Oct 23rd, 2009| 12:26 pm | Posted by hlee

I watched a movie in which one of the characters said, “*country A has nukes with 80% chance*” (perhaps, not 80% but it was a high percentage). One of the statements in that episode is that *people will not eat lettuce only if the 1% chance of e coli is reported, even lower. Therefore, with such a high percentage of having nukes, it is right to send troops to A.* This episode immediately brought me a thought about astronomers’ null hypothesis probability and their ways of concluding chi-square goodness of fit tests, likelihood ratio tests, or F-tests.

First of all, I’d like to ask how you would like to estimate the chance of having nukes in a country? What this 80% implies here? But, before getting to the question, I’d like to discuss computing the chance of e coli infection, first. Continue reading ‘The chance that A has nukes is p%’ »

Tags:

chances,

chi-square statistic,

composite likelihood,

delta chi-square,

F-test,

fiducial likelihood,

likelihood,

LRT,

p-value,

posterior,

prior Category:

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Uncertainty |

Comment
Mar 6th, 2009| 03:42 pm | Posted by hlee

Ah ha~ Once I questioned, “what is systematic error?” (see [Q] systematic error.) Thanks to L. Lyons’ work discussed in [ArXiv] Particle Physics, I found this paper, titled **Systematic Errors** describing the concept and statistical inference related to **systematic errors** in the field of particle physics. It, gladly, shares lots of similarity with high energy astrophysics. Continue reading ‘systematic errors’ »

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coverage,

Heinrich,

likelihood,

Lyons,

nuisance parameter,

objective priors,

p-value,

particle physics,

statistical error,

subjective priors,

systematic error Category:

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arXiv,

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Jul 1st, 2008| 10:10 pm | Posted by hlee

If getting the first derivative (score function) and the second derivative (empirical Fisher information) of a (pseudo) likelihood function is feasible and checking regularity conditions is viable, a test for global maximum (Li and Jiang, JASA, 1999, Vol. 94, pp. 847-854) seems to be a useful reference for verifying the best fit solution. Continue reading ‘A test for global maximum’ »

Jun 19th, 2008| 11:46 pm | Posted by hlee

While discussing different view points on the term, *clustering*, one of the conversers led me to his colleague’s poster. This poster (I don’t remember its title and abstract) was my favorite from all posters in the meeting. Continue reading ‘my first AAS. V. measurement error and EM’ »

Jun 18th, 2008| 01:00 pm | Posted by vlk

From Protassov et al. (2002, ApJ, 571, 545), here is a formal expression for the Likelihood Ratio Test Statistic,

**T**_{LRT} = -2 ln R(D,Θ_{0},Θ)

**R(D,Θ**_{0},Θ) = [ sup_{θεΘ}_{0} p(D|Θ_{0}) ] / [ sup_{θεΘ} p(D|Θ) ]

where D are an independent data sample, Θ are model parameters {θ_{i}, i=1,..M,M+1,..N}, and Θ_{0} form a subset of the model where θ_{i} = θ_{i}^{0}, i=1..M are held fixed at their nominal values. That is, Θ represents the full model and Θ_{0} represents the simpler model, which is a subset of Θ. R(D,Θ_{0},Θ) is the ratio of the maximal (technically, supremal) likelihoods of the simpler model to that of the full model.

Continue reading ‘Likelihood Ratio Test Statistic [Equation of the Week]’ »

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EotW,

Equation,

Equation of the Week,

F-test,

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likelihood ratio test,

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Protassov,

Rostislav Protassov Category:

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2 Comments
Jun 16th, 2008| 10:47 am | Posted by hlee

As Prof. Speed said, PCA is prevalent in astronomy, particularly this week. Furthermore, a paper explicitly discusses R, a popular statistics package. Continue reading ‘[ArXiv] 2nd week, June 2008’ »

Tags:

Bayesian evidence,

Binning,

broken power law,

cosmology,

K-S test,

LF,

lhs,

likelihood,

PCA,

power spectrum,

R,

SFH,

Sun,

Tully-Fisher Category:

arXiv,

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Mar 21st, 2008| 06:20 pm | Posted by hlee

Markov chain Monte Carlo (MCMC) never misses a week from recently astro-ph. A book titled *MCMC in astronomy* will be a best seller. There are, in addition, very interesting non MCMC preprints. Continue reading ‘[ArXiv] 3rd week, Mar. 2007’ »

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chi-sq,

Fourier Analysis,

GREAT08,

lensing,

likelihood,

misnomer,

Poisson noisy image,

sparse Category:

arXiv,

Cross-Cultural,

Jargon,

MCMC |

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Mar 5th, 2008| 04:46 pm | Posted by hlee

This is a quite long paper that I separated from [Arvix] 4th week, Feb. 2008:

[astro-ph:0802.3916] P. Carvalho, G. Rocha, & M.P.Hobso

**A fast Bayesian approach to discrete object detection in astronomical datasets – PowellSnakes I **

As the title suggests, it describes Bayesian source detection and provides me a chance to learn the foundation of source detection in astronomy. Continue reading ‘[ArXiv] A fast Bayesian object detection’ »

Tags:

Bayesian evidence,

coloured background,

CRLB,

decision theory,

filter,

Fisher informatoin,

likelihood,

PowellSnake,

prior,

simulated annealing,

SNR,

source detection,

state space,

Sunyaev-Zel'dovich effect,

symmetric loss,

templates Category:

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arXiv,

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Methods,

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Jan 25th, 2008| 12:37 pm | Posted by hlee

Only three papers this week. There were a few more with chi-square fitting and its error bars but excluded. Continue reading ‘[ArXiv] 4th week, Jan. 2008’ »

Jan 4th, 2008| 12:49 pm | Posted by hlee

It’s a rather short list, this week and I hope I can maintain this conciseness afterwards. Happy new year to everyone. Continue reading ‘[ArXiv] 1st week, Jan. 2008’ »

Aug 19th, 2007| 12:31 am | Posted by vlk

I think of Markov-Chain Monte Carlo (MCMC) as a kind of directed staggering about, a random walk with a goal. (Sort of like driving in Boston.) It is conceptually simple to grasp as a way to explore the posterior probability distribution of the parameters of interest by sampling only where it is worth sampling from. Thus, a major savings from brute force Monte Carlo, and far more robust than downhill fitting programs. It also gives you the error bar on the parameter for free. What could be better? Continue reading ‘An alternative to MCMC?’ »

Jul 16th, 2007| 03:31 pm | Posted by hlee

From arxiv/astro-ph:0707.2064v1

**Star Formation via the Little Guy: A Bayesian Study of Ultracool Dwarf Imaging Surveys for Companions ** by P. R. Allen.

I rather skip all technical details on ultracool dwarfs and binary stars, reviews on star formation studies, like initial mass function (IMF), astronomical survey studies, which Allen gave a fair explanation in arxiv/astro-ph:0707.2064v1 but want to emphasize that based on simple **Bayes’ rule** and careful set-ups for **likelihoods** and **priors** according to data (ultracool dwarfs), quite informative conclusions were drawn:

Continue reading ‘[ArXiv] Bayesian Star Formation Study, July 13, 2007’ »

Tags:

Bayesian,

binary,

dwarfs,

IMF,

likelihood,

prior,

star formation,

survey,

upper limit Category:

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