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Maximum likelihood estimation is an estimation procedure involving maximization of the likelihood or the log-likelihood with respect to the parameters. Such type of estimators is particularly important because of their many desirable statistical properties such as consistency, and asymptotic efficiency. As an example considers the number of successes, X, in a sequence of random variables from a Bernoulli distribution with success probability p. The likelihood can be given by differentiating the log-likelihood, L, with respect to p gives the following
Concordant mutations test : A statistical test used in the cancer studies to determine whether or not a diagnosed second primary tumour is biologically independent of the original
This is the powerful visualization tool for studying how the response relies on an explanatory variable given the values of other explanatory variables. The plot comprises of a num
Recurrence risk : Usually the probability that an individual experiences an event of interest given previous experience(s) of the event; for example, the probability of recurrence
Interim analyses : An analysis made before the planned end of a clinical trial, typically with the aim of detecting the treatment differences at the early stage and thus preventing
A vague concept which occurs all through statistics. Essentially the term means the number of independent units of the information in an easy relevant to the estimation of the para
How large would the sample need to be if we are to pick a 95% confidence level sample: (i) From a population of 70; (ii) From a population of 450; (iii) From a population of 1000;
Multi-hit model is the model for a toxic response which results from the random occurrence of one or the more fundamental biological events. A response is supposed to be induced o
5. Packages from a machine a normally distributed with a mean 200g and its standard deviation 2grams. Find the probability that a package from the machine weighs a) Less than
The approach to data analysis which emphasizes the use of informal graphical procedures not based on former assumptions about structure of the data or on the formal models for the
Buffon's needle problem : A problem proposed and solved by the scientist Comte de Buffon in 1777 which includes determining the probability, p, which a needle of length l will inte
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