0
votes
2answers
76 views

What is the likehood function in the noise free observation case

In the nonlinear Bayesian Tracking problem, if we consider the noise exists only in the state equation : x[k] = f(x[k-1],v[k-1]) where vk-1 here is an iid process noise sequence And we suppose that ...
1
vote
1answer
273 views

Conditional probability and independence

Suppose that we have vectors of events $\{H_1,...,H_n\}$ and $\{D_1,...,D_m\}$. Consider the following two sets of conditions: Condition set 1 (1) $P(H_i H_j)=0$ for any $i\neq j$ and ...
2
votes
0answers
278 views

Estimating Wiener process parameters

Consider a Wiener process with zero drift, infintesimal variance $\sigma^2$, and an unknown starting value $\nu$. That is, \begin{align} Y_t \sim \mathcal{N}(\nu, t\sigma^2). \end{align} Now, ...
2
votes
1answer
1k views

Derivatives of conditional expectations

Let $X$, $Y$ and $Z$ be independent, real-valued random variables, probably with continuous density functions. Define $A = X + Y$ and $B = X + Z$. Consider the regular conditional expectation ...
5
votes
3answers
926 views

Probability estimates for pairwise majority votes

This is related to the rank aggregation question I asked previously. I have items $I_1, \ldots, I_N$ and the observations of a number of pairwise trials which pit pairs $I_i$ and $I_j$ against ...