Number of rejected samples for the rejection algorithms.

<p>The average number of rejected samples per posterior <i>π</i>(<i>θ</i> ∣ <i>x</i>₊) out of <i>n</i> target distributions in the original Rejection algorithm (solid line) and when rejected values are recycled among the target distributions (points).</p

Acceptance rates of the original SVE and SVE with matching.

<p>The average proportion of accepted points when simultaneously sampling from <i>n</i> target distributions <i>π</i>(<i>θ</i> ∣ <i>x</i>₊) in the original SVE algorithm (solid line) and the proposal matching procedure (points).</p

Acceptance rates for the SVE algorithm with different bin sizes <i>a</i>.

<p>The average proportion of accepted points when proposals are generated until <i>t</i>(<i>x</i>*) falls in the range (<i>t</i>(<i>x</i>) − <i>a</i>, <i>t</i>(<i>x</i>) + <i>a</i>) using <i>a</i> ∈ {∞, 5, 3, 2}. The gray bars reflect both the range (left and right endpoints) and the proportion of accepted points (top).</p

Turning Simulation into Estimation: Generalized Exchange Algorithms for Exponential Family Models

<div><p>The Single Variable Exchange algorithm is based on a simple idea; any model that can be simulated can be estimated by producing draws from the posterior distribution. We build on this simple idea by framing the Exchange algorithm as a mixture of Metropolis transition kernels and propose strategies that automatically select the more efficient transition kernels. In this manner we achieve significant improvements in convergence rate and autocorrelation of the Markov chain without relying on more than being able to simulate from the model. Our focus will be on statistical models in the Exponential Family and use two simple models from educational measurement to illustrate the contribution.</p></div

A mixing distribution for the original SVE.

<p>The distribution of transition kernels, i.e., , for the original SVE algorithm in the Rasch model example with <i>k</i> = 20 items. In this example the average acceptance rate for sampling from the posterior <i>π</i>(<i>θ</i> ∣ <i>x</i>₊ = 9) was approximately 37% (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169787#pone.0169787.s001" target="_blank">S1 Script</a>).</p

Acceptance rates for the original SVE algorithm and SVE using as proposal.

<p>The average acceptance rate for sampling from posterior distributions <i>π</i>(<i>θ</i> ∣ <i>x</i>₊) when using the original SVE algorithm (left panel) and when using the proposal distribution (right panel).</p

Survey of violations (2).

<p>Survey of violations (2).</p

Two-process model probabilities conditional on the latent variables <i>θ</i>⁽¹⁾, <i>θ</i>⁽²⁾ and <i>θ</i>⁽³⁾.

<p>Two-process model probabilities conditional on the latent variables <i>θ</i>⁽¹⁾, <i>θ</i>⁽²⁾ and <i>θ</i>⁽³⁾.</p

Item pair contingency table for items 1 (100 × 3000) and 2 (80 × 2) constructed from 18744 response pairs.

<p>Item pair contingency table for items 1 (100 × 3000) and 2 (80 × 2) constructed from 18744 response pairs.</p

Manifest CIM probabilities.

<p>Manifest CIM probabilities.</p