# Homepage of Amit Moscovich Eiger

I am a Ph.D. candidate at the department of Computer Science and Applied Mathematics
at the Weizmann Institute of Science,
working with Prof. Boaz Nadler.
My research interests are in the theory of Statistics and Machine Learning, specifically in the development of new statistical tools and computational methods.

**contact:** moscovich (at gmail.com), office: 301, Ziskind building, Weizmann Institute of Science.

# Research

## Boundary crossing

Consider a one-dimensional homogeneous Poisson process.
How can we compute the boundary crossing probability of this process, given arbitrary boundaries from above and below?
Previously known methods can compute this probability in O(n^3) time, where **n** is an upper bound on the boundary functions.
In this work, we present a faster O(n^2 log n) algorithm.

Preprint on arXiv.org: http://arxiv.org/abs/1503.04363

Co-author: Boaz Nadler

This method has several potential applications, mainly in statistics, including the computation of exact p-values for continuous goodness-of-fit tests.

A fast C++ implementation of the algorithms discussed in the paper is available on github:
crossing-probability

## The calibrated Kolmogorov Smirnov test

Co-authors: Boaz Nadler, Clifford Spiegelman

### The calibrated what?

A continuous goodness-of-fit test that is uniformly sensitive throughout the entire range of the distribution.

Drop-in replacement for tests such as Kolmogorov-Smirnov, Anderson-Darling, Higher Criticism and others.

Particularly suited for the detection of alternatives that differ from the null hypothesis mainly at the tails of the distribution.

**Please email me if you are wondering whether or not CKS is applicable to your data (come on, don't be shy!)**

### Documentation

Preprint on arXiv.org: http://arxiv.org/abs/1311.3190

This paper presents the one-sided and two-sided CKS tests and proves asymptotic optimality under various alternatives. In addition to that, a practical method for the computation of one-sided p-values is given.

Slides I gave at the Weizmann department of Computer Science and Applied Math:
PDF,
LaTeX

Poster I presented at the 2014 "Structural Inference in Statistics: Adaptation and Efficiency" spring school:
PDF

### Reproducible research

Code for reproducing all of the figures in the paper: cks_paper_produce_figures.zip

### Code

Python CKS library