Topics covered:
This week we are going to be discussing how to interpret and estimate measurement uncertainties.
The statistical technique that will well cover is uncertainty propagation.
These topics are covered in chapters 3 and 4 of: “Measurements and Their Uncertainties : A Practical Guide to Modern Error Analysis” which is available online via the Stanford bookstore. You don’t need to read those chapters, but you may find them a useful reference, and they present the material in a somewhat different way than we will be presenting it, which you might find more intuitive.
We will also be measuring the area of the desk or table that we are working at using a rather complicated (and inaccurate) technique that captures some of the difficulty in measuring the Hubble constant, and in particular the “distance ladder” that is used to calibrate the distances to faraway galaxies.
We will also briefly mention the gamma-ray pulsar, Vela, which we will be seeing more of next week.
We will not be using a lot of new python functions this week. Here are the important ones that we will be using.
| Function Name | What it does |
|---|---|
| numpy.std | Compute the standard deviation of the values in an array |
| numpy.var | Compute the variance of the values in an array |
| numpy.random.normal | Generate random numbers from a normal or ‘Gaussian’ distribution |
| array.size | return the number of elements in an array |
| array.shape | return the shape of an array, i.e., arrays can have more that one dimension and this function tells you the shape of the array. The size of the array is the product of the size of all the axes of the array |
| plt.imshow | Plot a 2-dimensional array of values as a color image |
| plt.colorbar | Attach an color axes label to a figure |
| plt.legend | Attach a legend to a figure |