Package index • tulpa

Front door

The main fitter, its formula surface, and the mode / family helpers.

tulpa(): Fit a tulpa model
tulpa_parse_formula() print(<tulpa_parsed_formula>): Parse a mixed-model formula
findbars(): Find all bar terms in a formula's parse tree
nobars(): Remove all bar terms from a formula's parse tree
inference_mode_info(): Print inference mode information
validate_mode(): Validate that a fit used the expected mode
tulpa_family() print(<tulpa_family>): Construct a minimal tulpa_family for simulation
tulpa_gaussian(): Fit a Gaussian linear model via tulpa's generic engine
tulpa_build_model_data(): Build model matrices from a parsed formula
tulpa_simulate() print(<tulpa_simulate>): Simulate data from a tulpa model

Tier 2 – structured approximations

Laplace, nested Laplace, and the free-Sigma random-effect backends.

tulpa_laplace(): Fit a model via Laplace approximation
tulpa_laplace_beta(): Fit a beta-regression model via Laplace, estimating the precision
print(<tulpa_nested_laplace>) tulpa_nested_laplace(): Nested Laplace approximation for latent Gaussian models
print(<tulpa_nested_laplace_joint>) print(<tulpa_nested_laplace_joint_multi>) tulpa_nested_laplace_joint(): Joint multi-likelihood nested Laplace approximation
fit_st_nested() print(<tulpa_st_nested>): Fit an additive spatiotemporal GLM by nested Laplace
tulpa_hyper_grid(): Outer hyperparameter-grid integration with a user-supplied inner fit
tulpa_re_cov_nested(): Nested-Laplace integration over random-effect covariances
tulpa_re_aghq(): Adaptive Gauss-Hermite refinement of a grouped random-effect covariance
tulpa_eb(): Empirical-Bayes random-effect covariances
tulpa_em_laplace(): Fit a latent-variable model via EM + Laplace approximation
tulpa_em_mc(): Generic Monte-Carlo EM driver
agq_fit(): Adaptive Gauss-Hermite quadrature for one-RE GLMMs
fit_spde(): Fit a spatial model using SPDE Laplace approximation
tulpa_ep(): Expectation-Propagation fit for a GLM
tulpa_multinomial() print(<tulpa_multinomial>): Multinomial (nominal K-class) logistic regression via Laplace
tulpa_ordinal() coef(<tulpa_ordinal>) print(<tulpa_ordinal>): Ordinal (ordered K-class) cumulative-logit regression via Laplace
imh_laplace(): Independence Metropolis-Hastings with Laplace proposal

Tier 1 – exact MCMC and debias

tulpa_gibbs(): Fit via Polya-Gamma Gibbs sampler
tulpa_re_cov_gibbs(): Gibbs estimation of random-effect covariances (exact-target debias)
tulpa_nuts_beta(): Fit a beta-regression model via NUTS (joint sampling of beta + log_phi)
tulpa_nuts_spde(): Sample an SPDE GLM via NUTS, optionally jointly over Matern hypers
tulpa_tgmrf(): Fit a custom tgmrf latent block
tgmrf() print(<tgmrf>) summary(<tgmrf>): User-defined GMRF latent block
tgmrf_cpp(): User-defined GMRF latent block, compiled C++ backend
tulpa_cache_dir(): Default cache directory for tgmrf_cpp()-compiled DLLs
tulpa_cache_clear(): Remove compiled blocks from the tgmrf_cpp() cache
mala(): Metropolis-adjusted Langevin algorithm (MALA)
tulpa_integrator(): Select the symplectic integrator for HMC and NUTS
with_tulpa_integrator(): Run an expression under a chosen symplectic integrator

Other approximations

pathfinder(): Pathfinder: variational warm-start via L-BFGS + ELBO scoring
bridge_sampling(): Bridge sampling for marginal likelihood

Latent structure

Spatial, temporal, and varying-coefficient constructors.

