arXiv subjects

Joe Marion

Publications and source records attributed to Joe Marion.

3 recordsLinked to original sources

arXiv2024

Predictive Probabilities Made Simple: A Fast and Accurate Method for Clinical Trial Decision Making

Bayesian predictive probabilities are commonly used for interim monitoring of clinical trials through efficacy and futility stopping rules. Despite their usefulness, calculation of predictive probabilities, particularly in pre-experiment trial simulation, can be a significant challenge. We introduce an approximation for computing predictive probabilities using either a p-value or a posterior probability that significantly reduces this burden. We show the approximation has a high degree of concordance with standard Monte Carlo imputation methods for computing predictive probabilities, and present five simulation studies comparing the approximation to the full predictive probability for a range of primary analysis strategies: dichotomous, time-to-event, and ordinal endpoints, as well as historical borrowing and longitudinal modeling. We find that this faster method of predictive probability approximation works well in all five applications, thus significantly reducing the computational burden of trial simulation, allowing more virtual trials to be simulated to achieve greater precision in estimating trial operating characteristics.

stat.AP↗

arXiv2018

Finite Sample Bounds for Sequential Monte Carlo and Adaptive Path Selection Using the $L_2$ Norm

We prove a bound on the finite sample error of sequential Monte Carlo (SMC) on static spaces using the $L_2$ distance between interpolating distributions and the mixing times of Markov kernels. This result is unique in that it is the first finite sample convergence result for SMC that does not require an upper bound on the importance weights. Using this bound we show that careful selection of the interpolating distributions can lead to substantial improvements in the computational complexity of the algorithm. This result also justifies the adaptive selection of SMC distributions using the relative effective sample size commonly used in the literature, and we establish conditions guaranteeing the approximation accuracy of the adaptive SMC approach. We show that the commonly used data tempering approach fails to satisfy these conditions, and introduce a modified data tempering algorithm under which our guarantees do hold. We then demonstrate empirically that this procedure provides nearly-optimal sequences of distributions in an automatic fashion for realistic examples.

stat.CO↗

arXiv2018

Finite Sample Complexity of Sequential Monte Carlo Estimators

We present bounds for the finite sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties of the associated Markov kernels. This allows us to give the first finite sample comparison to other Monte Carlo schemes. We obtain bounds for the complexity of sequential Monte Carlo approximations for a variety of target distributions including finite spaces, product measures, and log-concave distributions including Bayesian logistic regression. The bounds obtained are within a logarithmic factor of similar bounds obtainable for Markov chain Monte Carlo.

stat.CO↗