {\bf y}) \propto \pi({\bf y}\vert{\bf x}) \pi({\bf x})$
Parameters:
• logL (LogLikelihood) – log-likelihood $$\log\pi({\bf y}\vert{\bf x})$$

• prior (Distribution) – prior density $$\pi({\bf x})$$

property observations[source]
get_ncalls_tree(indent='')[source]
get_nevals_tree(indent='')[source]
get_teval_tree(indent='')[source]
update_ncalls_tree(obj)[source]
update_nevals_tree(obj)[source]
update_teval_tree(obj)[source]
reset_counters()[source]
log_pdf(x, idxs_slice=slice(None, None, None), cache=None, **kwargs)[source]

Evaluate $$\log \pi({\bf x}\vert{\bf y})$$

Parameters:
• x (ndarray [$$m,d$$]) – evaluation points

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

• cache (dict) – cache

Returns:

(ndarray [$$m$$]) – values of $$\log\pi$$

at the x points.

grad_x_log_pdf(x, idxs_slice=slice(None, None, None), cache=None, **kwargs)[source]

Evaluate $$\nabla_{\bf x} \log \pi({\bf x}\vert{\bf y})$$

Parameters:
• x (ndarray [$$m,d$$]) – evaluation points

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

• cache (dict) – cache

Returns:

(ndarray [$$m,d$$]) – values of

$$\nabla_{\bf x}\log\pi$$ at the x points.

tuple_grad_x_log_pdf(x, idxs_slice=slice(None, None, None), cache=None, **kwargs)[source]

Evaluate $$\left(\log \pi({\bf x}\vert{\bf y}), \nabla_{\bf x} \log \pi({\bf x}\vert{\bf y})\right)$$

Parameters:
• x (ndarray [$$m,d$$]) – evaluation points

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

• cache (dict) – cache

Returns:

(tuple) –

$$\left(\log \pi({\bf x}\vert{\bf y}), \nabla_{\bf x} \log \pi({\bf x}\vert{\bf y})\right)$$

hess_x_log_pdf(x, idxs_slice=slice(None, None, None), cache=None, **kwargs)[source]

Evaluate $$\nabla^2_{\bf x} \log \pi({\bf x}\vert{\bf y})$$

Parameters:
• x (ndarray [$$m,d$$]) – evaluation points

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

• cache (dict) – cache

Returns:

(ndarray [$$m,d,d$$]) – values of

$$\nabla^2_{\bf x}\log\pi$$ at the x points.

action_hess_x_log_pdf(x, dx, idxs_slice=slice(None, None, None), cache=None, **kwargs)[source]

Evaluate $$\langle\nabla^2_{\bf x} \log \pi({\bf x}\vert{\bf y}), \delta{\bf x}\rangle$$

Parameters:
• x (ndarray [$$m,d$$]) – evaluation points

• dx (ndarray [$$m,d$$]) – direction on which to evaluate the Hessian

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

• cache (dict) – cache

Returns:

(ndarray [$$m,d$$]) – values of

$$\langle\nabla^2_{\bf x} \log \pi({\bf x}\vert{\bf y}), \delta{\bf x}\rangle$$ at the x points.