Lecture

Elements of Statistics: Exercises

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In course

MICRO-428: Metrology

The course deals with the concept of measuring in different domains, particularly in the electrical, optical, and microscale domains. The course will end with a perspective on quantum measurements, which could trigger the ultimate revolution in metrology. ...

Description

This lecture covers exercises related to statistics, including the usefulness of Bayes' Theorem in determining the probability of defective devices, moment generating functions for normal distributions, and calculations involving missed photon counts in single photon detectors. The exercises also involve rare disease probabilities and demonstrating properties of skew and kurtosis in distributions. Additionally, students are tasked with reproducing various random variable distributions using Matlab.

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Instructors (3)

Claudio Bruschini

Claudio Bruschini holds an MSc in high energy physics from the University of Genova and a PhD in Applied Sciences from the Vrije Universiteit Brussel (VUB). He started his career with INFN (Italy, 1993), in the WA92 CERN collaboration (particle physics), and then moved to CERN as a Fellow in the European GP-MIMD2 project, attached to the NA48 collaboration (particle physics, parallel programming, 1994-1995). He then started his close collaboration with EPFL, first in the DeTeC (Demining Technology Center) project (sensors for landmine detection/humanitarian demining, 1996-1997). After DeTeC's end, he started the first of a series of fruitful collaborations with the Vrije Universiteit Brussel (VUB) on humanitarian demining related R&D (1998). This was followed by the EUDEM survey project (The European Union in Humanitarian Demining, 1998), the EUDEM2 three year EC sponsored support measure (www.eudem.info, 2001-2004), and the DELVE support action (www.delve.vub.ac.be, 2007). In parallel he started working within the EPFL's AQUA group (Advanced Quantum Architectures, Edoardo Charbon), on topics as diverse as ultrasonic sensors for in-air application, optical 3D and high speed 2D sensing, sensor networks, or tracking/motion capture systems, in particular for the preparation of research projects. This culminated in the European MEGAFRAME (www.megaframe.eu, FP6, 2006-2010, SPAD arrays and related in-pixel time stamping electronics in deep submicron CMOS technology) and SPADnet (www.spadnet.eu, FP7, 2010-2014, networked SPAD arrays for Positron Emission Tomography) projects, coordinated by EPFL-AQUA. As from 2009 he also worked with Dario Floreano on the management of the CURVACE Curved Artificial Compound Eyes FP7 project (www.curvace.org), coordinated by EPFL-LIS. He was also active with CHUV (Lausanne University Hospital) within EndoTOFPET-US (endoscopic PET) as well as on a CTI project devoted to the development of a new hand-held standalone tool for tracer-guided medical procedures. In 2014 he had also the pleasure of joining the EPFL ICLAB of Christian Enz during its ramp-up phase, collaborating on device related topics (SNF GigaRadMOST) and biomedical R&D (NanoTera WiseSkin). Claudio is now fully with EPFL’s Advanced Quantum Architecture (AQUA). He has also been active as independent scientific consultant, under the label CBR Scientific Consulting, on the preparation of (European) R&D project proposals and the execution of individual studies, and worked in 2006 for a local start-up as operations manager and R&D advisor.... but this is another story. An unauthorized early biography is available at http://lami.epfl.ch/team/claudiob/...

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

Moment (mathematics)

In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph. If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia. If the function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized moment is the skewness, and the fourth standardized moment is the kurtosis.

Conditional probability

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(AB) or occasionally P_B(A).

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.

Kurtosis

In probability theory and statistics, kurtosis (from κυρτός, kyrtos or kurtos, meaning "curved, arching") is a measure of the "tailedness" of the probability distribution of a real-valued random variable. Like skewness, kurtosis describes a particular aspect of a probability distribution. There are different ways to quantify kurtosis for a theoretical distribution, and there are corresponding ways of estimating it using a sample from a population. Different measures of kurtosis may have different interpretations.

Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.

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