This Auto-correlated Bayesian Sampler model (ABS, Zhu et al. 2024) is developed by Zhu.
Zhu J, Sundh J, Spicer J, Chater N, Sanborn AN (2024). “The Autocorrelated Bayesian Sampler: A Rational Process for Probability Judgments, Estimates, Confidence Intervals, Choices, Confidence Judgments, and Response Times.” Psychological Review, 131(2), 456–493. doi:10.1037/rev0000427 .
samplr::CoreABS -> Zhu23ABS
widththe standard deviation of the proposal distribution for MC3.
lambdathe rate parameter of the Erlang distribution for decision time.
new()Create a new 'Zhu23ABS' object.
Zhu23ABS$new(
width,
n_chains,
nd_time,
s_nd_time,
lambda,
distr_name = NULL,
distr_params = NULL,
custom_distr = NULL,
custom_start = NULL
)widtha numeric value of the standard deviation of the proposal distribution for MC3.
n_chainsan integer of the number of chains for the sampler.
nd_timea numeric value of the non-decision time (in seconds). When s_nd_time is not 0, nd_time represents the lower bound of the non-decision time.
s_nd_timea numeric value of the inter-trial-variability of the non-decision time (in seconds).
lambdaa numeric value of the rate parameter of the Erlang distribution for decision time.
distr_namea character string indicating the type of the posterior hypothesis distribution.
distr_paramsa numeric vector of the additional parameters for the posterior hypothesis distribution.
custom_distra list of functions that define the posterior hypothesis distribution.
custom_starta numeric value of the starting point if "custom_distr" is provided.
zhuabs <- Zhu23ABS$new(
width = 1, n_chains = 5, nd_time = 0.3, s_nd_time = 0.5,
lambda = 10, distr_name = 'norm', distr_params = 1
)
simulate()Simulate the ABS model.
stopping_rulea character string indicating the stopping rule of ABS to be applied. Possible values are "fixed" and "relative". See also Details.
start_pointa numeric vector setting the start point of each trial for the sampler. By default, it's set to NA, indicating that the starting point of the first trial is a random point from the posterior of hypotheses, and the starting points of subsequent trials are set to the last sample of the previous trial. For more detailed information, please refer to the vignette "Simulations of the Autocorrelated Bayesian Sampler".
...further arguments passed to the ABS model, see also Details.
The ABS model has two types of stopping rules: fixed and relative. The fixed stopping rule means that a fixed number of samples are drawn to complete the tasks such as estimations and confidence intervals. This rule applies to tasks such as estimation tasks. On the other hand, the relative stopping rule means that the model counts the difference in evidence between the two hypotheses, and terminates the sampling process whenever the accumulated difference exceeds a threshold. This rule applies to tasks such as two-alternative force choice tasks.
When the stopping rule is "fixed", the following arguments are required:
n_sample an integer of the fixed number of samples for each trial.
trial_stim a numeric vector of the stimulus of each trial.
When the stopping rule is "relative", the following arguments are required:
delta an integer of the relative difference between the number of samples supporting each hypothesis.
dec_bdry a numeric value of the decision boundary that separates the posterior hypothesis distribution.
discrim a numeric value of the stimuli discriminability.
trial_stim a factor that indicates the stimuli of each trial. It only consists of either one level or two levels. By definition, level 1 represents the stimulus below the decision boundary, while level 2 represents the stimulus above the decision boundary.
prior_on_resp a numeric vector for the Beta prior on responses. Defaults to c(1,1) representing the distribution Beta(1,1).
prior_depend a boolean variable that control whether the prior on responses changes regarding the last stimulus. Defaults to TRUE. Please refer to the vignette for more information.
max_iterations an integer of the maximum length of the MC3 sampler. Defaults to 1000. The program will stop the sampling process after the length of the sampling sequence reaches to this limitation.
