Bayesian inference
stat bayes_proportionstat bayes_proportionstat bayes_meanstat bayes_meanstat bayes_ratestat bayes_ratestat bayes_glmstat bayes_glmstat bayes_abstat bayes_abstat bayes_factor_tstat bayes_factor_tstat bayes_hierarchicalstat bayes_hierarchicalstat waic
stat bayes_proportion <successes> <trials>
Description
Posterior of a proportion: k successes in n trials, uniform prior Beta(1, 1); mean, median, mode, sd, 95 % equal-tailed and HPD credible intervals
Posterior of a proportion: k successes in n trials, uniform prior Beta(1, 1); mean, median, mode, sd, 95 % equal-tailed and HPD credible intervals
Parameters
successes: The number of successes - Number - required
trials: The number of trials - Number - required
successes: The number of successes - Number - required
trials: The number of trials - Number - required
admin
stat bayes_proportion 6 20
mentdb
{"mean": 0.3181818181818182, "median": 0.31258409378594726, "sd": 0.09711986067435269, "lower": 0.14587694241093563, "upper": 0.5217511184193268, "hpd_lower": 0.1360694854964026, "hpd_upper": 0.5092998708702657, "mode": 0.3, "posterior": "Beta(7, 15)"}
stat bayes_proportion <successes> <trials> <json_params>
Description
Posterior of a proportion with parameters: prior [a, b] (Beta), level, threshold (probability that the proportion is above)
Posterior of a proportion with parameters: prior [a, b] (Beta), level, threshold (probability that the proportion is above)
Parameters
successes: The successes - Number - required
trials: The trials - Number - required
json_params: The parameters - String - required
successes: The successes - Number - required
trials: The trials - Number - required
json_params: The parameters - String - required
admin
stat bayes_proportion 6 20 "{\"prior\": [3, 12], \"threshold\": 0.25}"
mentdb
{"mean": 0.2571428571428571, "median": 0.2524754150024638, "sd": 0.07284313590846836, "lower": 0.12881739158350813, "upper": 0.41170784190726256, "hpd_lower": 0.12078167085665453, "hpd_upper": 0.4012533617137752, "threshold": 0.25, "probability_above": 0.5133938489032139, "mode": 0.24242424242424243, "posterior": "Beta(9, 26)"}
stat bayes_mean <json_values>
Description
Posterior of the mean (and of the standard deviation) of a normal sample with the Jeffreys prior: credible interval of the mean (Student) and of the sd
Posterior of the mean (and of the standard deviation) of a normal sample with the Jeffreys prior: credible interval of the mean (Student) and of the sd
Parameters
json_values: The values - String - required
json_values: The values - String - required
admin
stat bayes_mean "[5.1, 4.9, 5.6, 5.8, 4.7, 5.2, 5.0, 4.8, 5.5, 5.3]"
mentdb
{"n": 10, "mean": 5.19, "lower": 4.932184647704472, "upper": 5.447815352295529, "sd": 0.3604010112206802, "sd_lower": 0.24789650406552582, "sd_upper": 0.657951755876196, "prior": "Jeffreys (flat on mu and log sigma)"}
stat bayes_mean <json_values> <json_params>
Description
Posterior of the mean with parameters: level, threshold
Posterior of the mean with parameters: level, threshold
Parameters
json_values: The values - String - required
json_params: The parameters - String - required
json_values: The values - String - required
json_params: The parameters - String - required
admin
stat bayes_mean "[5.1, 4.9, 5.6, 5.8, 4.7, 5.2, 5.0, 4.8, 5.5, 5.3]" "{\"threshold\": 5}"
mentdb
{"n": 10, "mean": 5.19, "lower": 4.932184647704472, "upper": 5.447815352295529, "threshold": 5, "probability_above": 0.935080671221126, "sd": 0.3604010112206802, "sd_lower": 0.24789650406552582, "sd_upper": 0.657951755876196, "prior": "Jeffreys (flat on mu and log sigma)"}
