Marginal AMP Chain Graphs

We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph under marginalization of some of its nodes. However, MAMP chain graphs do not only subsume AMP chain graphs but also multivariate regression chain graphs. We describe global and pairwise Markov properties for MAMP chain graphs and prove their equivalence for compositional graphoids. We also characterize when two MAMP chain graphs are Markov equivalent. For Gaussian probability distributions, we also show that every MAMP chain graph is Markov equivalent to some directed and acyclic graph with deterministic nodes under marginalization and conditioning on some of its nodes. This is important because it implies that the independence model represented by a MAMP chain graph can be accounted for by some data generating process that is partially observed and has selection bias. Finally, we modify MAMP chain graphs so that they are closed under marginalization for Gaussian probability distributions. This is a desirable feature because it guarantees parsimonious models under marginalization.Comment: Changes from v1 to v2: Discussion section got extended. Changes from v2 to v3: New Sections 3 and 5. Changes from v3 to v4: Example 4 added to discussion section. Changes from v4 to v5: None. Changes from v5 to v6: Some minor and major errors have been corrected. The latter include the definitions of descending route and pairwise separation base, and the proofs of Theorems 5 and

Transfer pricing rules, OECD guidelines, and market distortions

We study the impact of transfer pricing rules on sales prices, firms’ organizational structure, and consumers’ utility within a two-country monopolistic competition model featuring source-based profit taxes that differ across countries. Firms can either become multinationals, i.e., they serve the foreign market through a fully controlled affiliate; or they can become exporters, i.e., they serve the foreign market by contracting with an independent distributor. Compared to the benchmark cases, where tax authorities are either unable to audit firms or where they are able to audit them perfectly, the use of the OECD’s Comparable Uncontrolled Price (CUP) or Cost-Plus (CP) rule distorts firms’ output and pricing decisions. The reason is that the comparable arm’s length transactions between exporters and distributors, which serve as benchmarks, are not efficient. We show that implementing the CUP or CP rules is detrimental to consumers in the low tax country, yet benefits consumers in the high tax country.transfer pricing, OECD guidelines, multinationals and exporters, organizational choice, arm's length principle

Multilevel Bayesian framework for modeling the production, propagation and detection of ultra-high energy cosmic rays

Ultra-high energy cosmic rays (UHECRs) are atomic nuclei with energies over ten million times energies accessible to human-made particle accelerators. Evidence suggests that they originate from relatively nearby extragalactic sources, but the nature of the sources is unknown. We develop a multilevel Bayesian framework for assessing association of UHECRs and candidate source populations, and Markov chain Monte Carlo algorithms for estimating model parameters and comparing models by computing, via Chib's method, marginal likelihoods and Bayes factors. We demonstrate the framework by analyzing measurements of 69 UHECRs observed by the Pierre Auger Observatory (PAO) from 2004-2009, using a volume-complete catalog of 17 local active galactic nuclei (AGN) out to 15 megaparsecs as candidate sources. An early portion of the data ("period 1," with 14 events) was used by PAO to set an energy cut maximizing the anisotropy in period 1; the 69 measurements include this "tuned" subset, and subsequent "untuned" events with energies above the same cutoff. Also, measurement errors are approximately summarized. These factors are problematic for independent analyses of PAO data. Within the context of "standard candle" source models (i.e., with a common isotropic emission rate), and considering only the 55 untuned events, there is no significant evidence favoring association of UHECRs with local AGN vs. an isotropic background. The highest-probability associations are with the two nearest, adjacent AGN, Centaurus A and NGC 4945. If the association model is adopted, the fraction of UHECRs that may be associated is likely nonzero but is well below 50%. Our framework enables estimation of the angular scale for deflection of cosmic rays by cosmic magnetic fields; relatively modest scales of $\approx\!3^{\circ}$ to $30^{\circ}$ are favored. Models that assign a large fraction of UHECRs to a single nearby source (e.g., Centaurus A) are ruled out unless very large deflection scales are specified a priori, and even then they are disfavored. However, including the period 1 data alters the conclusions significantly, and a simulation study supports the idea that the period 1 data are anomalous, presumably due to the tuning. Accurate and optimal analysis of future data will likely require more complete disclosure of the data.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS654 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Symbolic Planning and Code Generation for Grounded Dialogue

Large language models (LLMs) excel at processing and generating both text and code. However, LLMs have had limited applicability in grounded task-oriented dialogue as they are difficult to steer toward task objectives and fail to handle novel grounding. We present a modular and interpretable grounded dialogue system that addresses these shortcomings by composing LLMs with a symbolic planner and grounded code execution. Our system consists of a reader and planner: the reader leverages an LLM to convert partner utterances into executable code, calling functions that perform grounding. The translated code's output is stored to track dialogue state, while a symbolic planner determines the next appropriate response. We evaluate our system's performance on the demanding OneCommon dialogue task, involving collaborative reference resolution on abstract images of scattered dots. Our system substantially outperforms the previous state-of-the-art, including improving task success in human evaluations from 56% to 69% in the most challenging setting.Comment: Accepted to EMNLP 202

Graphical Markov models, unifying results and their interpretation

Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing. Longitudinal observational studies as well as intervention studies are best modeled via a subclass called regression graph models and, especially traceable regressions. Regression graphs include two types of undirected graph and directed acyclic graphs in ordered sequences of joint responses. Response components may correspond to discrete or continuous random variables and may depend exclusively on variables which have been generated earlier. These aspects are essential when causal hypothesis are the motivation for the planning of empirical studies. To turn the graphs into useful tools for tracing developmental pathways and for predicting structure in alternative models, the generated distributions have to mimic some properties of joint Gaussian distributions. Here, relevant results concerning these aspects are spelled out and illustrated by examples. With regression graph models, it becomes feasible, for the first time, to derive structural effects of (1) ignoring some of the variables, of (2) selecting subpopulations via fixed levels of some other variables or of (3) changing the order in which the variables might get generated. Thus, the most important future applications of these models will aim at the best possible integration of knowledge from related studies.Comment: 34 Pages, 11 figures, 1 tabl

A Theory of Emergent In-Context Learning as Implicit Structure Induction

Scaling large language models (LLMs) leads to an emergent capacity to learn in-context from example demonstrations. Despite progress, theoretical understanding of this phenomenon remains limited. We argue that in-context learning relies on recombination of compositional operations found in natural language data. We derive an information-theoretic bound showing how in-context learning abilities arise from generic next-token prediction when the pretraining distribution has sufficient amounts of compositional structure, under linguistically motivated assumptions. A second bound provides a theoretical justification for the empirical success of prompting LLMs to output intermediate steps towards an answer. To validate theoretical predictions, we introduce a controlled setup for inducing in-context learning; unlike previous approaches, it accounts for the compositional nature of language. Trained transformers can perform in-context learning for a range of tasks, in a manner consistent with the theoretical results. Mirroring real-world LLMs in a miniature setup, in-context learning emerges when scaling parameters and data, and models perform better when prompted to output intermediate steps. Probing shows that in-context learning is supported by a representation of the input's compositional structure. Taken together, these results provide a step towards theoretical understanding of emergent behavior in large language models