SSS_log_phi_psi_Cauchy

Calculate log of densities phi and psi for data vector x, where
$$phi[i] = Normal(x[i], sigma^2)$$
$$psi[i]) = E_Cauchy(\theta)[Normal(x[i] - \theta, sigma^2)]$$

Contains fast functions to calculate the exact Bayes posterior
for the Sparse Normal Sequence Model, implementing the algorithms
described in Van Erven and Szabo (2021,
<doi:10.1214/20-BA1227>). For general hierarchical
priors, sample sizes up to 10,000 are feasible within half an hour
on a standard laptop. For beta-binomial spike-and-slab priors, a
faster algorithm is provided, which can handle sample sizes of
100,000 in half an hour. In the implementation, special care has
been taken to assure numerical stability of the methods even for
such large sample sizes.

Tim van Erven

SequenceSpikeSlab

Exact Bayesian Model Selection Methods for the Sparse Normal
Sequence Model

Steven de Rooij

Botond Szabo

SSS_log_phi_psi_Cauchy function

<dl><dt>x</dt>
<dd>data vector</dd>
<dt>sigma</dt>
<dd>standard deviation of observations</dd>
<dt>gamma</dt>
<dd>parameter of Cauchy slab density</dd></dl>

Arguments

Calculate log of phi and psi marginal densities for Cauchy(gamma) slab — SSS_log_phi_psi_Cauchy

<dl>

<dt>x</dt>
<dd>data vector</dd>


<dt>sigma</dt>
<dd>standard deviation of observations</dd>


<dt>gamma</dt>
<dd>parameter of Cauchy slab density</dd>

</dl>

SSS_log_phi_psi_Cauchy: Calculate log of phi and psi marginal densities for Cauchy(gamma) slab

Description

Usage

Value

Arguments