DriftDiffusionModels.jl

DriftDiffusionModels.jl is a Julia package for simulating, fitting, and analyzing Drift Diffusion Models (DDMs), with support for multi-state Hidden Markov Models (HMMs) whose emission distributions are governed by DDMs. The package provides tools for simulation, inference, and model selection via cross-validation.

Note: This package is not intended as a production-ready DDM toolkit. For a more complete and sophisticated implementation of sequential sampling models including advanced DDM variants, we recommend using SequentialSamplingModels.jl.

---

Features

• Simulation of DDM trajectories using the Euler–Maruyama method
• Wiener First Passage Time (WFPT) density computation (Navarro & Fuss, 2009)
• Log-likelihood and parameter estimation for DDMs via MLE
• Hidden Markov Models with DDM emissions and Dirichlet priors
• Baum–Welch (EM) training with MAP updates

---

Installation

Clone the repository and include the module in your Julia environment:

include("DriftDiffusionModels.jl")
using .DriftDiffusionModels

---

Module Overview

DriftDiffusionModel

The core structure representing a DDM:

DriftDiffusionModel(B, v, a₀, τ)

• B: Boundary separation
• v: Drift rate
• a₀: Initial fraction of the boundary
• τ: Non-decision time

DDMResult

Result of a single DDM simulation:

DDMResult(rt, choice, stimulus)

• rt: Response time
• choice: Decision outcome (1 --> R or -1 --> L)
• stimulus: Whether evidence favored left vs. right trials (1 --> R, -1 --> L)

---

Key Functions

Simulation

simulateDDM(model::DriftDiffusionModel, dt::Float64=1e-5)
simulateDDM(model::DriftDiffusionModel, n::Int, dt::Float64=1e-5)

Simulates one or multiple trials of the DDM using Euler–Maruyama integration.

Likelihood

wfpt(t, v, B, w, τ)
logdensityof(model::DriftDiffusionModel, result::DDMResult)

Computes the WFPT density and log-likelihood for observed DDM results.

Fitting

StatsAPI.fit!(model::DriftDiffusionModel, data::Vector{DDMResult}, weights=ones(length(data)))

Fits a DDM to data using Maximum Likelihood Estimation (MLE), supporting observation weights (useful for HMM training).

---

Hidden Markov Models with DDM Emissions

PriorHMM

A wrapper for Hidden Markov Models with Dirichlet priors on initial probabilities and transition matrices:

PriorHMM(init, trans, dists; α_trans, α_init)

Supports MAP updates via Baum–Welch.

Training

baum_welch(hmm, data; seq_ends)

Trains an HMM-DDM model using EM.

---

Model Comparison

Log-Likelihood Ratio

calculate_ll_ratio(ll, ll₀, n)

Computes the per-observation log-likelihood ratio (in bits) between multi-state and single-state models.

---

References

• Navarro, D. J., & Fuss, I. G. (2009). Fast and accurate calculations for first-passage times in Wiener diffusion models.
• HiddenMarkovModels.jl — backend for HMM routines.

---

File Structure

• DriftDiffusionModels.jl – Main module file
• DDM.jl – Drift Diffusion Model definitions and utilities
• HMMDDM.jl – HMM wrapper with DDM emissions and training

---

Contributions

Feel free to contribute pull requests or file issues to suggest features or report bugs!