arXiv subjects

Adam Lane

Publications and source records attributed to Adam Lane.

6 recordsLinked to original sources

arXiv2025

On the Evidence for Violation of the Equivalence Principle in Disk Galaxies

We examine the claimed observations of a gravitational external field effect (EFE) reported in Chae et al. We show that observations suggestive of the EFE can be interpreted without violating Einstein's equivalence principle, namely from known correlations between morphology, environment and dynamics of galaxies. While Chae et al's analysis provides a valuable attempt at a clear test of Modified Newtonian Dynamics, an evidently important topic, a re-analysis of the observational data does not permit us to confidently assess the presence of an EFE or to distinguish this interpretation from that proposed in this article.

gr-qc↗

arXiv2022

Efficiency Requires Adaptation

The majority of historical designs are a priori in nature, where a priori indicates a design can be specified in advance of the experiment. The conventional wisdom is that the set of a priori designs is sufficient to produce efficient experiments. This work challenges this convention and finds that efficiency requires data dependent strategies. Specifically, in the context of a sequential experiment, where observations are accrued in a series of runs, an adaptive design is proposed that is guaranteed to be more efficient than any corresponding a priori design.

stat.ME↗

arXiv2021

Optimal Relevant Subset Designs in Nonlinear Models

Fisher (1934) argued that certain ancillary statistics form a relevant subset, a subset of the sample space on which inference should be restricted, and showed that conditioning on their observed value reduces the dimension of the data without a loss of information. The use of ancillary statistics in post-data inference has received significant attention; however, their role in the design of the experiment has not been well characterized. Ancillary statistics are unknown prior to data collection and as a result cannot be incorporated into the design a priori. However, if the data are observed sequentially then the ancillary statistics based on the data from the preceding observations can be used to determine the design assignment for the current observation. The main results of this work describe the benefits of incorporating ancillary statistics, specifically, the ancillary statistic that constitutes a relevant subset, into an adaptive design.

stat.ME↗

arXiv2019

Efficiency of Observed Information Adaptive Designs

In this work the primary objective is to maximize the precision of the maximum likelihood estimate in a linear regression model through the efficient design of the experiment. One common measure of precision is the unconditional mean square error. Unconditional mean square error has been a primary motivator for optimal designs; commonly, defined as the design that maximizes a concave function of the expected Fisher information. The inverse of expected Fisher information is asymptotically equal to the mean square error of the maximum likelihood estimate. There is a substantial amount of existing literature that argues the mean square error conditioned on an appropriate ancillary statistic better represents the precision of the maximum likelihood estimate. Despite evidence in favor of conditioning, limited effort has been made to find designs that are optimal with respect to conditional mean square error. The inverse of observed Fisher information is a higher order approximation of the conditional mean square error than the inverse of expected Fisher information [Efron and Hinkley (1978)]. In light of this, a more relevant objective is to find designs that optimize observed Fisher information. Unlike expected Fisher information, observed Fisher information depends on the observed data and cannot be used to design an experiment completely in advance of data collection. In a sequential experiment the observed Fisher information from past observations is available to inform the design of the next observation. In this work an adaptive design that incorporates observed Fisher information is proposed for linear regression models. It is shown that the proposed design is more efficient, at the limit, than any fixed design, including the optimal design, with respect to conditional mean square error.

stat.ME↗

arXiv2019

Conditional Information and Inference in Response-Adaptive Allocation Designs

Response-adaptive allocation designs refer to a class of designs where the probability an observation is assigned to a treatment is changed throughout an experiment based on the accrued responses. Such procedures result in random treatment sample sizes. Most of the current literature considers unconditional inference procedures in the analysis of response-adaptive allocation designs. The focus of this work is inference conditional on the observed treatment sample sizes. The inverse of information is a description of the large sample variance of the parameter estimates. A simple form for the conditional information relative to unconditional information is derived. It is found that conditional information can be greater than unconditional information. It is also shown that the variance of the conditional maximum likelihood estimate can be less than the variance of the unconditional maximum likelihood estimate. Finally, a conditional bootstrap procedure is developed that, in the majority of cases examined, resulted in narrower confidence intervals than relevant unconditional procedures.

stat.ME↗

arXiv2017

Adaptive Designs for Optimal Observed Fisher Information

Expected Fisher information can be found a priori and as a result its inverse is the primary variance approximation used in the design of experiments. This is in contrast to the common claim that the inverse of observed Fisher information is a better approximation to the variance of the maximum likelihood estimator. Observed Fisher information cannot be known a priori; however, if an experiment is conducted sequentially (in a series of runs) the observed Fisher information from previous runs is available. In the current work two adaptive designs are proposed that use the observed Fisher information from previous runs in the design of the current run.

stat.ME↗