on 22-Feb-2017 (Wed)

One way of thinking about this assumption is as follows: We assume that every datum is equally representative of the underlying process, regardless of when the datum was observed, and regardless of any data observed before or after.

a general phenomenon in Bayesian inference: The posterior is a compromise between the prior distribution and the likelihood function.

The compromise favors the prior to the extent that the prior distribution is sharply peaked and the data are few. The compromise favors the likelihood function (i.e., the data) to the extent that the prior distribution is flat and the data are many.

the mode of the posterior distribution is between the mode of the prior distribution and the mode of the likelihood function, but the posterior mode is closer to the likelihood mode for larger sample sizes

the width of the posterior highest density intervals (HDI) is smaller for the larger sample size. Even though both samples of data showed 25% heads, the larger sample implied a smaller range of credible underlying biases

In general, the more data we have, the more precise is the estimate of the parameter(s) in the model. Larger sample sizes yield greater precision or certainty of estimation

You can use logical vectors to extract a selection of rows or columns from a ma- trix, for example, if a is the original 3-by-3 matrix defined above, the statement a(:, logical([1 0 1])) results in ans = 13 46 79 (first and third columns extracted)

the functions zeros, ones and rand generate matrices of 1s, 0s and random numbers, respectively. With a single argument n, they generate n × n (square) matrices. With two arguments n and m they generate n × m ma- trices.

For very large matrices repmat is usually faster than ones and zeros.

The function eye(n) generates an n × n identity matrix, i.e., a matrix with 1s on the main ‘diagonal’, and 0s everywhere else

pascal(n) generates a Pascal matrix of order n. Technically, this is a symmetric positive definite matrix with entries made up from Pascal’s triangle

magic(n) generates an n × n magic square

the statement all(a) results in ans = 001 For each column of a where all the elements are true (non-zero) all returns 1, otherwise it returns 0. all therefore returns a logical vector when it takes a matrix argument. To test if all the elements of a are true, use all twice

diag extracts or creates a diagonal

fliplr flips from left to right

flipud flips from top to bottom

rot90 rotates.

tril extracts the lower triangular part

triu extracts the upper triangular part

It helps to think of the 3-D array a as a series of ‘pages’, with a matrix on each page. The third dimension of a numbers the pages. This is analogous to a spreadsheet with multiple sheets: each sheet contains a table (matrix)

The matrix operation A 2 means A × A,whereA must be a square matrix. The operator ^ is used for matrix exponentiation

det determinant. eig eigenvalue decomposition. expm matrix exponential, i.e., e A ,whereA is a matrix. The matrix exponen- tial may be used to evaluate analytical solutions of linear ordinary differential equations with constant coefficients. inv inverse. lu LU factorization (into lower and upper triangular matrices). qr orthogonal factorization. svd singular value decomposition

although the overall conformation of each pro- tein is unique, two regular folding patterns are often found within them. Both pat- terns were discovered more than 60 years ago from studies of hair and silk

The first folding pattern to be discovered, called the α helix, was found in the protein α-keratin, which is abundant in skin and its derivatives—such as hair, nails, and horns.

Within a year of the discovery of the α helix, a second folded structure, called a β sheet, was found in the protein fibroin, the major constituent of silk. These two patterns are particularly common because they result from hydro- gen-bonding between the N–H and C=O groups in the polypeptide backbone, without involving the side chains of the amino acids

By definition, the opposite of the word comprehensive is incomplete, empty, limited or narrow. Some may say it is exclusive of something or unfinished in some way. So it is not surprising that when accountants speak of detail, they reference the word comprehensive. The more comprehensive a financial statement, the more detailed

One of the most important financial statements is the income statement. It provides an overview of sales and expenses, including taxes and interest. At the end of the income statement is net income or earnings, but net income on the income statement is not necessarily all inclusive. That is, it only includes income from business operations. These are the activities that occur due to the company's business model and day-to-day activities. There are times when companies, especially large companies, make or lose money from the change in value of certain assets. These changes can be found on the cash flow statement; however, the net impact to earnings is found in comprehensive or other comprehensive income on the income statement.

A discontinued operation occurs when a segment or certain product line in a company's business has been sold, disposed of or abandoned and is subsequently reported on the company's income statement as income separate from continued operations.

However, the amount of revenue reported would be higher, and the amount of revenue can be important to a company’s valuation. In the earlier stages of e-commerce, for example, some equity valuations were based on sales (because many early internet companies reported no net income).