stat bayes_rate <events> <exposure>
Description
Posterior of a rate of events (Poisson): k events during an exposure (person-years, hours, km2...), Jeffreys prior Gamma(0.5, 0)
Posterior of a rate of events (Poisson): k events during an exposure (person-years, hours, km2...), Jeffreys prior Gamma(0.5, 0)
Parameters
events: The number of events - Number - required
exposure: The exposure - Number - required
events: The number of events - Number - required
exposure: The exposure - Number - required
admin
stat bayes_rate 12 1000
mentdb
{"mean": 0.0125, "median": 0.012168293825914783, "sd": 0.0035355339059327377, "lower": 0.00655986001238268, "upper": 0.02032323455767159, "hpd_lower": 0.006036528281824641, "hpd_upper": 0.019551724246317053, "posterior": "Gamma(12.5, 1000)"}
stat bayes_rate <events> <exposure> <json_params>
Description
Posterior of a rate with parameters: prior [shape, rate] (Gamma), level, threshold
Posterior of a rate with parameters: prior [shape, rate] (Gamma), level, threshold
Parameters
events: The events - Number - required
exposure: The exposure - Number - required
json_params: The parameters - String - required
events: The events - Number - required
exposure: The exposure - Number - required
json_params: The parameters - String - required
admin
stat bayes_rate 12 1000 "{\"threshold\": 0.01}"
mentdb
{"mean": 0.0125, "median": 0.012168293825914783, "sd": 0.0035355339059327377, "lower": 0.00655986001238268, "upper": 0.02032323455767159, "hpd_lower": 0.006036528281824641, "hpd_upper": 0.019551724246317053, "threshold": 0.01, "probability_above": 0.7468253060165375, "posterior": "Gamma(12.5, 1000)"}
stat bayes_glm <json_X> <json_y> <family>
Description
Bayesian regression (gaussian, binomial logit or poisson log) with weakly informative priors as rstanarm (normal(0, 2.5) on the standardized slopes), sampled by MCMC (4 chains): posterior mean, sd, median, credible interval, probability that each slope is positive, odds or rate ratio, R-hat and effective sample size
Bayesian regression (gaussian, binomial logit or poisson log) with weakly informative priors as rstanarm (normal(0, 2.5) on the standardized slopes), sampled by MCMC (4 chains): posterior mean, sd, median, credible interval, probability that each slope is positive, odds or rate ratio, R-hat and effective sample size
Parameters
json_X: The rows - String - required
json_y: The response - String - required
family: gaussian, binomial or poisson - String - required
json_X: The rows - String - required
json_y: The response - String - required
family: gaussian, binomial or poisson - String - required
admin
stat bayes_glm "[[4.7, 1], [1.3, 1], [3.1, 0], [2.1, 0], [2.8, 0], [4.9, 1], [3.1, 1], [1.2, 0], [3.6, 0], [2.5, 1], [2.1, 1], [4.3, 0], [3.4, 1], [1.7, 0], [3.7, 0], [1.3, 1], [2.1, 1], [2.3, 1], [3.2, 1], [2.0, 0], [1.5, 1], [3.2, 0], [1.7, 0], [2.7, 0], [1.9, 0], [4.2, 0], [5.0, 0], [4.9, 1], [1.1, 1], [1.8, 1], [1.9, 0], [3.6, 0], [2.7, 0], [2.4, 1], [4.6, 1], [4.8, 0], [2.7, 1], [3.2, 0], [1.4, 0], [3.2, 1]]" "[0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]" "binomial"
mentdb
