Related papers: Markov basis for design of experiments with three-…
In a general fractional factorial design, the $n$-levels of a factor are coded by the $n$-th roots of the unity. This device allows a full generalization to mixed-level designs of the theory of the polynomial indicator function which has…
Motivated by the work of Boston, Jones and Goksel, we propose a Markov model for the factorisation of post-critically finite (PCF) cubic polynomials f. Using the information encoded in the critical orbits, we define a Markov model for PCF…
Bipartite experiments arise in various fields, in which the treatments are randomized over one set of units, while the outcomes are measured over another separate set of units. However, existing methods often rely on strong model…
We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with…
We propose identification robust statistics for testing hypotheses on the risk premia in dynamic affine term structure models. We do so using the moment equation specification proposed for these models in Adrian et al. (2013). We extend the…
This article provides an introductory tutorial on structural results in partially observed Markov decision processes (POMDPs). Typically, computing the optimal policy of a POMDP is computationally intractable. We use lattice program- ming…
A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures…
Consider a setting where there are $N$ heterogeneous units and $p$ interventions. Our goal is to learn unit-specific potential outcomes for any combination of these $p$ interventions, i.e., $N \times 2^p$ causal parameters. Choosing a…
Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of…
In many fields$\unicode{x2013}$including genomics, epidemiology, natural language processing, social and behavioral sciences, and economics$\unicode{x2013}$it is increasingly important to address causal questions in the context of factor…
A computer code can simulate a system's propagation of variation from random inputs to output measures of quality. Our aim here is to estimate a critical output tail probability or quantile without a large Monte Carlo experiment. Instead,…
Psychosocial constructs can only be assessed indirectly, and measures are typically formed by a combination of indicators that are thought to relate to the construct. Reflective and formative measurement models offer different…
This paper presents a focused review of Markov random fields (MRFs)--commonly used probabilistic representations of spatial dependence in discrete spatial domains--for categorical data, with an emphasis on models for binary-valued…
In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component…
We consider a vector of $N$ independent binary variables, each with a different probability of success. The distribution of the vector conditional on its sum is known as the conditional Bernoulli distribution. Assuming that $N$ goes to…
We investigate the complexity of covariance matrix estimation for Gibbs distributions based on dependent samples from a Markov chain. We show that when $\pi$ satisfies a Poincar\'e inequality and the chain possesses a spectral gap, we can…
Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with…
Given two 2-level factors of interest, a 2^2 split-plot design} (a) takes each of the $2^2=4$ possible factorial combinations as a treatment, (b) identifies one factor as `whole-plot,' (c) divides the experimental units into blocks, and (d)…
We propose approaches for testing implementations of Markov Chain Monte Carlo methods as well as of general Monte Carlo methods. Based on statistical hypothesis tests, these approaches can be used in a unit testing framework to, for…
We provide a scheme for inferring causal relations from uncontrolled statistical data based on tools from computational algebraic geometry, in particular, the computation of Groebner bases. We focus on causal structures containing just two…