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Use experiments, modeling, and simulation to determine if perceptual confidence emerges from Bayesian or heuristic computations. 🧠
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DOI Code (papers 1–3) and behavioral data (papers 1–2)

DOI MCMC model fits to behavioral data (papers 1–2)

Are human confidence reports Bayesian?

This repository accompanies the following three peer-reviewed papers on the topic of whether human confidence reports are Bayesian, by Will Adler, Rachel Denison, Marisa Carrasco, and Wei Ji Ma:

1. Confidence when uncertainty is due to stimulus reliability

William T. Adler, Wei Ji Ma. (2018). Comparing Bayesian and non-Bayesian accounts of human confidence reports [pdf]. PLoS Computational Biology.

2. Confidence when uncertainty is due to inattention

Rachel N. Denison*, William T. Adler*, Marisa Carrasco, Wei Ji Ma. (2018). Humans incorporate attention-dependent uncertainty into perceptual decisions and confidence [pdf]. Proceedings of the National Academies of Sciences.

3. Theoretical exploration of Bayesian confidence signatures.

William T. Adler, Wei Ji Ma. (2018). Limitations of proposed signatures of Bayesian confidence [pdf]. Neural Computation.

Each of the above papers is associated with a chapter in Will Adler's 2018 dissertation in neural science at NYU.


Papers 1 and 2

The below instructions apply to Papers 1 and 2. The code for Paper 3 is relatively straightforward and you can find a different README with the corresponding code.


Clone or download this repository. In MATLAB, cd into this repository. Use addpath(genpath('helper_functions')) to add the necessary functions to your path.

Plot some data

Use show_data_or_fits to plot the human data. Try this to plot data from Paper 1:

axis.col = 'slice';
axis.row = 'depvar';
axis.fig = 'task';

show_data_or_fits('root_datadir', 'human_data/reliability_exp1', ...
                  'axis', axis, ...
                  'depvars', {'resp', 'Chat', 'tf'}, ...
                  'tasks', {'A', 'B'}, ...
                  'slices', {'c_s', 'c', 'c_C'});

To get two figures. The second one, for Task B, should look like this:

The parameters in axis indicate that:

  • The columns of the resulting figures should show different slices of the data. In this case, the data in the first column slices the data by reliability c and orientation s (slice c_s); the second column slices the data by just reliability c (slice c); and the third column slices the data by reliability c and true category C (slice c_C).
  • The rows of the resulting figures should show different dependent variables on the y-axis. In this case, those variables are mean button press (resp), proportional response "category 1" (Chat, as in C-hat, used in the papers), and proportion correct (tf, as in true-false).
  • You will get a figure like this for each task. In this case, a dataset was chosen that includes two tasks, and both tasks A and B were specified as arguments, so you will get two figures.

Options for the axis parameters are 'none', 'slice', 'depvar', 'task', 'subject', and 'model'. 'subject' will give you individual subject data rather than grouped, as shown above. 'model' will show you fits to different models (more on that below).

Options for depvars are:

  • resp Mean button press (choice and confidence), between 1 and 8
  • Chat Proportion response "category 1"
  • tf Proportion correct
  • g Mean confidence, between 1 and 4
  • rt Reaction time (s)

Options for slices are 's', 'Chat', 'g', 'resp', 'rt', 'C_s', 'c', 'c_s', 'c_C', 'c_Chat', 'c_g', and 'c_resp', which are just various combinations of the variables described above.

To plot data from Paper 2, try running this code:

axis.col = 'slice';
axis.row = 'depvar';
axis.fig = 'none';

show_data_or_fits('root_datadir', 'human_data/attention', ...
                  'axis', axis, ...
                  'depvars', {'resp', 'Chat', 'tf'}, ...
                  'slices', {'c_s', 'c', 'c_C'});

to get something like this:

Explore model fits

If you want to explore model fits, try going to this repository and downloading the .mat files into the model_fits folder. Be warned that these are 11 files averaging about 600MB. They're big because they include the thinned chains of samples generated when we fit the models with MCMC.

Once downloaded, run load_model_fits.m to load in all the files and organize the models as they are used in Paper 1. Now you will have several loaded structs containing all you need to know about model parameters (e.g., lower and upper bounds) and fits (e.g., MCMC samples and scores to each subject). For instance, the attention.modelmaster struct will contain all the models used in Paper 2. Try loading and printing out the names of the models:

models = attention.modelmaster;
>>> 1: Bayes_{Strong}-{\itd}N + non-param. \sigma, B
>>> 2: Bayes_{Weak}-{\itd}N + non-param. \sigma, B
>>> 3: Orientation Estimation + non-param. \sigma, B
>>> 4: Linear Neural + non-param. \sigma, B
>>> 5: Lin + non-param. \sigma, B
>>> 6: Quad + non-param. \sigma, B
>>> 7: Fixed + non-param. \sigma, B
>>> 8: Bayes-{\itd}N + non-param. \sigma, B, choice only
>>> 9: Orientation Estimation + non-param. \sigma, B, choice only
>>> 10: Linear Neural + non-param. \sigma, B, choice only
>>> 11: Lin + non-param. \sigma, B, choice only
>>> 12: Quad + non-param. \sigma, B, choice only
>>> 13: Fixed + non-param. \sigma, B, choice only

If you're interested in the Quad confidence model (model #6), for instance, here's some of the information you could pull out of the struct:

  • models(6).parameter_names: names of the model parameters
  • models(6).lb: parameter lower bound values
  • models(6).ub: parameter upper bound values
  • samples = vertcat(models(6).extracted(1).p{:}): MCMC samples (nSamples x nParams) for the model, subject 1. (Each cell in models(12).extracted(1).p is an MCMC chain)

With the models loaded, you can also use show_data_or_fits to plot model fits and scores. Try running this code:

axis.col = 'model';
axis.row = 'depvar';
axis.fig = 'none';

show_data_or_fits('root_datadir', 'human_data/attention', ...
                  'axis', axis, ...
                  'depvars', {'resp', 'tf'}, ...
                  'slices', {'c_s', 'c', 'c_C'}, ...
                  'models', models([1:2 5:7]), ...
                  'MCM', 'loopsis');

to get a plot that includes model fits as well as PSIS-LOO score comparisons for five models:

Understanding the computations behind each model

There are two functions that you might want to look through if you are interested in how the computations described in the paper are implemented in the code. One function is trial_generator.m, which shows how fake data is generated for each model. The other one is nloglik_fcn.m which is used for computing the (negative) log-likelihood of each model.

Run the psychophysical experiment

To run the experiment, you'll need to install Psychtoolbox. Then run_categorical_decision.m is used to set the parameters of the experiment and run it.

Paper 3

All of the code necessary to produce the simulations in Paper 3, as well as a README specific to Paper 3, can be found in the signatures folder. Paper 3 involves no human data.

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