The Augmented Synthetic Control Method

The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings. The "synthetic control" is a weighted average of control units that balances the treated unit's pre-treatment outcomes as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pre-treatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings where such pre-treatment fit is infeasible. Analogous to bias correction for inexact matching, Augmented SCM uses an outcome model to estimate the bias due to imperfect pre-treatment fit and then de-biases the original SCM estimate. Our main proposal, which uses ridge regression as the outcome model, directly controls pre-treatment fit while minimizing extrapolation from the convex hull. This estimator can also be expressed as a solution to a modified synthetic controls problem that allows negative weights on some donor units. We bound the estimation error of this approach under different data generating processes, including a linear factor model, and show how regularization helps to avoid over-fitting to noise. We demonstrate gains from Augmented SCM with extensive simulation studies and apply this framework to estimate the impact of the 2012 Kansas tax cuts on economic growth. We implement the proposed method in the new augsynth R package

Conditioned stochastic particle systems and integrable quantum spin systems

We consider from a microscopic perspective large deviation properties of several stochastic interacting particle systems, using their mapping to integrable quantum spin systems. A brief review of recent work is given and several new results are presented: (i) For the general disordered symmectric exclusion process (SEP) on some finite lattice conditioned on no jumps into some absorbing sublattice and with initial Bernoulli product measure with density $\rho$ we prove that the probability $S_\rho(t)$ of no absorption event up to microscopic time $t$ can be expressed in terms of the generating function for the particle number of a SEP with particle injection and empty initial lattice. Specifically, for the symmetric simple exclusion process on $\mathbb Z$ conditioned on no jumps into the origin we obtain the explicit first and second order expansion in $\rho$ of $S_\rho(t)$ and also to first order in $\rho$ the optimal microscopic density profile under this conditioning. For the disordered ASEP on the finite torus conditioned on a very large current we show that the effective dynamics that optimally realizes this rare event does not depend on the disorder, except for the time scale. For annihilating and coalescing random walkers we obtain the generating function of the number of annihilated particles up to time $t$, which turns out to exhibit some universal features.Comment: 25 page

Robust Chauvenet Outlier Rejection

Sigma clipping is commonly used in astronomy for outlier rejection, but the number of standard deviations beyond which one should clip data from a sample ultimately depends on the size of the sample. Chauvenet rejection is one of the oldest, and simplest, ways to account for this, but, like sigma clipping, depends on the sample's mean and standard deviation, neither of which are robust quantities: Both are easily contaminated by the very outliers they are being used to reject. Many, more robust measures of central tendency, and of sample deviation, exist, but each has a tradeoff with precision. Here, we demonstrate that outlier rejection can be both very robust and very precise if decreasingly robust but increasingly precise techniques are applied in sequence. To this end, we present a variation on Chauvenet rejection that we call "robust" Chauvenet rejection (RCR), which uses three decreasingly robust/increasingly precise measures of central tendency, and four decreasingly robust/increasingly precise measures of sample deviation. We show this sequential approach to be very effective for a wide variety of contaminant types, even when a significant -- even dominant -- fraction of the sample is contaminated, and especially when the contaminants are strong. Furthermore, we have developed a bulk-rejection variant, to significantly decrease computing times, and RCR can be applied both to weighted data, and when fitting parameterized models to data. We present aperture photometry in a contaminated, crowded field as an example. RCR may be used by anyone at https://skynet.unc.edu/rcr, and source code is available there as well.Comment: 62 pages, 48 figures, 7 tables, accepted for publication in ApJ

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts. --project scheduling,modeling,resource constraints,temporal constraints,networks

Algorithms for scheduling projects with generalized precedence relations.

Project scheduling under the assumption of renewable resource constraints and generalized precedence relations, i.e. arbitrary minimal and maximal time lags between the starting and completion times of the activities of the project, constitutes an important and challenging problem. Over the past few years considerable progress has been made in the use of exact solution procedure for this problem type and its variants. We review the fundamental logic and report new computational experience with a branch-and-bound procedure for optimally solving resource-constrained project scheduling problems with generalized precedence relations of the precedence diagramming type, i.e. start-start, start-finish, finish-start and finish-finish relations with minimal time lags for minimizing the project makespan. Subsequently, we review and report new results for several branch-and -bound procedures for the case of generalized precedence relations, including both minimal and maximal time lags, and demonstrate how the solution methodology can be expected to cope with other regular and nonregular objective functions such a smaximizing the net present value of a project.Networks; Problems; Scheduling; Algorithms; Functions; Net present value;