Statistical Inference in Economics, 1920-1965
... simply those of ordinary induction. He considered the argument that the mathematical theory of probability gave the statistician and the economic forecaster tools for drawing conclusions from statistical data beyond those traditionally associated with the logic of induction. But Persons rejected th ...
... simply those of ordinary induction. He considered the argument that the mathematical theory of probability gave the statistician and the economic forecaster tools for drawing conclusions from statistical data beyond those traditionally associated with the logic of induction. But Persons rejected th ...
4 Sums of Independent Random Variables
... If p = 1/2 then S n is called the simple nearest neighbor random walk. In general, if p 6= 1/2 then we shall assume that 0 < p < 1 to avoid trivialities. The Gambler’s Ruin Problem. Fix two integers A < 0 < B . What is the probability that a p ° q random walk S n (starting at the default initial sta ...
... If p = 1/2 then S n is called the simple nearest neighbor random walk. In general, if p 6= 1/2 then we shall assume that 0 < p < 1 to avoid trivialities. The Gambler’s Ruin Problem. Fix two integers A < 0 < B . What is the probability that a p ° q random walk S n (starting at the default initial sta ...
18th
... Dong Thap University ABSTRACT We extend the Hájek-Rényi inequality to M-dependent arrays and establish a general strong law of large numbers for double arrays. ...
... Dong Thap University ABSTRACT We extend the Hájek-Rényi inequality to M-dependent arrays and establish a general strong law of large numbers for double arrays. ...
Ordered Stick-Breaking Prior for Sequential MCMC Inference of
... Next we state one important result which says probability of adding new atoms can decrease exponentially with time. Theorem 2. For αkt as defined in Eq. (2) with parameters µ, ν, and any ∈ (0, 1), if µj > 1/2 for all j, then αk ≤ whenever k ≥ log2 2 log 1 with probability more than 1 − . Proof ...
... Next we state one important result which says probability of adding new atoms can decrease exponentially with time. Theorem 2. For αkt as defined in Eq. (2) with parameters µ, ν, and any ∈ (0, 1), if µj > 1/2 for all j, then αk ≤ whenever k ≥ log2 2 log 1 with probability more than 1 − . Proof ...
reprint
... Hypotheses (H1) and (H2) are natural and widely satisfied whenever µn satisfies the large deviation principle and the central tendency of Yn /n is directed away from the set A. Consider, for example, the case when Xi is an i.i.d. sequence of random variables and Yn = X1 + · · · + Xn : The fund ...
... Hypotheses (H1) and (H2) are natural and widely satisfied whenever µn satisfies the large deviation principle and the central tendency of Yn /n is directed away from the set A. Consider, for example, the case when Xi is an i.i.d. sequence of random variables and Yn = X1 + · · · + Xn : The fund ...
Nonparametric prior for adaptive sparsity
... In order to validate our proposed procedure we design the following simulation setup. A sequence β of length p = 500 is generated with different degree of sparsity and non-zero distribution. The sequence has βi = 0 at wp randomly chosen positions, where the parameter 0 < w < 1 controls the sparsity a ...
... In order to validate our proposed procedure we design the following simulation setup. A sequence β of length p = 500 is generated with different degree of sparsity and non-zero distribution. The sequence has βi = 0 at wp randomly chosen positions, where the parameter 0 < w < 1 controls the sparsity a ...
Entropy and Uncertainty
... where he is and attempts to find out by asking a passerby, who could be from either city. What is the least number of questions he must ask if the only replies are ‘yes’ and ‘no’? Alternatively, how many questions must he pose to find out where he is and where the passerby lives? Since there are two ...
... where he is and attempts to find out by asking a passerby, who could be from either city. What is the least number of questions he must ask if the only replies are ‘yes’ and ‘no’? Alternatively, how many questions must he pose to find out where he is and where the passerby lives? Since there are two ...
Chapter 5 The normal distribution
... which has very different properties from the normal distribution. An amusing aside is that this distribution now bears the name of Augustin Louis Cauchy (1789-1857) who worked on it twenty years or so later than Poisson did while, on the other hand, Poisson's contribution to the distribution that do ...
... which has very different properties from the normal distribution. An amusing aside is that this distribution now bears the name of Augustin Louis Cauchy (1789-1857) who worked on it twenty years or so later than Poisson did while, on the other hand, Poisson's contribution to the distribution that do ...
