Most of the papers in this list were found through one of a small number of methods:

• following references in Pearl's book,
• browsing Peter Spirtes's publications,
• following links from the TETRAD Project publications page,
• shamelessly ripping off links from Cosma Shalizi's notebook on "Causality", or
• following links in the references to one of the papers discovered by one of the above methods.

At some point, all the local links will disappear, and only the pointers to remote locations will remain.

If you assume a particular causal model has generated the observed data from an experiment, then the structure of the causal model often implies that certain "regularities" are present in the data. Most causal inference procedures turn this observation on its head -- having developed a statistical test for a particular regularity, the detection of that regularity in actual data is used to rule out causal models that would not have produced it. (This is a sound procedure given a property usually called "faithfulness," which can be roughly translated as "Nature won't fool you with spurious regularities by coincidence.") Most of the regularities that are induced by causal models are presented as either "conditional independencies" or "tetrad constraints."

From Section 2: "Markov equivalent DMAGs [directed maximal ancestral graphs] can be transformed to each other by a sequence of single mark changes that preserve Markov equivalence." The point, I suppose (and this is supported by their Conclusion section) is that you can use this result to prove that particular properties must by uniform across certain Markov equivalence classes of graphs.

Introduces inequality constraints on the probabilities of "intervential distributions."

The easiest task (of course, nothing is easy here) is to infer a "causal" network from a dataset where all the variables have been observed.

A fundamental negative result: "We show that the asymptotically consistent procedures [for estimation of causal effects] are 'pointwise consistent,' but 'uniformly consistent' tests do not exist. Thus, no finite sample size can ever be guaranteed to approximate the asymptotic results."

Outlines a method for building cyclic graph structures -- "linear non-recursive structural equation models." Doesn't explicitly address hidden variables, but can be used as a drop-in subroutine for the discovery of hidden variable graph structures in (for example) the Silva "Linear Latent Variable Models" paper, below.

Of course, in a complicated system we will be faced with incomplete data -- there may be unobserved common causes, which could explain correlations in the observed data. Papers in this section involve algorithmic and statistical methods for dealing with this problem: attempting to discover "hidden" variables, and to infer the causal networks that might hold among those hidden variables.

Partitions the "measurement" or observed variables up into separate blocks, and uses them to identify distinct latent variables; then, builds a network on those latent variables. They contrast their method with Elidan's (below), and briefly discuss alternative systems for building the network on the hidden variables (Richardson, above). Most of the focus of this paper appears to be on the identification of hidden variables via blocks of observations.

Attempts to build a hierarchical (i.e. tree-like) structure on the hidden class variables.

Causal network discovery seems to have gotten its start in the social sciences (economics, sociology, psychology and psychometrics) and other disciplines that measure human behavior. However, some of the most recent applications of these techniques have been focused on biological applications. Starting in the late '90s with the advent of microarray technology (and continuing today with cheap sequencing, but more on that in another place at another time), researchers have thought it possible to decode the "regulatory network" or "expression network" of a cell -- the causal network that underlies the varying transcription of genes, and (ultimately) the multifarious and dynamic phenotypes exhibited by cells and organisms.

A classic example of building an "expression network" from microarray-style experiments.

Another important negative result! Accurate reconstruction of genetic regulatory networks is unlikely to be possible unless we explicitly correct for temporal and population averaging effects inherent in microarray experiments.

Another negative result -- as of 2003, most gene regulatory network reconstructions managed to find accurate connections between gene pairs "at chance." I suppose it's an open question whether "gene pairs" are the right level at which to do this analysis, and it probably bears some investigation to figure out whether things have gotten better since 2003 (which was, let's point out, the year in which the first paper to attempt a complete measurement of the "regulatory network" of an organism was attempted, although we all know how well that turned out). But also, this might be simply interpreted as saying that the 'regulatory networks' which were built before 2003 could be reasonable in terms of their final predictions, as statistical models, but less-worthy of the term "causal models."

Also connected with some online software.

Some collected blog-posts about issues surrounding causal inference:

Andrew Gelman:

1. "Causal inference and regression, or, chapters 9, 10, and 23"
2. "How to think about instrumental variables when you get confused"
3. "Where do instrumental variables come from? And my own favorite (unused) example"

Cosma Shalizi:

1. "Quantuam Causal Influence"