{"family": "binomial", "n": 40, "coefficients": [{"term": "intercept", "mean": -3.045166362725433, "sd": 1.1791487125183955, "median": -2.988651465718638, "lower": -5.535189435561421, "upper": -0.9458920472901409, "rhat": 1.0075302168601545, "ess": 517.2406103017813}, {"term": "x0", "mean": 0.8428936132187604, "sd": 0.34510426764293634, "median": 0.828086471828713, "lower": 0.1982691074539022, "upper": 1.5377106612585467, "rhat": 1.0090988175200408, "ess": 585.2139485716135, "probability_positive": 0.996375, "odds_ratio": 2.2889346061687377}, {"term": "x1", "mean": 0.5741179117965046, "sd": 0.744006928977658, "median": 0.5680778212421411, "lower": -0.8327435271732218, "upper": 2.0889487033571412, "rhat": 1.0031567047495498, "ess": 589.8413129098493, "probability_positive": 0.77725, "odds_ratio": 1.7648713906482785}], "acceptance": 0.258125, "chains": 4, "draws": 8000, "converged": true, "priors": "normal(0, 2.5) on the standardized slopes, normal(0, 10) on the intercept"}
stat bayes_glm <json_X> <json_y> <family> <json_params>
Description
Bayesian regression with parameters: prior_sd (2.5, on the standardized slopes; smaller = more shrinkage), prior_intercept_sd (10), chains (4), iterations (2000), burn_in (1000), seed, level, trials (binomial), offset (poisson), samples (draws returned)
Bayesian regression with parameters: prior_sd (2.5, on the standardized slopes; smaller = more shrinkage), prior_intercept_sd (10), chains (4), iterations (2000), burn_in (1000), seed, level, trials (binomial), offset (poisson), samples (draws returned)
Parameters
json_X: The rows - String - required
json_y: The response - String - required
family: The family - String - required
json_params: The parameters - String - required
json_X: The rows - String - required
json_y: The response - String - required
family: The family - String - required
json_params: The parameters - String - required
admin
stat bayes_glm "[[4.7, 1], [1.3, 1], [3.1, 0], [2.1, 0], [2.8, 0], [4.9, 1], [3.1, 1], [1.2, 0], [3.6, 0], [2.5, 1], [2.1, 1], [4.3, 0], [3.4, 1], [1.7, 0], [3.7, 0], [1.3, 1], [2.1, 1], [2.3, 1], [3.2, 1], [2.0, 0], [1.5, 1], [3.2, 0], [1.7, 0], [2.7, 0], [1.9, 0], [4.2, 0], [5.0, 0], [4.9, 1], [1.1, 1], [1.8, 1], [1.9, 0], [3.6, 0], [2.7, 0], [2.4, 1], [4.6, 1], [4.8, 0], [2.7, 1], [3.2, 0], [1.4, 0], [3.2, 1]]" "[0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1]" "binomial" "{\"prior_sd\": 0.5}"
mentdb
{"family": "binomial", "n": 40, "coefficients": [{"term": "intercept", "mean": -1.9750302499982058, "sd": 0.8780384934132177, "median": -1.9286618718682957, "lower": -3.843296192070038, "upper": -0.32642244378986707, "rhat": 1.0074698418113566, "ess": 738.1303370843538}, {"term": "x0", "mean": 0.5090581633584876, "sd": 0.2555015717300446, "median": 0.5089401238901972, "lower": 0.01804001139646231, "upper": 1.0608417569677417, "rhat": 1.003971445441207, "ess": 758.0072439697914, "probability_positive": 0.98275, "odds_ratio": 1.6635271276040509}, {"term": "x1", "mean": 0.3411193989420448, "sd": 0.574068252789349, "median": 0.339489680986858, "lower": -0.7638241241901949, "upper": 1.4585427209642103, "rhat": 1.0140422084825844, "ess": 627.9064623953018, "probability_positive": 0.729375, "odds_ratio": 1.4042308020066314}], "acceptance": 0.286375, "chains": 4, "draws": 8000, "converged": true, "priors": "normal(0, 0.5) on the standardized slopes, normal(0, 10) on the intercept"}
Used in use cases (1 recipe)
Statistician & biostatistician › Small sample: Bayesian logistic regression and the probability of an effect
Statistician & biostatistician › Small sample: Bayesian logistic regression and the probability of an effect
stat bayes_ab <successes_a> <trials_a> <successes_b> <trials_b>
Description
Bayesian A/B test of two conversion rates (uniform priors): exact probability that B beats A, interval of the difference and of the lift, expected loss of each choice
