Data analysis: a Bayesian tutorial
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2007
|
| Edition: | 2. ed., reprinted |
| Series: | Oxford science publications
|
| Subjects: | |
| Online Access: | Weitere Informationen Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 246 S. graph. Darst. 24 cm |
| ISBN: | 0198568312 9780198568315 0198568320 9780198568322 |
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MARC
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Contents
PART I THE ESSENTIALS
1.
The basics
3
1.1
Introduction: deductive logic versus plausible reasoning
3
1.2
Probability: Cox and the rules for consistent reasoning
4
1.3
Corollaries:
Bayes'
theorem and marginalization
5
1.4
Some history:
Bayes,
Laplace and orthodox statistics
8
1.5
Outline of book
12
2.
Parameter estimation I
14
2.1
Example
1 :
is this a fair coin?
14
2.1.1
Different priors
17
2.1.2
Sequential or one-step data analysis?
19
2.2
Reliabilities: best estimates, error-bars and confidence intervals
20
2.2.1
The coin example
23
2.2.2
Asymmetric posterior pdfs
24
2.2.3 Multimodal
posterior pdfs
25
2.3
Example
2:
Gaussian noise and averages
26
2.3.1
Data with different-sized error-bars
29
2.4
Example
3:
the lighthouse problem
29
2.4.1
The central limit theorem
33
3.
Parameter estimation II
35
3.1
Example
4:
amplitude of a signal in the presence of background
35
3.1.1
Marginal distributions
39
3.1.2
Binning the data
42
3.2
Reliabilities: best estimates, correlations and error-bars
43
3.2.1
Generalization of the quadratic approximation
49
3.2.2
Asymmetric and
multimodal
posterior pdfs
50
3.3
Example
5:
Gaussian noise revisited
52
3.3.1
The Student-i and
χ2
distributions
54
3.4
Algorithms: a numerical interlude
55
3.4.1
Brute force and ignorance
56
3.4.2
The joys of linearity
57
3.4.3
Iterative linearization
58
3.4.4
Hard problems
60
3.5
Approximations: maximum likelihood and least-squares
61
3.5.1
Fitting a straight line
65
χ
Contents
3.6
Error-propagation: changing variables
68
3.6.1
A useful short cut
73
3.6.2
Taking the square root of a number
74
4.
Model selection
78
4.1
Introduction: the story of Mr A and Mr
В
78
4.1.1
Comparison with parameter estimation
83
4.1.2
Hypothesis testing
84
4.2
Example
6:
how many lines are there?
85
4.2.1
An algorithm
89
4.2.2
Simulated data
91
4.2.3
Real data
93
4.3
Other examples: means, variance, dating and so on
94
4.3.1
The analysis of means and variance
94
4.3.2
Luminescence dating
98
4.3.3
Interlude: what not to compute
100
5.
Assigning probabilities
103
5.1
Ignorance: indifference and transformation groups
103
5.1.1
The binomial distribution
107
5.1.2
Location and scale parameters
108
5.2
Testable information: the principle of maximum entropy
110
5.2.1
The monkey argument
113
5.2.2
The Lebesgue measure
115
5.3
MaxEnt examples: some common pdfs
117
5.3.1
Averages and exponentials
117
5.3.2
Variance and the Gaussian distribution
118
5.3.3
MaxEnt and the binomial distribution
120
5.3.4
Counting and
Poisson
statistics
121
5.4
Approximations: interconnections and simplifications
121
5.5
Hangups: priors versus likelihoods
124
5.5.1
Improper pdfs
124
5.5.2
Conjugate and reference priors
125
PART II ADVANCED TOPICS
6.
Non-parametric estimation
129
6.1
Introduction: free-form solutions
129
6.1.1
Singular value decomposition
130
6.1.2
A parametric free-form solution?
135
6.2
MaxEnt: images, monkeys and a non-uniform prior
136
6.2.1
Regularization
138
6.3
Smoothness: fuzzy pixels and spatial correlations
140
6.3.1
Interpolation
141
6.4
Generalizations: some extensions and comments
142
Contents xi
6.4.1
Summary of the basic strategy
144
6.4.2
Inference or inversion?
145
6.4.3
Advanced examples
148
7.
Experimental design
149
7.1
Introduction: general issues
149
7.2
Example
7:
optimizing resolution functions
151
7.2.
1 An isolated sharp peak
152
7.2.2
A free-form solution
156
7.3
Calibration, model selection and binning
161
7.4
Information gain: quantifying the worth of an experiment
163
8.
