2
votes
1answer
56 views

What is the problem with this model parameter estimation algorithm?

In a statistical model with parameters $\theta$ and unobserved laten variables $Z$, the model likelihood is $$L(\theta;X)=Pr(X|\theta)=\sum_ZPr(X,Z|\theta)$$ The standard way to estimate $\theta$ ...
1
vote
0answers
125 views

Doubts about Bayes' Theorem [closed]

I meet one problem on the probability and statistic theory. "Assume given a measure space $(X,S)$ with three probability measure $\mu_1,\mu_2,\lambda$ on the space. And there exsit functions ...
-1
votes
2answers
77 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
275 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
303 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
928 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 ...