Checking an inference result.
Markov chains: kernel-infer keeps each chain's draws together (the
measure's :chain-lengths), so the draws of a quantity split back into
chains (chains) and the convergence diagnostics of Vehtari, Gelman,
Simpson, Carpenter & Bürkner (2021) apply — rank-normalized split R-hat,
bulk and tail effective sample sizes, and the Monte Carlo standard error of
the mean, computed as Stan and ArviZ compute them:
(diagnostics/summary measure :mu) ;; => {:mean … :sd … :quantiles … :rhat 1.002 :ess-bulk 1830.0 ;; :ess-tail 1590.0 :mcse 0.004 :chains 4 :draws 4000}
An R-hat above 1.01 or an effective sample size below about 100 per chain says the chains have not mixed: run longer or change the kernel.
Particle methods: weights carry the information, so summary reports the
weighted moments with the weight-based ESS; after resampling that counts
particles, not distinct histories — distinct-count of an early site
says how many histories survive.
Model comparison: pointwise-log-likelihood gives each draw's log density
of each observation, the input of PSIS-LOO and WAIC; particle methods also
estimate the evidence (measure/log-marginal).
Checking an inference result.
Markov chains: `kernel-infer` keeps each chain's draws together (the
measure's `:chain-lengths`), so the draws of a quantity split back into
chains (`chains`) and the convergence diagnostics of Vehtari, Gelman,
Simpson, Carpenter & Bürkner (2021) apply — rank-normalized split R-hat,
bulk and tail effective sample sizes, and the Monte Carlo standard error of
the mean, computed as Stan and ArviZ compute them:
(diagnostics/summary measure :mu)
;; => {:mean … :sd … :quantiles … :rhat 1.002 :ess-bulk 1830.0
;; :ess-tail 1590.0 :mcse 0.004 :chains 4 :draws 4000}
An R-hat above 1.01 or an effective sample size below about 100 per chain
says the chains have not mixed: run longer or change the kernel.
Particle methods: weights carry the information, so `summary` reports the
weighted moments with the weight-based ESS; after resampling that counts
particles, not distinct histories — `distinct-count` of an early site
says how many histories survive.
Model comparison: `pointwise-log-likelihood` gives each draw's log density
of each observation, the input of PSIS-LOO and WAIC; particle methods also
estimate the evidence (`measure/log-marginal`).(chains measure f)The draws of f in measure, one vector per Markov chain, in draw order.
f is a function of the program's value, a keyword (a field of a map value,
else a site address) or a vector (a site address). A measure without chain
structure (particle methods) is one chain.
The draws of `f` in `measure`, one vector per Markov chain, in draw order. `f` is a function of the program's value, a keyword (a field of a map value, else a site address) or a vector (a site address). A measure without chain structure (particle methods) is one chain.
(distinct-count measure f)How many distinct values f (see chains) takes over the particles of
measure: for an early site after resampling, the number of histories
that survive.
How many distinct values `f` (see `chains`) takes over the particles of `measure`: for an early site after resampling, the number of histories that survive.
(ess-bulk cs)The bulk effective sample size of cs (draws by chain): of the
rank-normalized split chains.
The bulk effective sample size of `cs` (draws by chain): of the rank-normalized split chains.
(ess-tail cs)The tail effective sample size of cs: the smaller of the effective sample
sizes of the indicators of the 5% and the 95% quantile.
The tail effective sample size of `cs`: the smaller of the effective sample sizes of the indicators of the 5% and the 95% quantile.
(mcse cs)Monte Carlo standard error of the mean of cs: the sd of all draws over
√ESS, the ESS of the split chains themselves.
Monte Carlo standard error of the mean of `cs`: the sd of all draws over √ESS, the ESS of the split chains themselves.
(pointwise-log-likelihood measure)Each draw's log density of each observation: a vector, one map
{address log-p} per particle of measure, in particle order — the input of
PSIS-LOO and WAIC (with every draw equally weighted, as Markov chains give;
resample a weighted measure first).
Each draw's log density of each observation: a vector, one map
{address log-p} per particle of `measure`, in particle order — the input of
PSIS-LOO and WAIC (with every draw equally weighted, as Markov chains give;
resample a weighted measure first).(rhat cs)Rank-normalized split R-hat of cs (draws by chain): the larger of the
bulk and the folded (tail) statistic. Near 1 when the chains agree; above
1.01 they have not mixed.
Rank-normalized split R-hat of `cs` (draws by chain): the larger of the bulk and the folded (tail) statistic. Near 1 when the chains agree; above 1.01 they have not mixed.
(summary measure f)Summary of the quantity f (see chains) in measure: weighted mean, sd
and quantiles, and — for Markov chains — :rhat, :ess-bulk, :ess-tail
and :mcse; for weighted particles :ess, the weight-based effective
sample size.
Summary of the quantity `f` (see `chains`) in `measure`: weighted mean, sd and quantiles, and — for Markov chains — `:rhat`, `:ess-bulk`, `:ess-tail` and `:mcse`; for weighted particles `:ess`, the weight-based effective sample size.
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