Bayesian A/B test of two conversion rates (uniform priors): exact probability that B beats A, interval of the difference and of the lift, expected loss of each choice
Parameters
successes_a: Successes of A - Number - required
trials_a: Trials of A - Number - required
successes_b: Successes of B - Number - required
trials_b: Trials of B - Number - required
successes_a: Successes of A - Number - required
trials_a: Trials of A - Number - required
successes_b: Successes of B - Number - required
trials_b: Trials of B - Number - required
admin
stat bayes_ab 120 1000 145 1000
mentdb
{"rate_a": 0.12075848303393213, "rate_b": 0.14570858283433133, "prob_b_beats_a": 0.9501969076167952, "prob_b_beats_a_mc": 0.94879, "difference_lower": -0.004925832618116217, "difference_upper": 0.0548400618706738, "lift_median": 0.20701639650932668, "lift_lower": -0.03649317432149515, "lift_upper": 0.5152697337267359, "expected_loss_choosing_a": 0.02526414483566185, "expected_loss_choosing_b": 3.310556949133679E-4, "posteriors": "A ~ Beta(121, 881), B ~ Beta(146, 856)"}
stat bayes_ab <successes_a> <trials_a> <successes_b> <trials_b> <json_params>
Description
A/B test with parameters: prior [a, b], samples (100000), seed, level
A/B test with parameters: prior [a, b], samples (100000), seed, level
Parameters
successes_a: Successes of A - Number - required
trials_a: Trials of A - Number - required
successes_b: Successes of B - Number - required
trials_b: Trials of B - Number - required
json_params: The parameters - String - required
successes_a: Successes of A - Number - required
trials_a: Trials of A - Number - required
successes_b: Successes of B - Number - required
trials_b: Trials of B - Number - required
json_params: The parameters - String - required
admin
stat bayes_ab 12 100 19 100 "{\"prior\": [2, 20]}"
mentdb
{"rate_a": 0.11475409836065574, "rate_b": 0.1721311475409836, "prob_b_beats_a": 0.9025809144382274, "prob_b_beats_a_mc": 0.90337, "difference_lower": -0.029602471787841415, "difference_upper": 0.14556127823834009, "lift_median": 0.5096438103680319, "lift_lower": -0.18819250208903643, "lift_upper": 1.9330136022936333, "expected_loss_choosing_a": 0.05938053953519738, "expected_loss_choosing_b": 0.0020650454813194593, "posteriors": "A ~ Beta(14, 108), B ~ Beta(21, 101)"}
Used in use cases (1 recipe)
Statistician & biostatistician › A/B test of a landing page: probability to win and expected loss
Statistician & biostatistician › A/B test of a landing page: probability to win and expected loss
stat bayes_factor_t <json_values>
Description
Bayes factor of the one sample t test (JZS, Rouder 2009, Cauchy prior r = 0.707 on the effect size): BF10, BF01 and the strength of the evidence
Bayes factor of the one sample t test (JZS, Rouder 2009, Cauchy prior r = 0.707 on the effect size): BF10, BF01 and the strength of the evidence
Parameters
json_values: The values - String - required
json_values: The values - String - required
admin
stat bayes_factor_t "[0.8, 1.2, -0.3, 0.9, 1.5, 0.4, 1.1, 0.2, 0.7, 1.3]"
mentdb
{"design": "one sample", "t": 4.473606810475955, "df": 9, "r": 0.7071067811865476, "bf10": 28.438573590077308, "bf01": 0.03516350765035967, "evidence": "strong evidence for H1 (a difference)"}
stat bayes_factor_t <json_values> <json_params>
Description
Bayes factor with parameters: y (second sample), paired, mu (one sample), r (prior scale)
Bayes factor with parameters: y (second sample), paired, mu (one sample), r (prior scale)
Parameters