Least-squares extensions
165
8.1
Introduction: constraints and restraints
165
8.2
Noise scaling: a simple global adjustment
166
8.3
Outliers: dealing with erratic data
167
8.3.1
A conservative formulation
168
8.3.2
The good-and-bad data model
171
8.3.3
The Cauchy formulation
172
8.4
Background removal
173
8.5
Correlated noise: avoiding over-counting
174
8.5.1
Nearest-neighbour correlations
175
8.5.2
An elementary example
176
8.5.3
Time series
177
8.6
Log-normal: least-squares for magnitude data
179
9.
Nested sampling
181
9.1
Introduction: the computational problem
181
9.1.1
Evidence and posterior
182
9.2
Nested sampling: the basic idea
184
9.2.1
Iterating a sequence of objects
185
9.2.2
Terminating the iterations
186
9.2.3
Numerical uncertainty of computed results
187
9.2.4
Programming nested sampling in'C'
188
9.3
Generating a new object by random sampling
190
9.3.1
Markov chain Monte Carlo (MCMC) exploration
191
9.3.2
Programming the lighthouse problem in'C'
192
9.4
Monte Carlo sampling of the posterior
195
9.4.1
Posterior distribution
196
9.4.2
Equally-weighted posterior samples: staircase sampling
197
9.4.3
The lighthouse posterior
198
9.4.4
Metropolis exploration of the posterior
199
9.5
How many objects are needed?
200
9.5.1
Bi-modal likelihood with a single'gate'
200
9.5.2
Multi-modal likelihoods with several 'gates'
201
xii Contents
9.6
Simulated annealing
203
9.6.1
The problem of phase changes
203
9.6.2
Example: order/disorder in a pseudo-crystal
204
9.6.3
Programming the pseudo-crystal in 'C'
206
10.
Quantification
209
10.1
Exploring an intrinsically non-uniform prior
209
10.1.1
Binary trees for controlling MCMC transitions
210
10.2
Example: ON/OFF switching
212
10.2.1
The master engine: flipping switches individually
212
10.2.2
Programming which components are present
212
10.2.3
Another engine: exchanging neighbouring switches
215
10.2.4
The control of multiple engines
216
10.3
Estimating quantities
216
10.3.1
Programming the estimation of quantities in'C'
218
10.4
Final remarks
223
A. Gaussian integrals
224
A.
1
The univariate case
224
A.2 The bivariate extension
225
A.3 The multivariate generalization
226
B. Cox's derivation of probability
229
B.
1
Lemma
1 :
associativity equation
232
B.2 Lemma
2:
negation
235
Bibliography
237
Index
241 |
| any_adam_object | 1 |
| author | Sivia, Deviderjit S. Skilling, John |
| author_GND | (DE-588)143731424 |
| author_facet | Sivia, Deviderjit S. Skilling, John |
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| ctrlnum | (OCoLC)643229429 (DE-599)BVBBV037403551 |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed., reprinted |
| format | Book |
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| language | English |
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| spelling | Sivia, Deviderjit S. Verfasser (DE-588)143731424 aut Data analysis a Bayesian tutorial D. S. Sivia with J. Skilling 2. ed., reprinted Oxford [u.a.] Oxford Univ. Press 2007 XII, 246 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Oxford science publications Hier auch später erschienene, unveränderte Nachdrucke Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Datenanalyse (DE-588)4123037-1 s Bayes-Verfahren (DE-588)4204326-8 s 1\p DE-604 Bayes-Entscheidungstheorie (DE-588)4144220-9 s 2\p DE-604 Skilling, John Verfasser aut http://www.inference.phy.cam.ac.uk/bayesys/ Weitere Informationen Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022556158&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sivia, Deviderjit S. Skilling, John Data analysis a Bayesian tutorial Bayes-Verfahren (DE-588)4204326-8 gnd Datenanalyse (DE-588)4123037-1 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| subject_GND | (DE-588)4204326-8 (DE-588)4123037-1 (DE-588)4144220-9 |
| title | Data analysis a Bayesian tutorial |
| title_auth | Data analysis a Bayesian tutorial |
| title_exact_search | Data analysis a Bayesian tutorial |
| title_full | Data analysis a Bayesian tutorial D. S. Sivia with J. Skilling |
| title_fullStr | Data analysis a Bayesian tutorial D. S. Sivia with J. Skilling |
| title_full_unstemmed | Data analysis a Bayesian tutorial D. S. Sivia with J. Skilling |
| title_short | Data analysis |
| title_sort | data analysis a bayesian tutorial |
| title_sub | a Bayesian tutorial |
| topic | Bayes-Verfahren (DE-588)4204326-8 gnd Datenanalyse (DE-588)4123037-1 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| topic_facet | Bayes-Verfahren Datenanalyse Bayes-Entscheidungstheorie |
| url | http://www.inference.phy.cam.ac.uk/bayesys/ http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022556158&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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