Statistical parameter | EPFL Graph Search

In statistics, as opposed to its general use in mathematics, a parameter is any measured quantity of a statistical population that summarises or describes an aspect of the population, such as a mean or a standard deviation. If a population exactly follows a known and defined distribution, for example the normal distribution, then a small set of parameters can be measured which completely describes the population, and can be considered to define a probability distribution for the purposes of extracting samples from this population. A parameter is to a population as a statistic is to a sample; that is to say, a parameter describes the true value calculated from the full population, whereas a statistic is an estimated measurement of the parameter based on a sample. Thus a "statistical parameter" can be more specifically referred to as a population parameter. Suppose that we have an indexed family of distributions. If the index is also a parameter of the members of the family, then the family is a parameterized family. Among parameterized families of distributions are the normal distributions, the Poisson distributions, the binomial distributions, and the exponential family of distributions. For example, the family of normal distributions has two parameters, the mean and the variance: if those are specified, the distribution is known exactly. The family of chi-squared distributions can be indexed by the number of degrees of freedom: the number of degrees of freedom is a parameter for the distributions, and so the family is thereby parameterized. In statistical inference, parameters are sometimes taken to be unobservable, and in this case the statistician's task is to estimate or infer what they can about the parameter based on a random sample of observations taken from the full population. Estimators of a set of parameters of a specific distribution are often measured for a population, under the assumption that the population is (at least approximately) distributed according to that specific probability distribution.

Uncooperative Rendezvous in Space: Design of an Electronic Architecture for High Performance Avionic with Multi Sensor Input and Intensive Data Rate.

Michaël Yannick Juillard

Active Debris Removal missions consist of sending a satellite in space and removing one or more debris from their current orbit. A key challenge is to obtain information about the uncooperative target. By gathering the velocity, position, and rotation of the desired object, the satellite is able to plan its trajectory and define the sequence of approach. It requires the use of a variety of sensors with often a high data rate. For this task, a dedicated payload computer is envisioned with the responsibility of processing the information from the various rendezvous sensors. This component has the goal to provide meaningful information to the main satellite computer about the targeted debris. The focus of this work is on the data processing, the number of elements, and the electrical energy with constraints due to internal communication.First, an avionic testbench was built at the EPFL Space Center to assess early hardware and software architectures. The goal is to enable Hardware-In-the-Loop testing while developing the payload computer. A communication data bus has been implemented between the Platform and the Payload On-Board Computer. Emphasis was placed on the reliability of the high-level protocol and multiple concepts for improvement were analyzed.In a second phase, the testbench has been extended to support other data buses. The aim was to develop a reliable and efficient backup or fall-back data bus in case of failure in the main link. Four data buses have been tested with extensive analyses on their resilience to error and the efficiency of their data exchange.In parallel, extensive work has been performed to develop a simulation and optimization tool. Its goal is to support the design of payload avionic architectures for ADR missions by providing trade-offs and analyses. In the first iteration, a simulator has been created with instances of various high-level elements modeled.The second iteration introduced the additional dimension of optimization. It is trying to determine the best set of instruments and algorithms to use. With this capability, numerous analyses have been conducted on the influence of various parameters linked to the general optimizer behavior. It allows us to better understand the strength and limitations of the tool.The third step regarding the tool was to start its verification. The task has been to develop an Hardware-In-the-Loop architecture to compare its behavior with the results of the optimizer. The implementation of various mock-up algorithms enables the verification of their models in the tool. These analyses guarantee the feasibility of the outputted solution.The last part was dedicated to the creation and analysis of a realistic payload avionic architecture. The goal was to test the capability of the tool with hardware elements inspired by actual components. This work has shown the procedure to efficiently use the tool in the design phase of a mission.In conclusion, the work on the communication between the Payload and the Platform On-Board Computer has brought valuable lessons and experiences to the projects. They can now be used for the establishment of the high-level protocol into ClearSpace-1 flight software. In addition, the optimizer created allows tackling the design of complex payload avionic architecture where mass saving and processing resources are crucial. It is an essential point to develop a highly efficient payload computer for an Active Debris Removal satellite.

EPFL2022

Learning to Hit: A statistical Dynamical System based approach

Aude Billard, Michael Bosongo Bombile, Harshit Khurana

This paper proposes a manipulation scheme based on learning the motion of objects after being hit by a robotic end-effector. This allows for the object to be positioned at a desired location outside the physical workspace of the robot. An estimate of the object dynamics under friction and collisions is learnt and used to predict the desired hitting parameters (speed and direction), given the initial and desired location of the object. Based on the obtained hitting parameters, the desired pre-impact velocity of the end-effector is generated using a stable dynamical system. The performance of the proposed DS is validated in simulation and and is used to learn a model for hitting using real robot. The approach is tested on real robot with a KUKA LBR IIWA robot.

IEEE2021

Modeling Network Populations via Graph Distances

Sofia Charlotta Olhede

This article introduces a new class of models for multiple networks. The core idea is to parameterize a distribution on labeled graphs in terms of a Frechet mean graph (which depends on a user-specified choice of metric or graph distance) and a parameter that controls the concentration of this distribution about its mean. Entropy is the natural parameter for such control, varying from a point mass concentrated on the Frechet mean itself to a uniform distribution over all graphs on a given vertex set. We provide a hierarchical Bayesian approach for exploiting this construction, along with straightforward strategies for sampling from the resultant posterior distribution. We conclude by demonstrating the efficacy of our approach via simulation studies and two multiple-network data analysis examples: one drawn from systems biology and the other from neuroscience. This article has online.

AMER STATISTICAL ASSOC2020

Uncooperative Rendezvous in Space: Design of an Electronic Architecture for High Performance Avionic with Multi Sensor Input and Intensive Data Rate.

Michaël Yannick Juillard

EPFL2022