json_values: The values - String - required
json_params: The parameters - String - required
json_values: The values - String - required
json_params: The parameters - String - required
admin
stat bayes_factor_t "[5.1, 5.3, 4.9, 5.2, 5.0, 5.1]" "{\"y\": [5.0, 5.2, 5.1, 4.9, 5.1, 5.0]}"
mentdb
{"design": "two independent samples", "t": 0.6956083436402506, "df": 10, "r": 0.7071067811865476, "bf10": 0.5451424204080055, "bf01": 1.8343830209572787, "evidence": "anecdotal evidence for H0 (no difference)"}
stat bayes_hierarchical <json_estimates> <json_se>
Description
Normal hierarchical model (partial pooling) of group estimates with their standard errors: posterior of each group with its pooling factor (shrinkage: 0 = its own estimate, 1 = the common mean), of the mean mu and of the between-group sd tau (exact on a grid of tau, Gelman BDA 5.4)
Normal hierarchical model (partial pooling) of group estimates with their standard errors: posterior of each group with its pooling factor (shrinkage: 0 = its own estimate, 1 = the common mean), of the mean mu and of the between-group sd tau (exact on a grid of tau, Gelman BDA 5.4)
Parameters
json_estimates: The estimates - String - required
json_se: Their standard errors - String - required
json_estimates: The estimates - String - required
json_se: Their standard errors - String - required
admin
stat bayes_hierarchical "[28, 8, -3, 7, -1, 1, 18, 12]" "[15, 10, 16, 11, 9, 11, 10, 18]"
mentdb
{"groups": [{"group": "group0", "estimate": 28, "posterior_mean": 11.446474267415237, "posterior_median": 10.207915611763717, "lower": -2.266045017344238, "upper": 31.603588192496023, "shrinkage": 0.823132268075223}, {"group": "group1", "estimate": 8, "posterior_mean": 7.87697334256201, "posterior_median": 7.848240938968097, "lower": -4.7534826546219335, "upper": 20.723167786550682, "shrinkage": 0.7203277451131574}, {"group": "group2", "estimate": -3, "posterior_mean": 6.097477695116706, "posterior_median": 6.580398514295561, "lower": -11.234993821774902, "upper": 20.250606548450065, "shrinkage": 0.8370469893795458}, {"group": "group3", "estimate": 7, "posterior_mean": 7.671257315561344, "posterior_median": 7.6790886293094545, "lower": -5.692925570594904, "upper": 21.136431012768146, "shrinkage": 0.7466545784738269}, {"group": "group4", "estimate": -1, "posterior_mean": 5.0097981973834536, "posterior_median": 5.504932755144255, "lower": -9.052917867064533, "upper": 16.447703654375847, "shrinkage": 0.6899857482493}, {"group": "group5", "estimate": 1, "posterior_mean": 6.097460467199858, "posterior_median": 6.452949707483116, "lower": -8.61528985279986, "upper": 18.48455138953692, "shrinkage": 0.7466545784738269}, {"group": "group6", "estimate": 18, "posterior_mean": 10.62507581217583, "posterior_median": 10.01810218228756, "lower": -1.2217799319879121, "upper": 25.977914329884754, "shrinkage": 0.7203277451131574}, {"group": "group7", "estimate": 12, "posterior_mean": 8.497174296949941, "posterior_median": 8.228202371169552, "lower": -7.278646176706404, "upper": 25.916843406884453, "shrinkage": 0.8605468650509407}], "mu": {"mean": 7.884466639656354, "lower": -2.281694810528439, "upper": 18.190173617680063}, "tau": {"mean": 6.643413150000068, "median": 5.2855, "lower": 0.2325, "upper": 21.1265}, "tau_prior": "uniform"}
stat bayes_hierarchical <json_estimates> <json_se> <json_params>
Description
Hierarchical model with parameters: names, tau_prior (uniform, half_cauchy), tau_scale (5), samples (20000), seed, level
