Solving Linear Inverse Models

Functions that (1) find the minimum/maximum of a linear or quadratic function: min or max (f(x)), where f(x) = ||Ax-b||^2 or f(x) = sum(a_i*x_i) subject to equality constraints Ex=f and/or inequality constraints Gx>=h, (2) sample an underdetermined- or overdetermined system Ex=f subject to Gx>=h, and if applicable Ax~=b, (3) solve a linear system Ax=B for the unknown x. It includes banded and tridiagonal linear systems.

Bayesian Clustering Using the Table Invitation Prior (TIP)

Cluster data without specifying the number of clusters using the Table Invitation Prior (TIP) introduced in the paper "Clustering Gene Expression Using the Table Invitation Prior" by Charles W. Harrison, Qing He, and Hsin-Hsiung Huang (2022) . TIP is a Bayesian prior that uses pairwise distance and similarity information to cluster vectors, matrices, or tensors.

Charles's Utility Function using Formula

Utility functions that provides wrapper to descriptive base functions like cor, mean and table. It makes use of the formula interface to pass variables to functions. It also provides operators to concatenate (%+%), to repeat (%n%) and manage character vectors for nice display.

Continuous Time Structural Equation Modelling

Hierarchical continuous (and discrete) time state space modelling, for linear and nonlinear systems measured by continuous variables, with limited support for binary data. The subject specific dynamic system is modelled as a stochastic differential equation (SDE) or difference equation, measurement models are typically multivariate normal factor models. Linear mixed effects SDE's estimated via maximum likelihood and optimization are the default. Nonlinearities, (state dependent parameters) and random effects on all parameters are possible, using either max likelihood / max a posteriori optimization (with optional importance sampling) or Stan's Hamiltonian Monte Carlo sampling. See < https://github.com/cdriveraus/ctsem/raw/master/vignettes/hierarchicalmanual.pdf> for details. See < https://osf.io/preprints/psyarxiv/4q9ex_v2> for a detailed tutorial. Priors may be used. For the conceptual overview of the hierarchical Bayesian linear SDE approach, see < https://www.researchgate.net/publication/324093594_Hierarchical_Bayesian_Continuous_Time_Dynamic_Modeling>. Exogenous inputs may also be included, for an overview of such possibilities see < https://www.researchgate.net/publication/328221807_Understanding_the_Time_Course_of_Interventions_with_Continuous_Time_Dynamic_Models> . < https://cdriver.netlify.app/> contains some tutorial blog posts.

Robust Mixture Discriminant Analysis

Robust mixture discriminant analysis (RMDA), proposed in Bouveyron & Girard, 2009 , allows to build a robust supervised classifier from learning data with label noise. The idea of the proposed method is to confront an unsupervised modeling of the data with the supervised information carried by the labels of the learning data in order to detect inconsistencies. The method is able afterward to build a robust classifier taking into account the detected inconsistencies into the labels.

Logic Regression

Routines for fitting Logic Regression models. Logic Regression is described in Ruczinski, Kooperberg, and LeBlanc (2003) . Monte Carlo Logic Regression is described in and Kooperberg and Ruczinski (2005) .

The FisherEM Algorithm to Simultaneously Cluster and Visualize High-Dimensional Data

The FisherEM algorithm, proposed by Bouveyron & Brunet (2012) , is an efficient method for the clustering of high-dimensional data. FisherEM models and clusters the data in a discriminative and low-dimensional latent subspace. It also provides a low-dimensional representation of the clustered data. A sparse version of Fisher-EM algorithm is also provided.

Generalized Linear Mixed Models using Template Model Builder

Fit linear and generalized linear mixed models with various extensions, including zero-inflation. The models are fitted using maximum likelihood estimation via 'TMB' (Template Model Builder). Random effects are assumed to be Gaussian on the scale of the linear predictor and are integrated out using the Laplace approximation. Gradients are calculated using automatic differentiation.

Access Carbon Market Data from Emissions Trading Systems and Voluntary Registries

Unified access to carbon market data from compliance emissions trading systems ('EU ETS', 'UK ETS', 'RGGI', California Cap-and-Trade) and voluntary carbon markets (Verra, Gold Standard, American Carbon Registry, Climate Action Reserve, via the Berkeley Voluntary Registry Offsets Database and the 'CarbonPlan' 'OffsetsDB' API). Includes cross-market price data from the 'International Carbon Action Partnership' ('ICAP') Allowance Price Explorer < https://icapcarbonaction.com/en/ets-prices>, global carbon pricing from the World Bank Carbon Pricing Dashboard < https://carbonpricingdashboard.worldbank.org/>, and the historical 'RFF' World Carbon Pricing Database following Dolphin, Pollitt and Newbery (2020) . Data is downloaded from public sources on first use and cached locally.

Download Australian Energy Market Operator Data

Fetch Australian Energy Market Operator (AEMO) public data from 'NEMweb' < http://nemweb.com.au> and the Market Management System Data Model (MMSDM) historical archive. Provides tidy access to 5-minute and 30-minute wholesale electricity prices, regional demand, dispatch-unit output, interconnector flows, rooftop photovoltaic generation, generator bids, predispatch forecasts, frequency control ancillary services markets, and gas market data across the National Electricity Market (NEM) regions. Data is published by AEMO under its Copyright Permissions Notice < https://www.aemo.com.au/privacy-and-legal-notices/copyright-permissions>.