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1 |All Rights Reserved
OUTLINE
PART 1. The Five-Forces Framework
PART 2
DS-GA 1002 Lecture notes 5
Fall 2016
Random processes
1
Introduction
Random processes, also known as stochastic processes, allow us to model quantities that
evolve in time (or space) in an uncertain w
DS-GA 1002 Lecture notes 8
Fall 2016
Statistical Data Analysis
1
Descriptive statistics
In this section we consider the problem of analyzing a set of data. We describe several
techniques for visualizi
DS-GA 1002 Lecture notes 7
Fall 2016
Simulation
1
Introduction
Simulation is a powerful tool in probability and statistics. Probabilistic models are often too
complex for us to derive closed-form solu
DS-GA 1002 Lecture notes 0
Fall 2016
Linear Algebra
These notes provide a review of basic concepts in linear algebra.
1
Vector spaces
You are no doubt familiar with vectors in R2 or R3 , i.e.
1.1
2
DS-GA 1002 Lecture notes 6
Fall 2016
Convergence of random processes
1
Introduction
In these notes we study convergence of discrete random processes. This allows to characterize
phenomena such as the
DS-GA 1002 Lecture notes 10
Fall 2016
Hypothesis testing
In a medical study we observe that 10% of the women and 12.5% of the men suffer from
heart disease. If there are 20 people in the study, we wou
DS-GA 1002 Lecture notes 9
Fall 2016
Learning Models from Data
In this section we consider the problem of estimating distributions from data. This is a
crucial problem in statistics and in machine lea
DS-GA 1002 Lecture notes 12
Fall 2016
Linear regression
1
Linear models
In statistics, regression consists of learning a function relating a certain quantity of interest
y, the response or dependent v
DS-GA 1002 Lecture notes 11
Fall 2016
Bayesian statistics
In the frequentist paradigm we model the data as realizations from a distribution that
depends on deterministic parameters. In contrast, in Ba
4
Stochastic processes
In the previous two chapters, we discussed how probability measures can be
used to express our uncertainty in estimating quantities. We also introduced
some useful tools for cal
5
Bayesian inference
In this chapter, we dene Bayesian inference, explain what it is used for and
introduce some mathematical tools for applying it.
We are required to make inferences whenever we need
8
Data assimilation for
spatio-temporal processes
So far we have investigated the behaviour of data assimilation algorithms for
models with state space dimension Nz 3. Furthermore, we have investigate
6
Basic data assimilation algorithms
In this chapter, we return to the state estimation problem for dynamical systems as initially raised in Chapter 1. However, in contrast to Chapter 1, data
assimila
7
McKean approach to data
assimilation
The previous chapter introduced some well-established data assimilation algorithms. On the one hand, the Kalman lter provides a way to convert from a
forecast PD
2
Probability
B
The primitive theory
According to what I will call the primitive theory, the probability that a
trial or experiment will have a certain outcome is equal to the proportion
of possible r
4
Induction
B
The traditional problem of induction derives from Humes question:
What is the nature of that evidence which assures us of any real existence
and matter of fact beyond the present testimo
2
Introduction to probability
In the previous chapter we discussed how models can be used to interpolate data
from observations, and to make predictions about future states of physical systems. Since
5
Prediction
B
If a theory entails that a certain statement is true and it is known that the
statement is indeed true, this constitutes a reason to believe the theory.
However, various other factors m
3
Computational statistics
In Chapter 1 we introduced the idea of using models and data to estimate, or
predict, the state of a system in the past, present or future. We highlighted that
it is importa
3
Conrmation
B
Explications
If your unconditional degree of belief that elephants can y is lower than
your conditional degree of belief relative to the supposition that they have
wings, then, at least
6
Evidence
B
The evidential value of varied data
It is an undeniable element of scientic methodology that theories are
better conrmed by a broad variety of different sorts of evidence than by
a narrow
1
Methodology
B
Introduction
This book is about scientic knowledge, particularly the concept of
evidence. Its purpose is to explore scientic methodology in light of the
obvious yet frequently neglecte
7
Realism
B
There is no shortage of objections in the philosophical literature to the
general strategy and the particular concepts which have been employed
here. Some of these complaints have been air
1
Prologue: how to produce forecasts
This chapter sets out a simplied mathematical framework that allows us to
discuss the concept of forecasting and, more generally, prediction. Two key ingredients o
9
Dealing with imperfect models
Recall from our discussion in the Preface that Laplaces demon possessed (i) a
perfect mathematical model of the physical process under consideration, (ii) a
snapshot of