Hierarchical model with parameters: names, tau_prior (uniform, half_cauchy), tau_scale (5), samples (20000), seed, level
Parameters
json_estimates: The estimates - String - required
json_se: The standard errors - String - required
json_params: The parameters - String - required
json_estimates: The estimates - String - required
json_se: The standard errors - String - required
json_params: The parameters - String - required
admin
stat bayes_hierarchical "[28, 8, -3, 7, -1, 1, 18, 12]" "[15, 10, 16, 11, 9, 11, 10, 18]" "{\"tau_prior\": \"half_cauchy\", \"names\": [\"A\", \"B\", \"C\", \"D\", \"E\", \"F\", \"G\", \"H\"]}"
mentdb
{"groups": [{"group": "A", "estimate": 28, "posterior_mean": 9.350665705665135, "posterior_median": 8.79267484319304, "lower": -1.5637977762709994, "upper": 23.589960385829286, "shrinkage": 0.9222845014596}, {"group": "B", "estimate": 8, "posterior_mean": 7.77570908155682, "posterior_median": 7.758757641142926, "lower": -2.679295069135527, "upper": 18.349826632534644, "shrinkage": 0.8608663463283639}, {"group": "C", "estimate": -3, "posterior_mean": 7.0060516476061485, "posterior_median": 7.2129071498937165, "lower": -5.337871346757748, "upper": 18.071033282604898, "shrinkage": 0.9297063749768295}, {"group": "D", "estimate": 7, "posterior_mean": 7.688072841727333, "posterior_median": 7.671523495597151, "lower": -3.121035349740713, "upper": 18.595646156347357, "shrinkage": 0.8777102587194986}, {"group": "E", "estimate": -1, "posterior_mean": 6.291340686234295, "posterior_median": 6.536213245120178, "lower": -5.18834729375576, "upper": 16.1688800053874, "shrinkage": 0.8404777373196768}, {"group": "F", "estimate": 1, "posterior_mean": 6.917271333289778, "posterior_median": 7.08898250079468, "lower": -4.614668475706771, "upper": 17.18191439277522, "shrinkage": 0.8777102587194986}, {"group": "G", "estimate": 18, "posterior_mean": 9.140346623412684, "posterior_median": 8.800442803992464, "lower": -0.9518552578186301, "upper": 21.377426151500384, "shrinkage": 0.8608663463283639}, {"group": "H", "estimate": 12, "posterior_mean": 8.044708781417071, "posterior_median": 7.911903252287832, "lower": -3.778515152577678, "upper": 20.599358536539995, "shrinkage": 0.9417604389898303}], "mu": {"mean": 7.759566400908882, "lower": -0.9506826474420462, "upper": 16.471829672530735}, "tau": {"mean": 3.67252349999999, "median": 2.8055, "lower": 0.1395, "upper": 12.261274999999932}, "tau_prior": "half_cauchy"}
Used in use cases (1 recipe)
Statistician & biostatistician › Multi-center trial: partial pooling of the effects of 8 centers
Statistician & biostatistician › Multi-center trial: partial pooling of the effects of 8 centers
stat waic <json_loglik>
Description
Model comparison from the pointwise log-likelihood of posterior draws: WAIC and PSIS-LOO (Vehtari 2017) with their standard errors, effective number of parameters and Pareto k diagnostics
Model comparison from the pointwise log-likelihood of posterior draws: WAIC and PSIS-LOO (Vehtari 2017) with their standard errors, effective number of parameters and Pareto k diagnostics
Parameters
json_loglik: The log-likelihood (one row per draw, one column per observation) - String - required
json_loglik: The log-likelihood (one row per draw, one column per observation) - String - required
admin