spatial() print(<tulpa_spatial_field_fit>) print(<tulpa_spatial_field>): Areal spatially varying coefficient field
spatial_car(): CAR / ICAR spatial structure
spatial_car_proper(): Proper CAR spatial structure
spatial_bym2(): BYM2 spatial structure
spatial_gp() print(<tulpa_gp>) print(<tulpa_hsgp>): Gaussian process spatial structure (NNGP)
spatial_multiscale() print(<tulpa_multiscale>): Multi-scale Gaussian process spatial structure
spatial_svc() print(<tulpa_svc>): Spatially varying coefficient structure
spatial_rsr() print(<tulpa_rsr>): Restricted spatial regression (RSR)
spatial_spde(): SPDE spatial field (Matern via triangular mesh)
spatial_spde_custom(): SPDE spatial field from custom matrices
temporal_rw1(): RW1 temporal structure (first-order random walk)
temporal_rw2(): RW2 temporal structure (second-order random walk)
temporal_ar1(): AR1 temporal structure (first-order autoregressive)
temporal_ar2(): AR(2) temporal latent field (second-order autoregressive)
temporal_ar() print(<tulpa_temporal_latent_block>): AR(p) temporal latent field (general-order autoregressive)
temporal_gp() print(<tulpa_temporal_gp>): Gaussian process temporal structure
temporal_multiscale() print(<tulpa_temporal_multiscale>): Multi-scale temporal structure
temporal_tvc() print(<tulpa_tvc>): Time-varying coefficient structure
temporal_rtr(): Restricted temporal regression (RTR)
spatiotemporal(): Spatiotemporal interaction specifications for tulpa
spatiotemporal_gp(): Non-separable spatiotemporal GP
svc() summary(<tulpa_svc_posterior>) print(<tulpa_svc_posterior>) print(<tulpa_svc_summary>): Extract spatially-varying coefficients from a fitted model
tvc() print(<tulpa_tvc_posterior>) print(<tulpa_tvc_summary>) summary(<tulpa_tvc_posterior>): Extract temporally-varying coefficients from a fitted model
latent(): Mark an expression as a latent block in a tulpa formula
latent_factor() print(<tulpa_latent>): Create a latent factor specification
adjacency() print(<tulpa_adjacency>): Construct a spatial adjacency graph for areal models
check_adjacency() print(<tulpa_adjacency_check>): Validate a spatial adjacency matrix
node_index(): Map cell identifiers to graph node indices
compute_nngp_neighbors(): Compute nearest neighbors for NNGP
tulpa_bar_field_specs(): Expand a varying-coefficient bar into per-column field specs
tulpa_bar_field_replicate(): Replicate an areal graph across the levels of a factor (replicated CAR)
tulpa_is_spatial_bar(): Recognize an inline varying-coefficient bar

Priors

The prior surface and the individual prior builders.

tulpa_priors() print(<tulpa_priors>) print(<tulpa_prior>) format(<tulpa_prior_normal>) format(<tulpa_prior_half_normal>) format(<tulpa_prior_half_cauchy>) format(<tulpa_prior_gamma>) format(<tulpa_prior_exponential>) format(<tulpa_prior_beta>) format(<tulpa_prior_pc>) format(<tulpa_prior>): Prior specification for tulpa models
priors_default(): Show default priors for a tulpa family
prior_from_spec(): Build a prior list for tulpa_nested_laplace() from a tulpa spec object
prior_normal(): Normal prior
prior_beta(): Beta prior
prior_gamma(): Gamma prior
prior_exponential(): Exponential prior
prior_half_cauchy(): Half-Cauchy prior
prior_half_normal(): Half-normal prior
prior_pc(): Penalized complexity (PC) prior
re_cov_pc_lkj_prior(): PC + LKJ hyperprior for a random-effect covariance

Methods, criteria, and prediction

tulpa_criteria() print(<tulpa_criteria>): Model criteria from a pointwise log-likelihood
pointwise_loglik() dic() cpo() waic(<tulpa_fit>) loo(<tulpa_fit>): DIC, CPO, WAIC and PSIS-LOO on a fit
wbic() print(<tulpa_wbic>): Widely applicable Bayesian information criterion (WBIC)
tulpa_kfold(): K-fold cross-validation for a tulpa fit
tulpa_reloo(): Selective refit of high-Pareto-k observations (reloo)
tulpa_psis(): Pareto-smoothed importance sampling
tulpa_loglik(): Streaming pointwise log-likelihood
bayes_R2(): Bayesian R-squared
tulpa_powerscale_sensitivity(): Power-scaling prior / likelihood sensitivity
compare_models(): Compare models by information criteria
model_average(): Model-averaged predictions
posterior_predict(): Posterior predictive replicates
pp_check(): Posterior predictive check
prior_predict() print(<tulpa_prior_predict>): Prior predictive simulation
reexports tidy glance: Objects exported from other packages

Reading a fit

Accessors for a fitted model: the coefficient surface, the posterior draws in whatever representation the backend produced, and the extracted latent effects.

