It’s time for the 227thÂ meeting of the American Astronomical Society! A number of BDNYC members are there to present talks and posters so be sure to check them out! In this post we list the times and dates various posters/talks so you can go check them. We’ll be posting links to the posters as well once the conference is over.

# Category Archives: Data Analysis

# BDNYC at AAS 225

BDNYC (and friends) are out in force for the 225th meeting of the American Astronomical Society!

Please come see our posters and talks (mostly on Monday). To whet your appetite, or if you missed them, here are some samplers:

**Munazza Alam** *(Monday, 138.40)*

High-Resolution Spectral Analysis of Red & Blue L Dwarfs

**Sara Camnasio** *(Monday, 138.39)*

Multi-resolution Analysis of Red and Blue L Dwarfs

**Kelle Cruz** and **Stephanie Douglas** *(Monday, 138.37)*

When good fits go wrong: Untangling Physical Parameters of Warm Brown Dwarfs

**Stephanie Douglas** *(Monday 138.19)*

Rotation and Activity in Praesepe and the Hyades

**Jackie Faherty** *(Talk, Monday 130.05)*

Clouds in the Coldest Brown Dwarfs

**Joe Filippazzo** *(Monday, 138.34)*

Fundamental Parameters for an Age Calibrated Sequence of the Lowest Mass Stars to the Highest Mass Planets

**Paige Giorla** *(Monday, 138.44)*

T Dwarf Model Fits for Spectral Standards at Low Spectral Resolution

**Kay Hiranaka** *(Talk, Monday 130.04D)*

Constraining the Properties of the Dust Haze in the Atmospheres of Young Brown Dwarfs

**Erini Lambrides** *(Thursday, 432.02)*

Can 3000 IR spectra unveil the connection between AGN and the interstellar medium of their host galaxies?

**Emily Rice** *(Tuesday, 243.02)*

STARtorialist: Astronomy Outreach via Fashion, Sci-Fi, & Pop Culture

**Adric Riedel** *(Monday, 138.38)*

The Young and the Red: What we can learn from Young Brown Dwarfs

# Uncertainty Propagation

All observations have associated uncertainties which must be propagated through your analysis to a an uncertainty on a final result. The principle of uncertainty propagation is fairly simple:

$$!\sigma_x^2 = \sigma_u^2\left(\frac{\partial x}{\partial u}\right)^2 + \sigma_v^2\left(\frac{\partial x}{\partial v}\right)^2+\dots +2\sigma_{uv}^2\left(\frac{\partial x}{\partial u}\right)\left(\frac{\partial x}{\partial v}\right)+\dots$$

The first two terms on the right are the averages of the squares of the deviations in x produced by the uncertainties in observables u and v respectively. The third term on the right is the average of the cross terms, which cancel out if u and v are uncorrelated. Thus in most situations, a reasonable approximation is:

$$!\sigma_x^2 = \sum\limits_u\sigma_u^2\left(\frac{\partial x}{\partial u}\right)^2$$

### Examples

A typical situation is the sum of two observables each with a multiplicative factor:

$$!x=au+bv$$

$$!\left(\frac{\partial x}{\partial u}\right)=a,\hspace{10pt}\left(\frac{\partial x}{\partial v}\right)=b$$

$$!\sigma_x = \sqrt{\sigma_u^2a^2 + \sigma_v^2b^2}$$

which is the oft used “summing in quadrature.”

Perhaps you have the product of two observables:

$$!x=auv+b$$

$$!\left(\frac{\partial x}{\partial u}\right)=av,\hspace{10pt}\left(\frac{\partial x}{\partial v}\right)=au$$

$$!\sigma_x = \sqrt{\sigma_u^2(av)^2 + \sigma_v^2(au)^2}=a\sqrt{\sigma_u^2v^2 + \sigma_v^2u^2}$$

Finally, perhaps you have the inverse of one observable times the exponential of another:

$$!x=\frac{a}{u}e^{bv}$$

$$!\left(\frac{\partial x}{\partial u}\right)=\left(-\frac{a}{u^2}\right)e^{bv},\hspace{10pt}\left(\frac{\partial x}{\partial v}\right)=\frac{a}{u}be^{bv}$$

$$!\sigma_x = \sqrt{\sigma_u^2\left(\frac{a}{u^2}e^{bv}\right)^2 + \sigma_v^2\left(\frac{a}{u}be^{bv}\right)^2}=\frac{a}{u}e^{bv}\sqrt{\frac{\sigma_u^2}{u^2}+\sigma_v^2b^2}$$

Easy!