stat waic "[[-1.582, -2.004, -2.4889, -1.7755, -1.7597, -1.7597, -2.9143, -1.5651], [-1.695, -1.7792, -2.9017, -1.6268, -1.9766, -1.9766, -2.4994, -1.6591], [-1.7822, -1.6926, -3.1431, -1.5793, -2.1172, -2.1172, -2.315, -1.7365], [-1.5832, -1.9999, -2.4948, -1.7726, -1.7625, -1.7625, -2.9072, -1.566], [-1.6687, -1.8148, -2.8205, -1.6485, -1.9312, -1.9312, -2.5698, -1.6363], [-1.5449, -2.3739, -2.0906, -2.0539, -1.5975, -1.5975, -3.5133, -1.5509], [-1.5568, -2.1204, -2.338, -1.8601, -1.691, -1.691, -3.1104, -1.5479], [-1.553, -2.1478, -2.3066, -1.8805, -1.6776, -1.6776, -3.1554, -1.5458], [-1.5595, -2.5453, -1.966, -2.19, -1.5639, -1.5639, -3.773, -1.5743], [-1.5725, -2.6355, -1.9107, -2.2627, -1.5532, -1.5532, -3.9065, -1.5917], [-1.5835, -2.6982, -1.8757, -2.3138, -1.5483, -1.5483, -3.9983, -1.6056], [-1.5652, -2.0728, -2.3962, -1.8251, -1.7166, -1.7166, -3.0313, -1.5531], [-1.5703, -2.049, -2.427, -1.8078, -1.7306, -1.7306, -2.9911, -1.5566], [-1.5596, -2.1029, -2.3589, -1.8472, -1.7, -1.7, -3.0815, -1.5495], [-1.5938, -1.9667, -2.5442, -1.7493, -1.7865, -1.7865, -2.8495, -1.5741], [-1.5597, -2.547, -1.9649, -2.1913, -1.5636, -1.5636, -3.7754, -1.5746], [-1.5785, -2.0165, -2.4712, -1.7844, -1.7513, -1.7513, -2.9358, -1.5625], [-1.6145, -1.9136, -2.6305, -1.7128, -1.83, -1.83, -2.7547, -1.5907], [-1.6992, -1.774, -2.9143, -1.6237, -1.9837, -1.9837, -2.4889, -1.6628], [-1.5436, -2.3168, -2.1387, -2.0093, -1.6133, -1.6133, -3.4249, -1.5464], [-1.555, -2.133, -2.3234, -1.8695, -1.6847, -1.6847, -3.1312, -1.5469], [-1.6317, -2.9162, -1.7732, -2.4936, -1.5443, -1.5443, -4.3119, -1.6634], [-1.5501, -2.1736, -2.2782, -1.8998, -1.6659, -1.6659, -3.1972, -1.5445], [-1.6607, -3.0246, -1.7318, -2.5842, -1.5489, -1.5489, -4.465, -1.6969], [-1.5654, -2.5894, -1.9382, -2.2254, -1.5581, -1.5581, -3.8385, -1.5824], [-1.7761, -1.6976, -3.1272, -1.5818, -2.1076, -2.1076, -2.3262, -1.731], [-1.6616, -3.0276, -1.7307, -2.5867, -1.5491, -1.5491, -4.4692, -1.6978], [-1.7088, 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-1.6395], [-1.548, -2.4295, -2.0471, -2.0976, -1.5844, -1.5844, -3.5984, -1.557], [-1.5445, -2.3646, -2.0982, -2.0465, -1.5999, -1.5999, -3.4989, -1.55], [-1.6436, -2.9621, -1.755, -2.5319, -1.5458, -1.5458, -4.3769, -1.6772], [-2.0092, -1.5805, -3.6711, -1.5436, -2.4484, -2.4484, -2.0121, -1.9445], [-1.6998, -3.1562, -1.6887, -2.6949, -1.5595, -1.5595, -4.6487, -1.7411], [-1.562, -2.0891, -2.3757, -1.837, -1.7074, -1.7074, -3.0586, -1.5511], [-1.5492, -2.1821, -2.269, -1.9062, -1.6621, -1.6621, -3.2111, -1.5442], [-1.9289, -1.608, -3.4952, -1.5468, -2.335, -2.335, -2.1002, -1.8703], [-1.6274, -2.8988, -1.7804, -2.4792, -1.544, -1.544, -4.2872, -1.6583], [-1.769, -1.7034, -3.1085, -1.5847, -2.0965, -2.0965, -2.3394, -1.7246], [-1.5441, -2.2672, -2.1838, -1.971, -1.6293, -1.6293, -3.3469, -1.5442], [-1.5718, -2.0429, -2.4351, -1.8034, -1.7344, -1.7344, -2.9808, -1.5577], [-1.5451, -2.2417, -2.2082, -1.9514, -1.6384, -1.6384, -3.3066, -1.5436], [-1.6782, -1.8013, -2.8504, -1.6401, -1.9478, -1.9478, -2.5434, -1.6445], [-1.5496, -2.4503, -2.0316, -2.1141, -1.5801, -1.5801, -3.63, -1.5596], [-1.5785, -2.0163, -2.4715, -1.7843, -1.7514, -1.7514, -2.9354, -1.5625], [-1.6307, -1.8793, -2.6914, -1.6899, -1.8617, -1.8617, -2.6921, -1.604], [-1.9883, -1.5867, -3.6261, -1.5437, -2.4191, -2.4191, -2.0335, -1.9251], [-1.6992, -3.1543, -1.6892, -2.6933, -1.5593, -1.5593, -4.646, -1.7404], [-1.8894, -1.6256, -3.4049, -1.5516, -2.2779, -2.2779, -2.15, -1.8339], [-1.7405, -1.7291, -3.0321, -1.5983, -2.0515, -2.0515, -2.3955, -1.6993], [-1.5509, -2.1656, -2.2868, -1.8938, -1.6694, -1.6694, -3.1844, -1.5449], [-1.6237, -1.8935, -2.6656, -1.6993, -1.8481, -1.8481, -2.7182, -1.5982], [-1.5517, -2.1587, -2.2944, -1.8886, -1.6725, -1.6725, -3.1731, -1.5452], [-1.9261, -1.6091, -3.4