TAILIEUCHUNG - Ebook Data reduction and error analysis for the physical sciences (3rd edition): Part 2

(BQ) Part 2 book "Data reduction and error analysis for the physical sciences" has contents: Least-Squares fit to an arbitrary function, fitting composite curves, direct application of the maximum likelihood method, testing the fit. | CHAPTER 8 LEAST-SQUARES FIT TO AN ARBITRARY FUNCTION NONLINEAR FITTING The methods of least squares and multiple regression developed in the previous chapters are restricted to fitting functions that are linear in the parameters as in Equation m y x a7T x 8-1 j i This limitation is imposed by the fact that in general minimizing X2 can yield a set of coupled equations that are linear in the m unknown parameters only if the fitting functions y jr are themselves linear in the parameters. We shall distinguish between the two types of problems by referring to linear fitting for problems that involve equations that are linear in the parameters such as those discussed in Chapters 6 and 7 and nonlinear fitting for those problems that are nonlinear in the parameters. Example . In a popular undergraduate physics laboratory experiment a real silver quarter is irradiated with thermal neutrons to create two short-lived isotopes of silver 47Ag108 and 47Ag that subsequently decay by beta emission. Students count the emitted beta particles in 15-s intervals for about 4 min to obtain a decay curve. Data collected from such an experiment are listed in Table and plotted on a semi-logarithmic graph in Figure . The data are reported at the end of each 15-s interval just as they were recorded by a scaler. The data points do not fall on a straight 142 Least-Squares Fit to an Arbitrary Function 143 Time s FIGURE Number of counts detected from the decay of two excited states of silver as a function of time Example . Time is reported at the end of each interval. Statistical uncertainties are assumed. The curve was obtained by a nonlinear least-squares fit of Equation to the data. line because the probability function that describes the process is the sum of two exponential functions plus a constant background. We can represent the decay by the fitting function y x a J a2e t ữi a e a where the parameter dị corresponds to the background radiation and a2 and 3

• Toán học
• Data reduction
• Error analysis
• Probability distributions
• error analysis
• Least Squares fit
• Arbitrary function
• Fitting composite curves
• Direct application
• An Overview on Time Series Data Mining
• Similarity Search in Time Series Data
• Feature based Dimensionality Reduction
• Other Time Series Data Mining Tasks
• Data Mining
• Monte carlo techniques
• Information sciences
• Performance evaluation of methods
• Integrative dimension reduction
• Performance evaluation
• Dimension reduction
• Multi source data
• Journal of Earth Sciences
• Aeromagnetic survey
• Drape flying
• Level flying
• Terrain effect
• Uneven surface
• Nearest neighbor based classifiers
• Nearest Neighbor algorithm
• Variants of the NN algorithm
• Prototype reduction
• Z score normalization
• Journal of Automation and Control Engineering
• Interference reduction in tilt measurement
• The sensor mounting method and calculation formulas
• High resolution data
• High speed response
• Damage assessment
• Frame structure
• Incomplete modal data
• TeachingLearning based optimization
• Model reduction
• Objective function
• BMC Bioinformatics
• Coverage reduction
• Single cell
• Multiple displacement amplification
• Deep shotgun sequencing
• Next generation sequencing
• Energy consumption
• Panel data
• BRICS nations
• Energy consumption poverty reduction nexus
• Economic growth
• Lecture Data mining
• Bài giảng Khai thác dữ liệu
• Dimensionality reduction
• High dimensional datasets
• Multi dimensional scaling
• Lecture Data mining and analysis
• Khai thác dữ liệu
• Data analysis foundations
• Frequent pattern mining
• High dimensional data
• Stability selection
• Principal covariates regression
• Principal component analysis
• Structural information
• Genomic data
• Pattern recognition
• Genotype data
• Analyst’s toolbox
• Principle Component Analysis
• Integration of Omics data
• Latent variable regression
• Underlying systems biology
• RNA Seq
• Research methods
• Lecture Research methods
• Phương pháp nghiên cứu
• Bài giảng Phương pháp nghiên cứu
• Analysing qualitative data
• policy recommendations
• a data rich assessment
• reduction in poverty
• Structural change
• global economy
• Foreign investors
• Báo cáo sinh học hay
• cách trình bày báo cáo
• báo cáo sinh học
• công trình nghiên cứu sinh học
• tài liệu về sinh học
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• báo cáo khoa học
• Reference astrometry
• velocity determinations
• Coma parallaxes
• Refocusing instances
• Gyro properties
• astrometric catalogues