Causal inference in domain of point events with gamma delays.

The pilot experiment (condition selection randomised) and duplicates with the condition selection forced.

A script for making rudimentary videos from trial data.

All the analyses and plotting.

• analyses_for_mturk.r reads the processed data from the mTurk pilot and computes various statistics for the cogsci paper
• analyses_for_journal.r (unfinished) reads the processed data from the prolific replication and computes various statistics
• bayesian_predictions_*.r computes likelihoods and posteriors of models under full Bayesian inference algorithm (calls likelihood_functions.r; slow, only needs to be done once)
• compare_ppt_mod_*.r constructs the model comparison table counting consistency between model and participants judgments (slow, prolific version still buggy)
• compare_sims.r pertains to intervention selections. Compares the achieved information under humans actions against simulated interventions that are either 'even', 'reactive' or 'random' in their timing of actions
• construct_belief_simulations_*.r steps through all behavioural data creating the heuristic judgment predictions at every time point and saving them to separate named .. data/*.rdata files
• create_cogsci_data.r subsets the full ../data/pilot_data.rdata(N=60 containing three delay conditions: between, within and reliable) to keep within and unreliable (renaming as unreliable, reliable) to create ../cogsci_data.rdata
• create_DBN_space_and_funs.r creates 3-D arrays DBN3 (3 3,64) and_DBN4_ (4,4,4096) containing all possible 3 and 4 variable causal structures in the form of adjacency matrices (connection from i to j ingraph k if cell[i,j,k]=1 and stores them along with a function that can match a 2-D array graph input with its index in the 3D array, saving these to dbn.rdtata
• get_posterior_entropies_*.r takes the posteriors and computes Shannon entropy for each time point and adds to the dataframes (only needs to run once)
• intervention_simulation_*.r simulates the task applying several heuristic intervention rules
• likelihood_functions.r contains function that computes likelihoods of some trial data under all causal structures
• notes_plots.r misc exploratory plotting
• order_only_predictions.r linking to The Order of Things (2014 cogsci paper) we wondered if a pure event order constraint heuristic would work at all on these data (it doesn't because it doesn't prefer the more recent event over all other prior events so no signal)
• plots_design.r some plotting of the task itself without behavioural data
• plots_*.r lots of plotting, lots of redundancy, variants for talks,thesis, conference paper etc
• read_in_sql_data*.r reads the csv files (exported from the sql database) and cleans up the data into R dataframes.
• simulate_data.r creates some hand chosen toy data for plotting I think
• tacits some extra plotting for the Time and Causality in the Sciences book chapter

Many of these .rdata files probably obselete but keeping incase.

• *.csv original data files from mTurk and prolific

• cogsci_data.rdata the dataset used in the cogsci paper (subset from pilot_data.rdata used in thesis)

  • df.sw subjectwise (one row per participant) data.frame

    • upi unique personal identifier
    • learn_cond learning condition, all participants were active. This variable is just in case we ever run versions with passive (observation only) participants that might watch another participant play or just watch a device activate by itself
    • delay_cond which delay condition was the participant in? the actual parameters of the delay distributions are in alpha and beta
    • final_score how many of the 54 edges (6 3-variabl 3-edge and 6 4-variable 6-edge problems) were correctly identified (out of their 4 states: no edge, forward, backward, bidirectional) at the end of each trial
    • final_bonus how many of the 54 edges were identified at the randomly timed bonus points across all trials (recalling we paid based on accuracy at random moments to incentivise efficiency and reporting of struture beliefs as soon as possible). This determined how much bonus each participant made (5 cents per correct edge).
    • *_acc the scores /54 to get the proportion of correct edge judgments
    • n_ints how many interventions (left clicks on components) werperformed overall by the participant
    • n_effects how many activations of components did theexperience (aside from the interventions)
    • prop_nodes_tested proportion of the components did they clicon at least once?
    • int_space* how long did they wait between one intervention anthe next?
    • int_space_event* how long did they wait on average between thmost recent event and their next intervention?
    • int_pref_parent how many times did they intervene on a roo (parentless) component per time they intervened on a non-roocomponent (or something like that, might be rescaled by ratio oroots to non-roots)
    • *.cy measures computed for the 6 cyclic problems only
    • *.ncy measures computed for the 6 noncyclic problems only
    • m_ent the average posterior entropy (i.e. uncertainty) achieveby this participant under the ideal Bayesian analysis (lower ibetter, indicative of more informative intervention selection)
    • *3/4 variants restricted to the three variable problems or variable problems (initial uncertainty is very different for thescases because there is a much larger space of 4 variable problems)

  • df.tw a trialwise data.frame (one row per trial). As with df.sw conventions except: - trial what position during the participants run though the experiment did this trial appear

    • trial_type which of the 12 devices (in the order depicted in the paper figure 2) was the participant interacting with on this trial
    • n_nodes how many components were there
    • n_ints how many of the (max 6) interventional clicks did they perform
    • score as with final score
    • bonus as with final bonus
    • n_edges how many edges (potential links) are in the network (3 variable network have 3 and 4 variable network have 6)
    • practice there were two practice problems that were repeats ahead of the other problems. I think they've already been subset out of cogsci_data so this column is always FALSE (they exist in the raw csv)
    • graph the index in DBN3 or DBN4 for the true network
    • cyclic does this network contain a loop?
    • n_ev how many events occurred in total
    • n_ef how many were activations (rather than interventions)
    • n_* how many for each component separately
    • prop_int_root what proportion were on a parentless node
    • final_belief the index of their final judgment
    • n*_dir breaking this down into individual edge judgments (0 =no link, 1 = forward link, 2 = backward link, 3 = bidirectionallink)
    • n*_cor was it right?
    • n_be_ch how often did this learner update their model duringthis trial?
    • initial_ent how much uncertainty in bits is there at thebeginning of the trial i.e. -sum(p * logn(p)) for a uniform overthe space of graphs.
    • igain information gain = final - initial entropy
    • max_p how likely was the most likely graph in the set at the end
    • p_truth how likely was the true graph at the end (often this is the same graph as the most likely one but not necessarily).

  • df.be a beliefwise data.frame (one row per updated participant belief). As with df.tw conventions except: - time when in ms since beginning of the trial was this belief registered by the interface. A new belief was registered whenever participants hit the "confirm" button in the middle of the device after making some changes to their marked connections. Total trial length 45,000 ms (the final response which is subject of most other analyses is automatically registered when timer hits zero, so at 45000 + a few 100ms lag)

  • df.ev an eventwise data.frame (one row per activation or intervention). As with other data.frames except: - location which component was activating - type was it an intervention "action" or an activation "effect"? - from what is the ground truth as to which variable caused this activation if applicable - with_delay how long was the ground truth actual causal delay from the cause event to this activation event?

• mf_results.rdata the model predictions (for cogsci paper)

• individual_fits* likelihoods and posteriors saved separately for each participant

• NS_* "Neuraths ship" referring to the varieties of heuristic compared in the cogsci paper

  • boost variants that overwrite online evolving belief with participants latest online judgment where available (this inflates the correlation with participants but also probably distorts the comparison, we didn't do this in the end)
  • adapt_between a subtle hacky addition meaning that for the between condition, the learner would store the inferred delay for a putative causal link and use that to shape their judgements about subsequent candidate causation

• bonus* bonus payment stuff

Hundreds of figures arranged by purpose.

Demo movies created with quicktime or using the python script for demonstration purposes.

Latex projects for the cogsci paper, the book chapter and some very old notes.