888, -1.547, -2.3309, -2.3309, -2.1036, -1.8676], [-1.6107, -1.9223, -2.6157, -1.7187, -1.8224, -1.8224, -2.7704, -1.5876], [-1.5669, -2.0644, -2.4069, -1.819, -1.7214, -1.7214, -3.0172, -1.5543], [-1.566, -2.0689, -2.4011, -1.8223, -1.7188, -1.7188, -3.0248, -1.5537], [-1.5681, -2.0588, -2.4142, -1.8149, -1.7248, -1.7248, -3.0077, -1.5551], [-1.57, -2.0505, -2.425, -1.8089, -1.7297, -1.7297, -2.9937, -1.5564], [-1.5437, -2.3313, -2.1262, -2.0206, -1.609, -1.609, -3.4474, -1.5474], [-2.064, -1.567, -3.7864, -1.5454, -2.5241, -2.5241, -1.9602, -1.9954], [-1.6169, -2.8559, -1.7989, -2.4435, -1.5435, -1.5435, -4.2259, -1.646], [-2.026, -4.0061, -1.5502, -3.4269, -1.7248, -1.7248, -5.7933, -2.0968], [-1.5746, -2.0315, -2.4505, -1.7952, -1.7415, -1.7415, -2.9615, -1.5596], [-1.5725, -2.0398, -2.4392, -1.8012, -1.7363, -1.7363, -2.9756, -1.5582], [-1.6335, -1.8738, -2.7016, -1.6863, -1.867, -1.867, -2.6819, -1.6064], [-1.5678, -2.0604, -2.412, -1.8161, -1.7238, -1.7238, -3.0105, -1.5549], [-1.5724, -2.0404, -2.4385, -1.8016, -1.7359, -1.7359, -2.9765, -1.5581], [-1.6276, -1.8855, -2.6802, -1.694, -1.8557, -1.8557, -2.7034, -1.6015], [-1.7451, -1.7248, -3.0445, -1.5959, -2.0587, -2.0587, -2.3862, -1.7033], [-1.5525, -2.1517, -2.3023, -1.8833, -1.6758, -1.6758, -3.1616, -1.5456], [-1.5564, -2.1227, -2.3353, -1.8618, -1.6898, -1.6898, -3.1142, -1.5477], [-2.0223, -1.5769, -3.6991, -1.5437, -2.4667, -2.4667, -1.9991, -1.9567], [-1.6587, -1.8301, -2.788, -1.6581, -1.9134, -1.9134, -2.5994, -1.6277], [-1.5451, -2.3793, -2.0862, -2.058, -1.5961, -1.5961, -3.5215, -1.5514], [-2.1642, -1.5511, -3.9897, -1.5556, -2.66, -2.66, -1.8789, -2.0891], [-1.7042, -1.7681, -2.9289, -1.6202, -1.992, -1.992, -2.4768, -1.6671], [-1.5471, -2.2079, -2.2421, -1.9257, -1.6514, -1.6514, -3.2526, -1.5436], [-1.5511, -2.4679, -2.0189, -2.1281, -1.5767, -1.5767, -3.6567, -1.562], [-1.6227, -1.8955, -2.6621, -1.7006, -1.8463, -1.8463, -2.7218, -1.5974], [-1.5435, -2.3107, -2.1441, -2.0046, -1.6152, -1.6152, -3.4153, -1.5461], [-1.5468, -2.4126, -2.06, -2.0842, -1.5882, -1.5882, -3.5726, -1.5549], [-1.5573, -2.5273, -1.9779, -2.1755, -1.5665, -1.5665, -3.746, -1.5712], [-1.55, -2.1746, -2.2771, 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[-1.6062, -1.9334, -2.5972, -1.7263, -1.813, -1.813, -2.7903, -1.584], [-1.5653, -2.0723, -2.3967, -1.8247, -1.7168, -1.7168, -3.0305, -1.5532], [-1.5637, -2.0805, -2.3864, -1.8307, -1.7122, -1.7122, -3.0442, -1.5521], [-1.5437, -2.2883, -2.1643, -1.9872, -1.6222, -1.6222, -3.3801, -1.5449], [-1.5436, -2.2984, -2.1552, -1.995, -1.619, -1.619, -3.396, -1.5454], [-1.5549, -2.1334, -2.3229, -1.8697, -1.6845, -1.6845, -3.1318, -1.5468], [-1.5436, -2.315, -2.1404, -2.0079, -1.6139, -1.6139, -3.4219, -1.5463], [-1.553, -2.1475, -2.3069, -1.8803, -1.6777, -1.6777, -3.1549, -1.5459], [-1.5787, -2.6717, -1.8901, -2.2922, -1.5502, -1.5502, -3.9596, -1.5996], [-1.6302, -1.8803, -2.6896, -1.6905, -1.8607, -1.8607, -2.6939, -1.6036], [-1.5915, -1.9733, -2.5342, -1.7539, -1.7816, -1.7816, -2.8609, -1.5724]]"
mentdb
{"observations": 8, "draws": 120, "lppd": -15.96245178568815, "elpd_waic": -17.034457581414344, "p_waic": 1.0720057957261906, "waic": 34.06891516282869, "waic_se": 3.3152839706164983, "elpd_loo": -17.06531227252752, "p_loo": 1.1028604868393703, "looic": 34.13062454505504, "looic_se": 3.3396730610428524, "pareto_k_max": 0.49840401505344417, "pareto_k_above_0_7": 0, "rule": "lower waic \/ looic = better model; a Pareto k > 0.7 makes the LOO of that observation unreliable"}