No values will be return after running this method, but the field sim_results will be updated instead. If the stopping rule is "fixed", simulation_results will be a data frame with five columns:
trial: The index of trials;
samples: The samples of ABS sampler for the trial;
stimulus: The stimuli of the experiment;
rt: The response time;
point_est: The response of point estimation;
On the other hand, if the stopping rule is "relative", sim_results will be a data frame with seven columns:
trial: The index of trials;
samples: The samples of ABS sampler for the trial;
response: The response predicted by ABS;
stimulus: The stimuli of the experiment;
accuracy: Whether the response is the same as the feedback. 0 represents error, and 1 represents correct;
rt: The response time, including both the non-decision and the decision time;
confidence: The confidence of the response.
trial_stim <- round(runif(5, 10, 50))
zhuabs$simulate(stopping_rule='fixed', n_sample = 5, trial_stim = trial_stim)
zhuabs$sim_results
zhuabs$reset_sim_results()
trial_stim <- factor(sample(c('left', 'right'), 5, TRUE))
zhuabs$simulate(stopping_rule='relative',
delta = 4, dec_bdry = 0,
discrim = 1, trial_stim = trial_stim
)
zhuabs$sim_results
confidence_interval()This function calculates the confidence interval of the simulate method's results when the "fixed" stopping rule was used.
## ------------------------------------------------
## Method `Zhu23ABS$new`
## ------------------------------------------------
zhuabs <- Zhu23ABS$new(
width = 1, n_chains = 5, nd_time = 0.3, s_nd_time = 0.5,
lambda = 10, distr_name = 'norm', distr_params = 1
)
## ------------------------------------------------
## Method `Zhu23ABS$simulate`
## ------------------------------------------------
trial_stim <- round(runif(5, 10, 50))
zhuabs$simulate(stopping_rule='fixed', n_sample = 5, trial_stim = trial_stim)
zhuabs$sim_results
#> trial samples stimulus rt
#> 1 1 49.46205, 50.15568, 50.13782, 49.49812, 48.70987 49 1.323156
#> 2 2 46.37790, 46.37790, 46.37790, 46.10574, 44.83523 11 0.981617
#> 3 3 43.83680, 42.27428, 41.99898, 41.99898, 41.84585 37 1.264902
#> 4 4 39.38179, 38.99805, 38.99805, 38.99805, 38.87522 25 0.9102649
#> 5 5 47.69700, 47.69700, 47.69700, 46.86499, 46.39406 47 1.050115
#> point_est
#> 1 48.70987
#> 2 44.83523
#> 3 41.84585
#> 4 38.87522
#> 5 46.39406
zhuabs$reset_sim_results()
trial_stim <- factor(sample(c('left', 'right'), 5, TRUE))
zhuabs$simulate(stopping_rule='relative',
delta = 4, dec_bdry = 0,
discrim = 1, trial_stim = trial_stim
)
zhuabs$sim_results
#> trial
#> 1 1
#> 2 2
#> 3 3
#> 4 4
#> 5 5
#> samples
#> 1 -1.55761552, -1.55761552, -0.92738114, -0.05299664
#> 2 -0.90371355, -0.06320349, -0.69308594
#> 3 0.1998162, -0.2475284, -1.4510945, -1.8265552, -2.3712877
#> 4 -1.0035810, -1.2238617, -0.2688994
#> 5 -0.09982374, 0.31810194, 1.38978580, 1.35273434, -0.08451240, 0.76244935, 0.76244935
#> response stimulus accuracy rt confidence
#> 1 left left 1 1.201335 0.8333333
#> 2 left left 1 1.004604 0.8333333
#> 3 left left 1 1.230430 0.7500000
#> 4 left right 0 1.413864 0.8333333
#> 5 right right 1 1.140226 0.7000000
## ------------------------------------------------
## Method `Zhu23ABS$confidence_interval`
## ------------------------------------------------
zhuabs$confidence_interval(conf_level = 0.9)
#> Warning: The simulation results were geneated with the relative stopping rule.