Bayes

PT on an unidentifiable problem

Poorly approximated posterior distribution based on standard MCMC (in Blang, this is done by disabling parallel tempering, using the option --engine.nChains 1

ex.pt.UnidentifiableProduct
package ex.pt model UnidentifiableProduct { random RealVar x ?: latentReal random RealVar y ?: latentReal param IntVar nTrials ?: 100000 random IntVar nFails ?: nTrials/2 laws { x ~ ContinuousUniform(0.0, 1.0) y ~ ContinuousUniform(0.0, 1.0) nFails | nTrials, x, y ~ Binomial(nTrials, x * y) } }

Same model, but this time the posterior is approximated with parallel tempering (using 20 chains, specified via --engine.nChains 20)

ex.pt.UnidentifiableProduct
package ex.pt model UnidentifiableProduct { random RealVar x ?: latentReal random RealVar y ?: latentReal param IntVar nTrials ?: 100000 random IntVar nFails ?: nTrials/2 laws { x ~ ContinuousUniform(0.0, 1.0) y ~ ContinuousUniform(0.0, 1.0) nFails | nTrials, x, y ~ Binomial(nTrials, x * y) } }