print(<tulpa_fit>) summary(<tulpa_fit>) coef(<summary.tulpa_fit>) print(<summary.tulpa_fit>): Summarize and print a tulpa fit
tulpa_fit_summary(): Build the summary of a tulpa fit around a coefficient table
fixef(): Fixed-effect coefficients (lme4-compatible)
ranef(): Random-effect summaries
VarCorr(): Random-effect variances and correlations
posterior_sample(): Posterior parameter sample from a fit
mcmc_draws(): MCMC chain draws from a fit
tulpa_posterior_draws(): Posterior draws from a nested-Laplace fit
tulpa_outer_grid(): The outer hyperparameter grid of a nested-Laplace fit
tulpa_draws_array(): Posterior draws as a 3D array
as_draws() as_draws_array() as_draws_matrix() as_draws_df() as_draws_rvars(): Posterior draws in the posterior package's format
print(<tulpa_temporal_field_fit>) print(<tulpa_temporal_field>) temporal() print(<tulpa_temporal_posterior>) summary(<tulpa_temporal_posterior>) print(<tulpa_temporal_summary>): Extract temporal effects from a fitted model
spatiotemporal_effects() print(<tulpa_st_summary>): Extract spatiotemporal effects from fitted model
smooth_effects(): Extract fitted covariate smooths
field_effects(): Spatial field effects per unit
latent_factors(): Extract latent factor posteriors from fit

Diagnostics

Convergence for sampled fits, approximation reliability for deterministic ones, and the residual / goodness-of-fit surface both share.

diagnostics() print(<laplace_diagnostics>): Posterior diagnostics for a fitted model
check_diagnostics(): Quick convergence check
diagnostic_summary() print(<tulpa_diagnostic_summary>): Comprehensive diagnostic summary
energy_bfmi(): Energy Bayesian Fraction of Missing Information (E-BFMI)
select_main_params(): Select the "main" model parameters for diagnostic display
n_divergent(): Number of divergent transitions
geweke_test() print(<tulpa_geweke>): Geweke convergence test
moran_i(): Moran's I test for spatial autocorrelation in residuals
durbin_watson(): Durbin-Watson test for temporal autocorrelation
tulpa_variogram() plot(<tulpa_variogram>) print(<tulpa_variogram>): Empirical semivariogram of residuals
pit_residuals(): PIT (probability integral transform) residuals
tulpa_pit(): Probability integral transform from a predictive CDF
test_uniformity(): Test uniformity of PIT residuals
test_dispersion(): Test for over- or underdispersion
test_outliers(): Test for outliers (simulation envelope)
test_zero_inflation(): Test for zero inflation
check_model(): Diagnostic panel plot
spatial_range(): Extract spatial range and variance from a fitted spatial model
temporal_corr(): Extract temporal correlation parameters from a fitted model
post_hoc_lm() print(<post_hoc_lm>): Fit a post-hoc linear model on estimated parameters

Calibration

Simulation-based calibration. Where the diagnostics above score one fit, these score whether an inference algorithm’s posteriors are calibrated across the generative model, by reading the whole marginal CDF.

sbc() print(<sbc>) summary(<sbc>) print(<sbc_summary>) plot(<sbc>): Simulation-based calibration
sbc_mixture() sbc_normal() sbc_discrete() sbc_rank() sbc_draws(): Predictive shapes an SBC fitter reports

Plots

plot_rhat(): Plot Rhat convergence diagnostic
plot_ess(): Plot effective sample size diagnostic
plot_acf(): Plot autocorrelation functions
plot_energy(): Plot energy diagnostic (E-BFMI)
plot_divergences(): Plot divergent transitions
plot_pairs(): Plot bivariate parameter posteriors (pairs plot)
plot_diagnostics(): Diagnostic plotting functions for tulpa models
plot_map(): Plot spatial predictions as a map
plot_map_panel(): Plot multiple maps in a grid

Outer-grid integration and utilities

The node designs the outer hyperparameter integration is laid on, the axis-provenance surface, and the small numerical helpers.

ccd_grid(): Central composite design (CCD) grid for nested-Laplace integration
ccd_weights(): Corrected R-INLA CCD integration weights
ccd_to_theta(): Map standardised CCD coordinates to physical hyperparameters
hyper_axis_spec() print(<tulpa_hyper_axis_spec>): Describe one outer-grid hyperparameter axis
auto_grid(): Mark an outer-grid setting as a default rather than a pin
is_auto_grid(): Is an outer-grid setting marked as a default?
rubins_pool(): Pool multiple imputation draws via Rubin's rules
sn_cdf(): Skew-normal CDF
sn_quantile(): Skew-normal quantile
sn_match(): Match three cumulants to a skew-normal parameterisation
tulpa_profile(): Profile a fit by solver phase
tulpa_check_control(): Validate a control = list() surface against its canonical key set